TSTP Solution File: SWW390+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWW390+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:16:53 EDT 2022
% Result : Theorem 192.14s 192.08s
% Output : Refutation 192.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW390+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 5 02:56:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 6.01/6.00 ============================== Prover9 ===============================
% 6.01/6.00 Prover9 (32) version 2009-11A, November 2009.
% 6.01/6.00 Process 19349 was started by sandbox on n017.cluster.edu,
% 6.01/6.00 Sun Jun 5 02:56:35 2022
% 6.01/6.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19195_n017.cluster.edu".
% 6.01/6.00 ============================== end of head ===========================
% 6.01/6.00
% 6.01/6.00 ============================== INPUT =================================
% 6.01/6.00
% 6.01/6.00 % Reading from file /tmp/Prover9_19195_n017.cluster.edu
% 6.01/6.00
% 6.01/6.00 set(prolog_style_variables).
% 6.01/6.00 set(auto2).
% 6.01/6.00 % set(auto2) -> set(auto).
% 6.01/6.00 % set(auto) -> set(auto_inference).
% 6.01/6.00 % set(auto) -> set(auto_setup).
% 6.01/6.00 % set(auto_setup) -> set(predicate_elim).
% 6.01/6.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.01/6.00 % set(auto) -> set(auto_limits).
% 6.01/6.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.01/6.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.01/6.00 % set(auto) -> set(auto_denials).
% 6.01/6.00 % set(auto) -> set(auto_process).
% 6.01/6.00 % set(auto2) -> assign(new_constants, 1).
% 6.01/6.00 % set(auto2) -> assign(fold_denial_max, 3).
% 6.01/6.00 % set(auto2) -> assign(max_weight, "200.000").
% 6.01/6.00 % set(auto2) -> assign(max_hours, 1).
% 6.01/6.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.01/6.00 % set(auto2) -> assign(max_seconds, 0).
% 6.01/6.00 % set(auto2) -> assign(max_minutes, 5).
% 6.01/6.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.01/6.00 % set(auto2) -> set(sort_initial_sos).
% 6.01/6.00 % set(auto2) -> assign(sos_limit, -1).
% 6.01/6.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.01/6.00 % set(auto2) -> assign(max_megs, 400).
% 6.01/6.00 % set(auto2) -> assign(stats, some).
% 6.01/6.00 % set(auto2) -> clear(echo_input).
% 6.01/6.00 % set(auto2) -> set(quiet).
% 6.01/6.00 % set(auto2) -> clear(print_initial_clauses).
% 6.01/6.00 % set(auto2) -> clear(print_given).
% 6.01/6.00 assign(lrs_ticks,-1).
% 6.01/6.00 assign(sos_limit,10000).
% 6.01/6.00 assign(order,kbo).
% 6.01/6.00 set(lex_order_vars).
% 6.01/6.00 clear(print_given).
% 6.01/6.00
% 6.01/6.00 % formulas(sos). % not echoed (5228 formulas)
% 6.01/6.00
% 6.01/6.00 ============================== end of input ==========================
% 6.01/6.00
% 6.01/6.00 % From the command line: assign(max_seconds, 300).
% 6.01/6.00
% 6.01/6.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.01/6.00
% 6.01/6.00 % Formulas that are not ordinary clauses:
% 6.01/6.00 1 (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].
% 6.01/6.00 2 (all V_Ga_2 all T_b c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) # label(fact_empty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 3 (all V_a_2 all T_b c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) # label(fact_hoare__derivs_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 4 (all V_fun2_H_2 all V_com_H_2 all V_fun1_H_2 all V_fun2_2 all V_com_2 all V_fun1_2 all T_b (hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_H_2),V_com_H_2),V_fun2_H_2) <-> V_fun1_2 = V_fun1_H_2 & V_com_2 = V_com_H_2 & V_fun2_2 = V_fun2_H_2)) # label(fact_triple_Oinject) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 5 (all V_Ga_2 all V_ts_2 all V_G_H_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) -> (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)))) # label(fact_cut) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 6 (all V_ts_2 all V_t_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2))))) # label(fact_hoare__derivs_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 7 (all V_ts_2 all V_t_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2))) # label(fact_derivs__insertD) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 8 (all V_fun2_2 all V_com_2 all V_fun1_2 all V_f1_2 all T_b all T_c c_Hoare__Mirabelle_Otriple_Otriple__rec(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2)) # label(fact_triple_Orecs) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 9 (all V_fun2_2 all V_com_2 all V_fun1_2 all V_f1_2 all T_b all T_c c_Hoare__Mirabelle_Otriple_Otriple__case(T_c,T_b,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2)) # label(fact_triple_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 10 (all V_A_2 all V_a_2 all T_b c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) # label(fact_empty__not__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 11 (all V_A_2 all V_a_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_insert__not__empty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 12 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) <-> V_a_2 = V_ca_2 & V_b_2 = V_d_2 | V_a_2 = V_d_2 & V_b_2 = V_ca_2)) # label(fact_doubleton__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 13 (all V_b_2 all V_a_2 all T_b (hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) -> V_a_2 = V_b_2)) # label(fact_singleton__inject) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 14 (all V_x_2 all T_c all T_b (class_Orderings_Obot(T_b) -> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b))) # label(fact_bot__apply) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 15 (all V_Pa_2 all V_Ga_2 all T_b c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))) # label(fact_hoare__derivs_OSkip) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 16 (all V_a2_2 all V_a1_2 all T_b c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))) # label(fact_hoare__derivs_Oequations_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 17 (all V_Q_2 all V_Q_H_2 all V_ca_2 all V_Pa_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> ((all B_Z all B_s (hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) -> hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)))) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))))) # label(fact_conseq2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 18 (all V_Pa_2 all V_Q_2 all V_ca_2 all V_P_H_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> ((all B_Z all B_s (hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) -> hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)))) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))))) # label(fact_conseq1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 19 (all V_R_2 all V_d_2 all V_Q_2 all V_ca_2 all V_Pa_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))))) # label(fact_Comp) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 20 (all V_x_2 all V_A_2 all V_y_2 all T_b (hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) <-> V_y_2 = V_x_2 | hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_insert__code) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 21 (all V_A_2 all V_y_2 all V_x_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2))) # label(fact_insert__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 22 (all V_A_2 all V_x_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) # label(fact_insert__absorb2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 23 (all V_x_2 all T_b c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2) # label(fact_the__elem__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 24 (all V_com2_H all V_com1_H c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H)) # label(fact_com_Osimps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 25 (all V_com2_H all V_com1_H c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP) # label(fact_com_Osimps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 26 (all V_com2_H_2 all V_com1_H_2 all V_com2_2 all V_com1_2 (c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) <-> V_com1_2 = V_com1_H_2 & V_com2_2 = V_com2_H_2)) # label(fact_com_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 27 (all V_ts_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) -> c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2))) # label(fact_hoare__sound) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 28 (all V_Q_2 all V_Pa_2 all V_Q_H_2 all V_ca_2 all V_P_H_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> ((all B_Z all B_s (hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) -> (all B_s_H ((all B_Z_H (hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s)) -> hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)))) -> hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)))))) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))))) # label(fact_conseq12) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 29 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) -> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_subset__singletonD) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 30 (all V_a_2 all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) -> V_b_2 = V_a_2)) # label(fact_singletonE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 31 (all V_a_2 all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) <-> V_b_2 = V_a_2)) # label(fact_singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 32 (all V_x_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2)) # label(fact_folding__one_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 33 (all V_b_2 all V_a_2 all V_f_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2)) <-> V_a_2 = V_b_2)) # label(fact_fold1Set__sing) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 34 (all V_A_2 all V_a_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2)) # label(fact_insert__is__Un) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 35 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)))) # label(fact_order__refl) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 36 (all V_ca_2 all T_b all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> ((hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))) -> -(-hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)))))) # label(fact_equalityCE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 37 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> V_A_2 = V_B_2))) # label(fact_equalityI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 38 (all V_a_2 all T_b -hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_emptyE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 39 (all V_A_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) -> (V_a_2 != V_b_2 -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))))) # label(fact_insertE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 40 (all V_b_2 all V_B_2 all V_a_2 all T_b ((-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) -> V_a_2 = V_b_2) -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))))) # label(fact_insertCI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 41 (all V_ca_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))))) # label(fact_subsetD) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 42 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))))) # label(fact_UnE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 43 (all V_A_2 all V_B_2 all V_ca_2 all T_b ((-hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_UnCI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 44 (all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2))) # label(fact_empty__subsetI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 45 (all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2))) # label(fact_subset__refl) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 46 (all V_B_2 all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_Un__upper1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 47 (all V_A_2 all V_B_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_Un__upper2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 48 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2) # label(fact_Un__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 49 (all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oord(T_c) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) <-> (all B_x hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))))))) # label(fact_le__fun__def) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 50 (all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) <-> hBOOL(hAPP(V_A_2,V_x_2)))) # label(fact_mem__def) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 51 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) # label(fact_Un__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 52 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)))) # label(fact_linorder__linear) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 53 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) <-> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2)) # label(fact_subset__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 54 (all T_b all V_B_2 all V_A_2 (V_A_2 = V_B_2 <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))) # label(fact_set__eq__subset) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 55 (all V_y_2 all V_x_2 all T_b (class_Orderings_Oorder(T_b) -> (V_x_2 = V_y_2 <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))))) # label(fact_order__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 56 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Un__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 57 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Un__left__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 58 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)))) # label(fact_Un__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 59 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Un__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 60 (all V_Pa_2 all V_B_2 all V_A_2 all T_b ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hBOOL(hAPP(V_Pa_2,B_x)))) | (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_bex__Un) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 61 (all V_Pa_2 all V_B_2 all V_A_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(V_Pa_2,B_x)))) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ball__Un) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 62 (all T_b all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_equalityD1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 63 (all T_b all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))) # label(fact_equalityD2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 64 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (V_x = V_y -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))))) # label(fact_order__eq__refl) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 65 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_UnI1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 66 (all V_A_2 all V_B_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_UnI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 67 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oord(T_c) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))))) # label(fact_le__funD) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 68 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2)) # label(fact_Un__absorb1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 69 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2)) # label(fact_Un__absorb2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 70 (all V_x_2 all T_b all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))))) # label(fact_eqset__imp__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 71 (all V_A_2 all T_b all V_y_2 all V_x_2 (V_x_2 = V_y_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))))) # label(fact_eqelem__imp__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 72 (all V_x_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))))) # label(fact_in__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 73 (all V_x_2 all V_y_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_order__antisym__conv) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 74 (all V_A_2 all T_b all V_b_2 all V_a_2 (V_a_2 = V_b_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))))) # label(fact_eq__mem__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 75 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)))))) # label(fact_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 76 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)))))) # label(fact_xt1_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 77 (all V_B_2 all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))))) # label(fact_set__rev__mp) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 78 (all V_x_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))))) # label(fact_set__mp) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 79 (all V_C_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))))) # label(fact_subset__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 80 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)))))) # label(fact_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 81 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)))))) # label(fact_xt1_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 82 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> V_x = V_y)))) # label(fact_order__antisym) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 83 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)))))) # label(fact_order__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 84 (all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> V_x = V_y)))) # label(fact_xt1_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 85 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)))))) # label(fact_xt1_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 86 (all V_B_2 all V_C_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))))) # label(fact_Un__least) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 87 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))))) # label(fact_Un__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 88 (all T_b all V_B_2 all V_A_2 (V_A_2 = V_B_2 -> -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))))) # label(fact_equalityE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 89 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oord(T_c) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))))) # label(fact_le__funE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 90 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))))) # label(fact_linorder__le__cases) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 91 (all V_B_2 all V_A_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_subset__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 92 (all V_B_2 all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_insert__subset) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 93 (all V_x_2 all V_f_2 all T_b -hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))) # label(fact_empty__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 94 (all V_x_2 all V_A_2 all V_f_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) -> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_fold1Set__nonempty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 95 (all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2) # label(fact_Un__empty__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 96 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2) # label(fact_Un__empty__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 97 (all V_B_2 all V_A_2 all T_b (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_Un__empty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 98 (all V_B_2 all V_a_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_Un__insert__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 99 (all V_C_2 all V_B_2 all V_a_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Un__insert__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 100 (all V_x all T_a (class_Orderings_Obot(T_a) -> hBOOL(hAPP(hAPP(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].
% 6.01/6.00 101 (all V_A_2 all T_b ((all B_x -hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_all__not__in__conv) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 102 (all V_A_2 all T_b ((exists B_x hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))) <-> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ex__in__conv) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 103 (all V_ca_2 all T_b -hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 104 (all V_a_2 all T_b all V_A_2 (V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)))) # label(fact_equals0D) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 105 (all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_subset__empty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 106 (all V_B_2 all V_a_2 all T_b hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))) # label(fact_insertI1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 107 (all V_A_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) <-> V_a_2 = V_b_2 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)))) # label(fact_insert__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 108 (all V_B_2 all V_A_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) -> (hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2) <-> V_A_2 = V_B_2)))) # label(fact_insert__ident) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 109 (all V_b_2 all V_B_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))))) # label(fact_insertI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 110 (all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2)) # label(fact_insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 111 (all V_a_2 all V_B_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))) # label(fact_subset__insertI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 112 (all V_b_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))))) # label(fact_subset__insertI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 113 (all V_a_2 all V_D_2 all V_C_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))))) # label(fact_insert__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 114 (all V_Ga_2 all V_ts_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2)) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2))) # label(fact_asm) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 115 (all V_ts_2 all V_ts_H_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)))) # label(fact_weaken) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 116 (all V_Ga_2 all V_ts_2 all V_G_H_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2)) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)))) # label(fact_thin) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 117 (all T_b 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(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)))) # label(fact_sup1CI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 118 (all V_x_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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].
% 6.01/6.00 119 (all V_x_2 all V_g_2 all V_f_2 all T_c all T_b (class_Lattices_Olattice(T_b) -> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))) # label(fact_sup__apply) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 120 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> hAPP(hAPP(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].
% 6.01/6.00 121 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> hAPP(hAPP(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].
% 6.01/6.00 122 (all V_y_2 all V_x_2 all T_b (class_Lattices_Obounded__lattice__bot(T_b) -> (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b) <-> V_x_2 = c_Orderings_Obot__class_Obot(T_b) & V_y_2 = c_Orderings_Obot__class_Obot(T_b)))) # label(fact_sup__eq__bot__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 123 (all V_x all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) -> -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)))))) # label(fact_le__supE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 124 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))))))) # label(fact_sup__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 125 (all V_z all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)))))) # label(fact_sup__least) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 126 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)))))) # label(fact_le__supI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 127 (all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x))) # label(fact_sup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 128 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y))) # label(fact_sup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 129 (all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) <-> V_x_2 = V_y_2)) # label(fact_eq__mem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 130 (all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a)) # label(fact_sup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 131 (all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x)) # label(fact_sup__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 132 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a))) # label(fact_sup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 133 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x))) # label(fact_inf__sup__aci_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 134 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x))) # label(fact_sup__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 135 (all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) # label(fact_sup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 136 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(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].
% 6.01/6.00 137 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) # label(fact_sup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 138 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)))) # label(fact_sup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 139 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(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].
% 6.01/6.00 140 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) # label(fact_sup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 141 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)))) # label(fact_sup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 142 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(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].
% 6.01/6.00 143 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) # label(fact_sup__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 144 (all V_Q_2 all T_b all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,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].
% 6.01/6.00 145 (all V_x_2 all V_Q_2 all V_Pa_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,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].
% 6.01/6.00 146 (all V_B_2 all T_b all V_x_2 all V_A_2 (hBOOL(hAPP(V_A_2,V_x_2)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)))) # label(fact_sup1I1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 147 (all V_A_2 all T_b all V_x_2 all V_B_2 (hBOOL(hAPP(V_B_2,V_x_2)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)))) # label(fact_sup1I2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 148 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(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].
% 6.01/6.00 149 (all V_y all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))))) # label(fact_sup__ge1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 150 (all V_x all V_y all T_a (class_Lattices_Olattice(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(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].
% 6.01/6.00 151 (all V_x all V_y all T_a (class_Lattices_Osemilattice__sup(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))))) # label(fact_sup__ge2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 152 (all V_y_2 all V_x_2 all T_b (class_Lattices_Osemilattice__sup(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) <-> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2))) # label(fact_le__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 153 (all V_z_2 all V_y_2 all V_x_2 all T_b (class_Lattices_Osemilattice__sup(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))))) # label(fact_le__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 154 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))))) # label(fact_le__supI1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 155 (all V_a all V_b all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))))) # label(fact_le__supI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 156 (all V_x_2 all V_A_2 all V_a_2 all V_f_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2))))) # label(fact_fold1Set_Ointros) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 157 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2))))))) # label(fact_folding__one_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 158 (all V_B_2 all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))))) # label(fact_diff__single__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 159 (all V_B_2 all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) <-> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_subset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 160 (all T_b all V_A_2 (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> (exists B_x exists B_B (V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B) & -hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B)))))) # label(fact_nonempty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 161 (all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x)) # label(fact_Sup__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 162 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))))) # label(fact_Powp__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 163 (all V_B_2 all V_A_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_subsetI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 164 (all V_B_2 all V_a_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) # label(fact_vimage__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 165 (all V_b_2 all V_f_2 all T_c all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) <-> hAPP(V_f_2,V_a_2) = V_b_2)) # label(fact_vimage__singleton__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 166 (all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2)) # label(fact_insert__Diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 167 (all T_b hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_finite_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 168 (all V_a_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))))) # label(fact_finite_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 169 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_DiffI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 170 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> -(hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))))) # label(fact_DiffE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 171 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_finite__Diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 172 (all T_c all V_B_2 all T_b all V_b_2 all V_a_2 all V_f_2 (hAPP(V_f_2,V_a_2) = V_b_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)))))) # label(fact_vimageI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 173 (all V_x_2 all V_B_2 all V_A_2 all T_c all T_b (class_Groups_Ominus(T_b) -> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)))) # label(fact_minus__apply) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 174 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) # label(fact_vimage__Diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 175 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Diff__idemp) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 176 (all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) <-> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))))) # label(fact_vimage__code) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 177 (all V_A_2 all T_b (class_Finite__Set_Ofinite(T_b) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_finite) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 178 (all V_A_2 all T_b (class_Finite__Set_Ofinite(T_b) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_finite__code) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.00 179 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))))) # label(fact_finite__Diff2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 180 (all V_x_2 all V_A_2 all V_z_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_fold__graph__imp__finite) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 181 (all V_B_2 all V_a_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_finite__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 182 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) & -hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)))) # label(fact_Diff__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 183 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)))) # label(fact_DiffD1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 184 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)))) # label(fact_DiffD2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 185 (all V_B_2 all V_f_2 all T_c all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) <-> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)))) # label(fact_vimage__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 186 (all V_A_2 all V_f_2 all T_c all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) -> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)))) # label(fact_vimageD) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 187 (all T_c all V_A_2 all V_a_2 all V_f_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))))) # label(fact_vimageI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 188 (all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_empty__Diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 189 (all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2) # label(fact_Diff__empty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 190 (all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 191 (all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_vimage__empty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 192 (all V_B_2 all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2))) # label(fact_Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 193 (all V_B_2 all V_D_2 all V_C_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))))) # label(fact_Diff__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 194 (all V_C_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2))) # label(fact_double__diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 195 (all V_f_2 all T_c all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))))) # label(fact_vimage__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 196 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Un__Diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 197 (all V_A_2 all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) # label(fact_Un__Diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 198 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Un__Diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 199 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) # label(fact_vimage__Un) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 200 (all T_b hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_finite_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 201 (all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_finite__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 202 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))))) # label(fact_finite__subset) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 203 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))))) # label(fact_rev__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 204 (all V_Ga_2 all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))))) # label(fact_finite__UnI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 205 (all V_Ga_2 all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)))) # label(fact_finite__Un) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 206 (all V_z_2 all V_f_2 all T_c all T_b hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2))) # label(fact_fold__graph_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 207 (all V_z_2 all V_f_2 all T_c all T_b hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2))) # label(fact_fold__graph_OemptyI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 208 (all V_x_2 all V_z_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) -> V_x_2 = V_z_2)) # label(fact_empty__fold__graphE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 209 (all V_y_2 all V_x_2 all V_A_2 all V_z_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))))) # label(fact_Diff1__fold__graph) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 210 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_folding__one_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 211 (all V_A_2 all V_B_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_insert__Diff1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 212 (all V_A_2 all V_B_2 all V_x_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_insert__Diff__if) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 213 (all V_B_2 all V_a_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 214 (all V_B_2 all V_a_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) # label(fact_Diff__insert2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 215 (all V_A_2 all V_a_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) # label(fact_insert__Diff__single) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 216 (all V_C_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))))) # label(fact_Diff__subset__conv) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 217 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2)) # label(fact_Diff__partition) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 218 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,V_A_2) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))))) # label(fact_folding__one_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 219 (all V_y_2 all V_z_2 all V_f_2 all T_c all V_A_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) -> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))))) # label(fact_fold__graph_OinsertI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 220 (all V_A_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2)) # label(fact_Diff__insert__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 221 (all V_x_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) -> hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))))))) # label(fact_folding__image__simple_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 222 (all V_x_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))))) # label(fact_folding__image__simple_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 223 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))))) # label(fact_Sup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 224 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)))))) # label(fact_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 225 (all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x all B_y hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2))))))) # label(fact_folding__one_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 226 (all V_Pa_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(V_Pa_2,V_A_2)) -> ((all B_a all B_A (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) -> (hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) -> (hBOOL(hAPP(V_Pa_2,B_A)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) -> hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))) # label(fact_finite__empty__induct) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 227 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)))))))) # label(fact_folding__one__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 228 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)))))) # label(fact_folding__one__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 229 (all V_Pa_2 all V_A_2 all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2)) -> (hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) -> ((all B_a all B_F (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) -> (hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F)) -> (hBOOL(hAPP(V_Pa_2,B_F)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F)))))))) -> hBOOL(hAPP(V_Pa_2,V_F_2))))))) # label(fact_finite__subset__induct) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 230 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)))))) # label(fact_folding__one__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 231 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_Sup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 232 (all V_x_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) -> hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2)) # label(fact_folding__one__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 233 (all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2)) # label(fact_folding__image__simple_Oempty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 234 (all V_x_2 all T_b (class_Lattices_Olattice(T_b) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2)) # label(fact_Sup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 235 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Groups_Oab__group__add(T_b) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) -> (V_a_2 = V_b_2 <-> V_ca_2 = V_d_2)))) # label(fact_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 236 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))))) # label(fact_Sup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 237 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2))))) # label(fact_folding__one__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 238 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)))))) # label(fact_Sup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 239 (all V_B_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)))))) # label(fact_Sup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 240 (all V_B_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)))))))) # label(fact_Sup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 241 (all V_x_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)))))) # label(fact_folding__image__simple_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 242 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))))))) # label(fact_Sup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 243 (all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x all B_y hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2))))))) # label(fact_Sup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 244 (all V_x_2 all V_X_2 all V_a_2 all V_f_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2)) -> -(all B_a all B_A (hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))))))) # label(fact_insert__fold1SetE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 245 (all V_a3_2 all V_a2_2 all V_a1_2 all V_f_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2)) <-> (exists B_a exists B_A (hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2)) & -hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)))))) # label(fact_fold1Set_Oequations) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 246 (all V_f_2 all V_a_2 all V_A_2 all T_b all T_c (class_Rings_Oring(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)))))) # label(fact_setsum__diff1__ring) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 247 (all V_f_2 all V_a_2 all V_A_2 all T_b all T_c (class_Groups_Oab__group__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2))))) # label(fact_setsum__diff1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 248 (all V_a_2 all V_x_2 all V_A_2 all V_b_2 all T_b (class_Groups_Oab__semigroup__mult(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2))))))) # label(fact_fold__graph__permute__diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 249 (all V_B_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))))))))) # label(fact_Sup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 250 (all V_B_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))))))) # label(fact_Sup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 251 (all V_B_2 all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) <-> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_psubset__insert__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 252 (all V_B_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)))))) # label(fact_folding__image__simple__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 253 (all V_B_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2))))) # label(fact_folding__image__simple__idem_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 254 (all T_b 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(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))))) # label(fact_inf1I) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 255 (all V_x_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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].
% 6.01/6.01 256 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_IntI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 257 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> -(hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))))) # label(fact_IntE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 258 (all V_Ga_2 all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))))) # label(fact_finite__Int) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 259 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 260 (all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a)) # label(fact_times_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 261 (all V_x all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x)) # label(fact_mult__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 262 (all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a)) # label(fact_inf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 263 (all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x)) # label(fact_inf__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 264 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a))) # label(fact_inf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 265 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x))) # label(fact_inf__sup__aci_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 266 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x))) # label(fact_inf__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 267 (all V_b all V_a all T_a (class_Lattices_Oab__semigroup__idem__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) # label(fact_mult__left__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 268 (all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) # label(fact_inf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 269 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(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].
% 6.01/6.01 270 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y))) # label(fact_inf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 271 (all V_c all V_a all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)))) # label(fact_inf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 272 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(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].
% 6.01/6.01 273 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)))) # label(fact_inf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 274 (all V_c all V_b all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)))) # label(fact_inf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 275 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(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].
% 6.01/6.01 276 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)))) # label(fact_inf__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 277 (all V_x_2 all V_g_2 all V_f_2 all T_c all T_b (class_Lattices_Olattice(T_b) -> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))) # label(fact_inf__apply) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 278 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))))) # label(fact_less__infI1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 279 (all V_a all V_x all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))))) # label(fact_less__infI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 280 (all V_x_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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].
% 6.01/6.01 281 (all V_x_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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].
% 6.01/6.01 282 (all V_x all T_a (class_Orderings_Opreorder(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)))) # label(fact_order__less__irrefl) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 283 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (V_x_2 != V_y_2 <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))))) # label(fact_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 284 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) | V_x_2 = V_y_2))) # label(fact_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 285 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2) # label(fact_Int__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 286 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) # label(fact_Int__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 287 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) | V_x = V_y | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))) # label(fact_linorder__less__linear) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 288 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Int__left__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 289 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Int__left__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 290 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Int__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 291 (all V_x_2 all V_y_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 292 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__neqE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 293 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_x != V_y))) # label(fact_less__imp__neq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 294 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__not__sym) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 295 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 296 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_x != V_y))) # label(fact_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 297 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> V_y != V_x))) # label(fact_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 298 (all V_b all V_a all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))))) # label(fact_order__less__asym_H) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 299 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_xt1_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 300 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)))))) # label(fact_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 301 (all V_c all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a = V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)))))) # label(fact_xt1_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 302 (all V_C_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))))) # label(fact_psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 303 (all V_c all V_b all V_a all T_a (class_Orderings_Oord(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)))))) # label(fact_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 304 (all V_c all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (V_b = V_c -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)))))) # label(fact_xt1_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 305 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__less__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 306 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 307 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))))) # label(fact_order__less__asym) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 308 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (V_x != V_y -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__cases) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 309 (all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x)) # label(fact_Inf__fin_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 310 (all V_x_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2)) # label(fact_folding__image__simple__idem_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 311 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) -> -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)))))) # label(fact_le__infE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 312 (all V_d all V_b all V_c all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))))))) # label(fact_inf__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 313 (all V_z all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))))))) # label(fact_inf__greatest) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 314 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))))))) # label(fact_le__infI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 315 (all V_x all V_y all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y))) # label(fact_inf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 316 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x))) # label(fact_inf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 317 (all V_a all V_x all V_b all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))))) # label(fact_le__infI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 318 (all V_b all V_x all V_a all T_a (class_Lattices_Osemilattice__inf(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))))) # label(fact_le__infI1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 319 (all V_z_2 all V_y_2 all V_x_2 all T_b (class_Lattices_Osemilattice__inf(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))))) # label(fact_le__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 320 (all V_y_2 all V_x_2 all T_b (class_Lattices_Osemilattice__inf(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) <-> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2))) # label(fact_le__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 321 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)))) # label(fact_inf__le2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 322 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(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].
% 6.01/6.01 323 (all V_y all V_x all T_a (class_Lattices_Osemilattice__inf(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)))) # label(fact_inf__le1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 324 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(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].
% 6.01/6.01 325 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_inf__bot__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 326 (all V_x all T_a (class_Lattices_Obounded__lattice__bot(T_a) -> hAPP(hAPP(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].
% 6.01/6.01 327 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)))) # label(fact_sup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 328 (all V_x all V_z all V_y all T_a (class_Lattices_Odistrib__lattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)))) # label(fact_inf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 329 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) # label(fact_sup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 330 (all V_z all V_y all V_x all T_a (class_Lattices_Odistrib__lattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)))) # label(fact_inf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 331 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(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].
% 6.01/6.01 332 (all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x)) # label(fact_inf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 333 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)))) # label(fact_Int__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 334 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)))) # label(fact_IntD1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 335 (all V_B_2 all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)))) # label(fact_IntD2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 336 (all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oord(T_c) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) & -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))))) # label(fact_less__fun__def) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 337 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))))) # label(fact_linorder__not__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 338 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))))) # label(fact_linorder__not__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 339 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))) # label(fact_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 340 (all V_y_2 all V_x_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) & V_x_2 != V_y_2))) # label(fact_order__less__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 341 (all V_y_2 all V_x_2 all T_b (class_Orderings_Opreorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) & -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))))) # label(fact_less__le__not__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 342 (all V_y_2 all V_x_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) | V_x_2 = V_y_2))) # label(fact_order__le__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 343 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))))) # label(fact_leI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 344 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))))) # label(fact_not__leE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 345 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 346 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 347 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (V_a != V_b -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)))))) # label(fact_xt1_I12_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 348 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))))) # label(fact_leD) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 349 (all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))))) # label(fact_order__less__imp__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 350 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) <-> V_x_2 = V_y_2)))) # label(fact_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 351 (all V_y all V_x all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) | V_x = V_y))) # label(fact_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 352 (all V_b all V_a all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (V_a != V_b -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 353 (all V_a all V_b all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) -> (V_a != V_b -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)))))) # label(fact_xt1_I11_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 354 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__less__le__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 355 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 356 (all V_z all V_y all V_x all T_a (class_Orderings_Opreorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)))))) # label(fact_order__le__less__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 357 (all V_z all V_x all V_y all T_a (class_Orderings_Oorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)))))) # label(fact_xt1_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 358 (all V_ca_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))))) # label(fact_psubsetD) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 359 (all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Int__empty__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 360 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Int__empty__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 361 (all V_B_2 all V_A_2 all T_b (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) -> B_x != B_xa)))))) # label(fact_disjoint__iff__not__equal) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 362 (all V_B_2 all V_A_2 all V_a_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_insert__inter__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 363 (all V_A_2 all T_b -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_not__psubset__empty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 364 (all V_B_2 all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2))) # label(fact_Int__lower1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 365 (all V_B_2 all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2))) # label(fact_Int__lower2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 366 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2)) # label(fact_Int__absorb2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 367 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2)) # label(fact_Int__absorb1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 368 (all V_B_2 all V_A_2 all V_C_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_Int__greatest) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 369 (all V_D_2 all V_B_2 all V_C_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))))) # label(fact_Int__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 370 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)))))) # label(fact_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 371 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Int__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 372 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Un__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 373 (all V_A_2 all V_C_2 all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))) # label(fact_Int__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 374 (all V_A_2 all V_C_2 all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))) # label(fact_Un__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 375 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))) # label(fact_Un__Int__crazy) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 376 (all V_a all V_b all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))))) # label(fact_less__supI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 377 (all V_b all V_a all V_x all T_a (class_Lattices_Osemilattice__sup(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))))) # label(fact_less__supI1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 378 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) & V_A_2 != V_B_2)) # label(fact_psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 379 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) | V_A_2 = V_B_2)) # label(fact_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 380 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 381 (all V_C_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))))) # label(fact_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 382 (all V_C_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))))) # label(fact_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 383 (all V_B_2 all V_A_2 all V_C_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))) # label(fact_Diff__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 384 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Int__Diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 385 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Diff__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 386 (all V_B_2 all V_C_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2)) # label(fact_Diff__Int2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 387 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) # label(fact_vimage__Int) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 388 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))))) # label(fact_distrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 389 (all V_z all V_y all V_x all T_a (class_Lattices_Olattice(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))))) # label(fact_distrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 390 (all V_B_2 all V_C_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)))) # label(fact_Int__insert__left__if1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 391 (all V_B_2 all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_Int__insert__right__if1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 392 (all V_B_2 all V_C_2 all V_a_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) # label(fact_Int__insert__left__if0) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 393 (all V_B_2 all V_A_2 all V_a_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_Int__insert__right__if0) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 394 (all V_B_2 all V_C_2 all V_a_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)))) # label(fact_Int__insert__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 395 (all V_B_2 all V_A_2 all V_a_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_Int__insert__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 396 (all V_B_2 all V_A_2 all T_b (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2)) # label(fact_Diff__triv) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.01 397 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Diff__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 398 (all V_C_2 all V_B_2 all V_A_2 all T_b (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)))) # label(fact_Un__Int__assoc__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 399 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 400 (all V_C_2 all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))) # label(fact_Diff__Un) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 401 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2) # label(fact_Un__Diff__Int) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 402 (all V_f_2 all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))))) # label(fact_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 403 (all V_a_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2)))) # label(fact_inf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 404 (all V_z_2 all V_y_2 all V_A_2 all V_b_2 all T_b (class_Groups_Oab__semigroup__mult(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))))))) # label(fact_fold__graph__insert__swap) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 405 (all V_B_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)))))) # label(fact_folding__image__simple_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 406 (all V_f_2 all V_A_2 all V_a_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)))) # label(fact_setsum__diff1__nat) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 407 (all V_f_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Oab__group__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))))) # label(fact_setsum__diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 408 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))))))) # label(fact_folding__one_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 409 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))))))))) # label(fact_folding__one_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 410 (all V_B_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) -> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))))))) # label(fact_folding__image__simple_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 411 (all V_x_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) -> hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2))))) # label(fact_folding__image__simple__idem_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 412 (all V_x_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))))) # label(fact_folding__image__simple__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 413 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))))) # label(fact_Inf__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 414 (all V_g_2 all V_f_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)))))))) # label(fact_setsum__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 415 (all V_f_2 all V_a_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_setsum__diff1_H) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 416 (all V_g_2 all V_x_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_setsum_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 417 (all V_B_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))))))) # label(fact_Inf__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 418 (all V_B_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))))))))) # label(fact_Inf__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 419 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_Inf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 420 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2))))))) # label(fact_Inf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 421 (all V_B_2 all V_A_2 all T_b (class_Groups_Oab__semigroup__mult(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2))))))))) # label(fact_fold1__Un) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 422 (all V_B_2 all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) -> hAPP(V_g_2,B_x) = V_z_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))))))) # label(fact_folding__image__simple_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 423 (all V_x_2 all V_A_2 all T_b (class_Groups_Oab__semigroup__mult(T_b) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2))))))) # label(fact_fold1__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 424 (all V_c all V_a all V_b all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) -> V_b = V_c))) # label(fact_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 425 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__ab__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) -> V_b = V_c))) # label(fact_add__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 426 (all V_c all V_b all V_a all T_a (class_Groups_Ocancel__semigroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) -> V_b = V_c))) # label(fact_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 427 (all V_ca_2 all V_a_2 all V_b_2 all T_b (class_Groups_Ocancel__semigroup__add(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2) <-> V_b_2 = V_ca_2))) # label(fact_add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 428 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Groups_Ocancel__semigroup__add(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2) <-> V_b_2 = V_ca_2))) # label(fact_add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 429 (all V_c all V_b all V_a all T_a (class_Groups_Oab__semigroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 430 (all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))))) # label(fact_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 431 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))))) # label(fact_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 432 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))))) # label(fact_add__right__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 433 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))))) # label(fact_add__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 434 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 435 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))))) # label(fact_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 436 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))))) # label(fact_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 437 (all V_b all V_a all V_c all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 438 (all V_b all V_c all V_a all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))))) # label(fact_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 439 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 440 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))))) # label(fact_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 441 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))))) # label(fact_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 442 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))))) # label(fact_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 443 (all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))))) # label(fact_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 444 (all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))) # label(fact_Inf__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 445 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a)) # label(fact_diff__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 446 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a)) # label(fact_add__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 447 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__le__less__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 448 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))))) # label(fact_add__less__le__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 449 (all V_a_2 all V_f_2 all T_b all V_g_2 (V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2) -> hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2)) # label(fact_fold1__singleton__def) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 450 (all V_a_2 all V_f_2 all T_b hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2) # label(fact_fold1__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 451 (all V_x_2 all T_b (class_Lattices_Olattice(T_b) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2)) # label(fact_Inf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 452 (all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)))) # label(fact_folding__one_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 453 (all V_f_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_setsum__Un__nat) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 454 (all V_a_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2)))) # label(fact_sup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 455 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2))))) # label(fact_Inf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 456 (all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2)))) # label(fact_Sup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 457 (all V_g_2 all V_x_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)))))) # label(fact_setsum_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 458 (all V_f_2 all V_a_2 all V_F_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)))))) # label(fact_setsum__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 459 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)))))) # label(fact_setsum__Un__Int) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 460 (all V_a_2 all V_A_2 all T_b (class_Lattices_Osemilattice__inf(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)))))) # label(fact_fold1__belowI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 461 (all V_x_2 all V_A_2 all T_b (class_Lattices_Osemilattice__inf(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))))))))) # label(fact_below__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 462 (all V_x_2 all V_A_2 all T_b (class_Lattices_Oab__semigroup__idem__mult(T_b) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)))))) # label(fact_fold1__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 463 (all V_B_2 all V_A_2 all T_b (class_Lattices_Oab__semigroup__idem__mult(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)))))))) # label(fact_fold1__Un2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 464 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)))))) # label(fact_Inf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 465 (all V_B_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)))))) # label(fact_Inf__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 466 (all V_B_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)))))))) # label(fact_Inf__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 467 (all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))))))) # label(fact_Inf__le__Sup) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 468 (all V_x_2 all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_setsum_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 469 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))))))) # label(fact_setsum__Un__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 470 (all V_f_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Oab__group__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))))) # label(fact_setsum__Un) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 471 (all V_A_2 all V_F_2 all V_f_2 all T_b (c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)))) # label(fact_semilattice__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 472 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oordered__ring(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))))) # label(fact_less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 473 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oordered__ring(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2))))) # label(fact_less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 474 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oordered__ring(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))))) # label(fact_le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 475 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oordered__ring(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2))))) # label(fact_le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 476 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oring(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) <-> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))) # label(fact_eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 477 (all V_d_2 all V_b_2 all V_ca_2 all V_e_2 all V_a_2 all T_b (class_Rings_Oring(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2))) # label(fact_eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 478 (all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x all B_y hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2))))))) # label(fact_Inf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 479 (all V_A_2 all T_b (class_Groups_Oab__semigroup__mult(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x all B_y hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2))))))) # label(fact_fold1__in) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 480 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 481 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)))))) # label(fact_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 482 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 483 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 484 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 485 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 486 (all V_d all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 487 (all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 488 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 489 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 490 (all V_ry all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 491 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 492 (all V_rx all V_ly all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 493 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 494 (all V_ry all V_rx all V_lx all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 495 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 496 (all V_z_2 all V_x_2 all V_y_2 all V_w_2 all T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2)) <-> V_w_2 = V_x_2 | V_y_2 = V_z_2))) # label(fact_crossproduct__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 497 (all V_c all V_b all V_e all V_a all T_a (class_Rings_Osemiring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c))) # label(fact_combine__common__factor) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 498 (all V_b all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 499 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 500 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))) # label(fact_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 501 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) -> (V_a_2 != V_b_2 & V_ca_2 != V_d_2 <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))))) # label(fact_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 502 (all V_i all V_j all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i))) # label(fact_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 503 (all V_i all V_j all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k))) # label(fact_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 504 (all V_i all V_j all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)))) # label(fact_diff__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 505 (all V_k_2 all V_j_2 all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 <-> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2)))) # label(fact_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 506 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m)) # label(fact_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 507 (all V_i_2 all V_j_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))))) # label(fact_le__diff__conv2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 508 (all V_i all V_j all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))) # label(fact_add__diff__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 509 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m)) # label(fact_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 510 (all V_m all V_n all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))))) # label(fact_le__add__diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 511 (all V_i_2 all V_k_2 all V_j_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))))) # label(fact_le__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 512 (all V_m hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))) # label(fact_le__square) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 513 (all V_m hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))))) # label(fact_le__cube) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 514 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))))) # label(fact_mult__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 515 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))))) # label(fact_mult__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 516 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)))))) # label(fact_mult__le__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 517 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> V_m = V_n))) # label(fact_le__antisym) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 518 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k))))) # label(fact_le__trans) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 519 (all V_n all V_m (V_m = V_n -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)))) # label(fact_eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 520 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)))) # label(fact_nat__le__linear) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 521 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n))) # label(fact_le__refl) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 522 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) | V_m = V_n -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)))) # label(fact_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 523 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> (V_m != V_n -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 524 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)))) # label(fact_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 525 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) | V_m_2 = V_n_2)) # label(fact_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 526 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) & V_m_2 != V_n_2)) # label(fact_nat__less__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 527 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 528 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 529 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__add__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 530 (all V_z all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z))) # label(fact_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 531 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__add__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 532 (all V_m all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)))) # label(fact_le__add2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 533 (all V_m all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)))) # label(fact_le__add1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 534 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) <-> (exists B_k V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)))) # label(fact_le__iff__add) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 535 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 536 (all V_m all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))))) # label(fact_trans__le__add1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 537 (all V_m all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))))) # label(fact_trans__le__add2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 538 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))))) # label(fact_add__le__mono1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 539 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))))) # label(fact_add__le__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 540 (all V_n all V_k all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)))) # label(fact_add__leD2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 541 (all V_n all V_k all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)))) # label(fact_add__leD1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 542 (all V_n all V_k all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) -> -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))))) # label(fact_add__leE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 543 (all V_j all V_i -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i))) # label(fact_not__add__less1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 544 (all V_i all V_j -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i))) # label(fact_not__add__less2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 545 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 546 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 547 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 548 (all V_m all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))))) # label(fact_trans__less__add1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 549 (all V_m all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))))) # label(fact_trans__less__add2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 550 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))))) # label(fact_add__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 551 (all V_l all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))))) # label(fact_add__less__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 552 (all V_n all V_m all V_l all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_less__add__eq__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 553 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)))) # label(fact_add__lessD1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 554 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))))) # label(fact_less__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 555 (all V_c all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c)))))) # label(fact_diff__less__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 556 (all V_l all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))))) # label(fact_diff__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 557 (all V_n all V_k all V_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)))) # label(fact_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 558 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 559 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 560 (all V_k all V_j all V_i hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j)) # label(fact_diff__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 561 (all V_n all V_m hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m))) # label(fact_diff__le__self) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 562 (all V_l all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))))) # label(fact_diff__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 563 (all V_l all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))))) # label(fact_diff__le__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 564 (all V_n all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i)) # label(fact_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 565 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2)))) # label(fact_eq__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 566 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))) # label(fact_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 567 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)))))) # label(fact_le__diff__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 568 (all V_n all V_m (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m)) # label(fact_add__diff__inverse) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 569 (all V_k_2 all V_j_2 all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)))) # label(fact_less__diff__conv) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 570 (all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m) # label(fact_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 571 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m) # label(fact_diff__add__inverse) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 572 (all V_k all V_j all V_i hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) # label(fact_diff__diff__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 573 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 574 (all V_n all V_k all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__cancel2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 575 (all V_i all V_j all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))) # label(fact_diff__diff__right) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 576 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2))))) # label(fact_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 577 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2))))) # label(fact_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 578 (all V_n all V_m all V_u all V_i all V_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n))) # label(fact_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 579 (all V_n_2 all V_m_2 all V_u_2 all V_i_2 all V_j_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2))) # label(fact_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 580 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))))) # label(fact_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 581 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))))) # label(fact_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 582 (all V_n all V_m all V_u all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)))) # label(fact_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 583 (all V_n_2 all V_m_2 all V_u_2 all V_j_2 all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) <-> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))) # label(fact_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 584 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 585 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 586 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 587 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n))) # label(fact_less__not__refl) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 588 (all V_n_2 all V_m_2 (V_m_2 != V_n_2 <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)))) # label(fact_nat__neq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 589 (all V_y all V_x (V_x != V_y -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x))))) # label(fact_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 590 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n))) # label(fact_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 591 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) -> V_m != V_n)) # label(fact_less__not__refl2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 592 (all V_t all V_s (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) -> V_s != V_t)) # label(fact_less__not__refl3) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 593 (all V_Pa_2 all V_n_2 all V_m_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))) -> ((V_m_2 = V_n_2 -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)))))) # label(fact_nat__less__cases) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 594 (all V_y all V_z all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.02 595 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 596 (all V_k all V_j all V_u all V_i hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k)) # label(fact_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 597 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)))) # label(fact_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 598 (all V_y all V_z all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))))) # label(fact_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 599 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))))) # label(fact_card__Diff1__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 600 (all V_y_2 all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))))))) # label(fact_card__Diff2__less) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 601 (all V_g_2 all V_x_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_setprod_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 602 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2))))) # label(fact_Inf__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 603 (all V_x_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2))))) # label(fact_Sup__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 604 (all V_a_2 all V_A_2 all T_b (class_Groups_Oab__semigroup__mult(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2))))) # label(fact_fold1__eq__fold) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 605 (all V_Pa_2 all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) -> (hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) -> ((all B_x all B_F (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F)) -> (hBOOL(hAPP(V_Pa_2,B_F)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))))))) -> hBOOL(hAPP(V_Pa_2,V_F_2)))))) # label(fact_finite__induct) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 606 (all V_y_2 all V_z_2 all V_f_2 all T_c all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2) -> c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2))))) # label(fact_fold__graph_H_Ointros_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 607 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))))))) # label(fact_fold1__antimono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 608 (all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x)) # label(fact_Min_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 609 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)))) # label(fact_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 610 (all V_c all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)))) # label(fact_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 611 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)))) # label(fact_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 612 (all V_c all V_a all V_b all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)))) # label(fact_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 613 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y))) # label(fact_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 614 (all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) # label(fact_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 615 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x))) # label(fact_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 616 (all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a))) # label(fact_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 617 (all V_a all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a)) # label(fact_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 618 (all V_a_2 all V_b_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2))))) # label(fact_min__max_Ofold__inf__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 619 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)))) # label(fact_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 620 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)))) # label(fact_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 621 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) <-> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2))) # label(fact_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 622 (all V_z_2 all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))))) # label(fact_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 623 (all V_b all V_x all V_a all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))))) # label(fact_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 624 (all V_a all V_x all V_b all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))))) # label(fact_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 625 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x))) # label(fact_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 626 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y))) # label(fact_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 627 (all V_b all V_a all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))))))) # label(fact_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 628 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))))))) # label(fact_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 629 (all V_d all V_b all V_c all V_a all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))))))) # label(fact_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 630 (all V_b all V_a all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) -> -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)))))) # label(fact_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 631 (all V_z_2 all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))))) # label(fact_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 632 (all V_z_2 all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))))) # label(fact_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 633 (all V_y_2 all V_x_2 all V_z_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))))) # label(fact_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 634 (all V_a all V_x all V_b all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))))) # label(fact_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 635 (all V_b all V_x all V_a all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))))) # label(fact_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 636 (all V_z all V_y all V_x all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)))) # label(fact_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 637 (all V_z all V_y all V_x all T_a (class_Groups_Oordered__ab__group__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)))) # label(fact_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 638 (all V_z_2 all V_f_2 all T_c all T_b c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2)) # label(fact_fold__graph_H_Ointros_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 639 (all V_a2_2 all V_a1_2 all T_c all T_b c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2)) # label(fact_fold__graph_H_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 640 (all T_b (class_Lattices_Osemilattice__inf(T_b) & class_Orderings_Olinorder(T_b) -> c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b))) # label(fact_inf__min) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 641 (all V_z_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2) # label(fact_fold__empty) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 642 (all V_n all V_i all V_m hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i)) # label(fact_min__diff) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 643 (all V_b_2 all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))))))) # label(fact_min__max_Ofold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 644 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))))) # label(fact_card__insert__le) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 645 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) -> V_A_2 = V_B_2)))) # label(fact_card__seteq) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 646 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))))) # label(fact_card__mono) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 647 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2))) # label(fact_union__fold__insert) # label(axiom) # label(non_clause). [assumption].
% 6.01/6.03 648 (all V_a_2 all V_b_2 all V_A_2 all T_b (class_Lattices_Osemilattice__sup(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))))) # label(fact_fold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 649 (all V_a_2 all V_b_2 all V_A_2 all T_b (class_Lattices_Osemilattice__inf(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2))))) # label(fact_fold__inf__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 650 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))))) # label(fact_psubset__card__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 651 (all V_a_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2)))) # label(fact_folding__one__idem_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 652 (all V_f_2 all V_a_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))))) # label(fact_setprod__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 653 (all V_g_2 all V_x_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)))))) # label(fact_setprod_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 654 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)))))) # label(fact_setprod__Un__Int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 655 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)))))) # label(fact_setprod_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 656 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_card__Un__Int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 657 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))))) # label(fact_card_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 658 (all V_b_2 all V_a_2 all V_A_2 all T_b (class_Lattices_Osemilattice__sup(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))))))) # label(fact_sup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 659 (all V_b_2 all V_a_2 all V_A_2 all T_b (class_Lattices_Osemilattice__inf(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))))))) # label(fact_fold__inf__le__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 660 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))))) # label(fact_card__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 661 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_card__Diff__subset__Int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 662 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 663 (all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)))))) # label(fact_min__max_Ofold1__belowI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 664 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))))))))) # label(fact_fold1__below__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 665 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))))))))) # label(fact_min__max_Obelow__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 666 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))))))))) # label(fact_fold1__strict__below__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 667 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))))))))) # label(fact_strict__below__fold1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 668 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_card__psubset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 669 (all V_a_2 all V_A_2 all T_b (class_Lattices_Oab__semigroup__idem__mult(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2)))) # label(fact_fold1__eq__fold__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 670 (all V_a_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2)))) # label(fact_Sup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 671 (all V_a_2 all V_A_2 all T_b (class_Lattices_Olattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2)))) # label(fact_Inf__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 672 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2))))) # label(fact_folding__one_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 673 (all V_x_2 all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_setprod_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 674 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))))))) # label(fact_setprod_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 675 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))))))) # label(fact_setprod__Un__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 676 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))))) # label(fact_card__Un__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 677 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))))) # label(fact_card__Diff1__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 678 (all V_z_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_fun__left__comm_Ofold__rec) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 679 (all T_b (class_Orderings_Oord(T_b) -> c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)))) # label(fact_min__ord__min) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 680 (all V_x_2 all V_z_2 all V_A_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_fun__left__comm_Ofold__insert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 681 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_card__Diff__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 682 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))) # label(fact_card__Diff__singleton__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 683 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_card_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 684 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))))) # label(fact_Min_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 685 (all V_a5_2 all V_a1_2 all V_a2_2 all V_a4_2 all V_a3_2 all T_c all T_b (c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) <-> V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 | (exists B_x exists B_y (hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2)) & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y))))) # label(fact_fold__graph_H_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 686 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))))) # label(fact_min__max_OInf__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 687 (all V_x_2 all T_b (class_Groups_Oone(T_b) -> (c_Groups_Oone__class_Oone(T_b) = V_x_2 <-> V_x_2 = c_Groups_Oone__class_Oone(T_b)))) # label(fact_one__reorient) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 688 (all V_z_2 all V_y_2 all V_x_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)))) # label(fact_fun__left__comm_Ofun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 689 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 690 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 691 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 692 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a)) # label(fact_mult__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 693 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 694 (all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 695 (all V_f_2 all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) -> (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) -> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) # label(fact_setprod__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 696 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 697 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 698 (all V_n_2 all V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 699 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n) # label(fact_nat__mult__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 700 (all T_b (class_Groups_Oab__semigroup__mult(T_b) -> c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)))) # label(fact_fun__left__comm) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 701 (all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))))) # label(fact_less__add__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 702 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))))) # label(fact_less__1__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 703 (all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 704 (all V_a all V_m all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 705 (all V_m all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 706 (all V_y_2 all V_x_2 all V_A_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) -> V_y_2 = V_x_2)))) # label(fact_fun__left__comm_Ofold__graph__determ) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 707 (all V_g_2 all T_c all T_b (class_Groups_Ocomm__monoid__mult(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b))) # label(fact_setprod_Oempty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 708 (all V_f_2 all T_c all T_b (class_Groups_Ocomm__monoid__mult(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b))) # label(fact_setprod__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 709 (all V_f_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)))) # label(fact_setprod__infinite) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 710 (all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)))) # label(fact_setprod_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 711 (all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2)) # label(fact_Min_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 712 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))))) # label(fact_min__max_OInf__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 713 (all V_z_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)))) # label(fact_fun__left__comm_Ofold__fun__comm) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 714 (all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2)) # label(fact_min__max_OInf__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 715 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)))))) # label(fact_Min__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 716 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)))))) # label(fact_Min__in) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 717 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2))))) # label(fact_Min_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 718 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))) # label(fact_min__max_OInf__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 719 (all V_y_2 all V_A_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2))) # label(fact_fun__left__comm_Ofold__equality) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 720 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))) # label(fact_Min_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 721 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)))))) # label(fact_min__max_OInf__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 722 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)))))) # label(fact_min__max_OInf__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 723 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)))))))) # label(fact_min__max_OInf__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 724 (all V_N_2 all V_M_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) -> (V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2)))))))) # label(fact_Min__antimono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 725 (all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2)))) # label(fact_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 726 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)))))) # label(fact_Min__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 727 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)))))) # label(fact_Min_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 728 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)))))))) # label(fact_Min__Un) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 729 (all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2)))) # label(fact_Min_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 730 (all V_z_2 all V_A_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)))))) # label(fact_fun__left__comm_Ofold__graph__fold) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 731 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))))) # label(fact_card_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 732 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))))))) # label(fact_min__max_OInf__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 733 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_min__max_OInf__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 734 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))))))) # label(fact_min__max_OInf__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 735 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))))))))) # label(fact_min__max_OInf__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 736 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2))))) # label(fact_min__max_OInf__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 737 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2))))))) # label(fact_Min_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 738 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_Min_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 739 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))))))) # label(fact_Min_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 740 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))))))))) # label(fact_Min_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 741 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2))))) # label(fact_Min_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 742 (all V_B_2 all V_a_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) # label(fact_card__Diff__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 743 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))) # label(fact_card_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 744 (all V_z_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)))))) # label(fact_fun__left__comm_Ofold__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 745 (all V_z_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2))))) # label(fact_fun__left__comm_Ofold__insert2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 746 (all V_a_2 all V_y_2 all V_A_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> (exists B_y_H (V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)))))))) # label(fact_fun__left__comm_Ofold__graph__insertE__aux) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 747 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x all B_y hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2))))))) # label(fact_min__max_OInf__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 748 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x all B_y hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))))))) # label(fact_Min_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 749 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))))))) # label(fact_setprod_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 750 (all V_f_2 all V_T_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) -> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2))))))) # label(fact_setprod__Un__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 751 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2))))))) # label(fact_fold__Un__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 752 (all V_f_2 all V_S_2 all V_T_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) -> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)))))) # label(fact_setprod__mono__one__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 753 (all V_f_2 all V_S_2 all V_T_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) -> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)))))) # label(fact_setprod__mono__one__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 754 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))) # label(fact_card__Suc__Diff1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 755 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))))) # label(fact_Suc__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 756 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n)))) # label(fact_lessI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 757 (all V_y all V_x (hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) -> V_x = V_y)) # label(fact_Suc__inject) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 758 (all V_nat_H_2 all V_nat_2 (hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) <-> V_nat_2 = V_nat_H_2)) # label(fact_nat_Oinject) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 759 (all V_n hAPP(c_Nat_OSuc,V_n) != V_n) # label(fact_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 760 (all V_n V_n != hAPP(c_Nat_OSuc,V_n)) # label(fact_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 761 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 762 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__lessD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 763 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> V_m = V_n))) # label(fact_less__SucE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 764 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k))))) # label(fact_less__trans__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 765 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> (hAPP(c_Nat_OSuc,V_m) != V_n -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))))) # label(fact_Suc__lessI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 766 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_less__SucI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 767 (all V_m all V_n (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) -> V_m = V_n))) # label(fact_less__antisym) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 768 (all V_m_2 all V_n_2 (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) <-> V_n_2 = V_m_2))) # label(fact_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 769 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_Suc__less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 770 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) | V_m_2 = V_n_2)) # label(fact_less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 771 (all V_n_2 all V_m_2 (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))))) # label(fact_not__less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 772 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) # label(fact_add__Suc__shift) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 773 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_add__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 774 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_add__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 775 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__leD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.03 776 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> V_m = hAPP(c_Nat_OSuc,V_n)))) # label(fact_le__SucE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 777 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_le__SucI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 778 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)))) # label(fact_Suc__le__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 779 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) | V_m_2 = hAPP(c_Nat_OSuc,V_n_2))) # label(fact_le__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 780 (all V_n_2 all V_m_2 (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)))) # label(fact_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 781 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n))) # label(fact_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 782 (all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) # label(fact_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 783 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k)) # label(fact_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 784 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 785 (all V_z_2 all V_g_2 all V_f_2 all T_c all T_b hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2) # label(fact_fold__image__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 786 (all V_n all V_m hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n))) # label(fact_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 787 (all V_m all V_i hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))))) # label(fact_less__add__Suc1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 788 (all V_m all V_i hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i))))) # label(fact_less__add__Suc2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 789 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) <-> (exists B_k V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))))) # label(fact_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 790 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 791 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) <-> V_n_2 = V_m_2))) # label(fact_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 792 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)))) # label(fact_Suc__leI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 793 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))))) # label(fact_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 794 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_Suc__le__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 795 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 796 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)))) # label(fact_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 797 (all V_n all V_m hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m)))) # label(fact_diff__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 798 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 799 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) # label(fact_mult__Suc__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 800 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) # label(fact_mult__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 801 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))) # label(fact_Suc__diff__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 802 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 803 (all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n) # label(fact_diff__Suc__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 804 (all V_A_2 all V_F_2 all V_g_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)))) # label(fact_folding__image__simple_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 805 (all V_m all V_j all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)))) # label(fact_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 806 (all V_m all V_j all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)))) # label(fact_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 807 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2))))) # label(fact_card__insert__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 808 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2))))) # label(fact_card__insert__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 809 (all V_z_2 all V_g_2 all V_a_2 all V_A_2 all T_b all T_c (class_Groups_Oab__semigroup__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)))))) # label(fact_fold__image__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 810 (all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) & (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)))) # label(fact_setprod_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 811 (all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)))) # label(fact_setprod_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 812 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))) # label(fact_card__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 813 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))))) # label(fact_fold__image__Un__Int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 814 (all V_n all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) # label(fact_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 815 (all V_n hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) # label(fact_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 816 (all V_n hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 817 (all V_g_2 all V_A_2 all V_F_2 all V_z_2 all V_f_2 all T_c all T_b (c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)) & (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2))) # label(fact_comm__monoid__big_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 818 (all V_f_2 all V_T_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) -> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c))) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2))))))) # label(fact_fold__image__Un__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 819 (all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2)))) # label(fact_Sup__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 820 (all V_v_2 all V_A_2 all V_x_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> -(all B_y (V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) -> -hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)))))))) # label(fact_fun__left__comm_Ofold__graph__insertE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 821 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) # label(fact_finite__UnionD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 822 (all V_B_2 all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2)))) # label(fact_sup__Sup__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 823 (all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))))) # label(fact_Sup__fin__Sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 824 (all V_g_2 all V_A_2 all V_F_2 all V_z_2 all V_f_2 all T_c all T_b (c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) -> (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2))) # label(fact_comm__monoid__big_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 825 (all V_b_2 all V_a_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2))) # label(fact_Sup__binary) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 826 (all V_A_2 all V_a_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)))) # label(fact_Sup__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 827 (all V_a_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2)) # label(fact_Sup__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 828 (all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b))) # label(fact_Sup__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 829 (all V_A_2 all V_x_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)))))) # label(fact_Sup__upper) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 830 (all V_A_2 all V_C_2 all V_X_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))))) # label(fact_UnionI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 831 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))))) # label(fact_Union__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 832 (all V_S_2 all V_a_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) & class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))))))) # label(fact_less__Sup__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 833 (all T_b c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Union__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 834 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))))) # label(fact_Union__upper) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 835 (all V_B_2 all V_a_2 all T_b c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) # label(fact_Union__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 836 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))))) # label(fact_Un__eq__Union) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 837 (all V_B_2 all V_A_2 all T_b c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) # label(fact_Union__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 838 (all V_A_2 all V_C_2 all T_b (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_Union__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 839 (all V_B_2 all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))))) # label(fact_Union__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 840 (all V_b_2 all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))))))) # label(fact_Sup__le__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 841 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) -> ((all B_M (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))))) # label(fact_finite__Union) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 842 (all V_x_2 all V_z_2 all V_A_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))))) # label(fact_fun__left__comm__idem_Ofold__insert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 843 (all V_x_2 all V_z_2 all V_A_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)))) # label(fact_fun__left__comm__idem_Ofold__insert__idem2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 844 (all V_F_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) -> (B_x != B_xa -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_insert__partition) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 845 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))))))))) # label(fact_convex__bound__lt) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 846 (all V_k_2 all V_C_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) -> ((all B_c (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) -> hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2)) -> ((all B_c1 (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) -> (all B_c2 (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) -> (B_c1 != B_c2 -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))))))) # label(fact_card__partition) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 847 (all V_f_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) -> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c))) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c))))) # label(fact_fold__image__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 848 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))))) # label(fact_card__Plus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 849 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__zeroE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 850 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))) # label(fact_le0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 851 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n)))) # label(fact_zero__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 852 (all V_x_2 all T_b (class_Groups_Ozero(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = V_x_2 <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_zero__reorient) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 853 (all V_z_2 all V_x_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) -> hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2))) # label(fact_fun__left__comm__idem_Ofun__left__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 854 (all V_a_2 all V_b_2 all T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) -> (V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_add__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 855 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 856 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 857 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_add__0__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 858 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a)) # label(fact_add__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 859 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_double__zero__sym) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 860 (all V_a all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add__0__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 861 (all V_a all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 862 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) -> V_a = c_Groups_Ozero__class_Ozero(T_a) | V_b = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_divisors__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 863 (all V_b all V_a all T_a (class_Rings_Ono__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_no__zero__divisors) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 864 (all V_b_2 all V_a_2 all T_b (class_Rings_Oring__no__zero__divisors(T_b) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) | V_b_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 865 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 866 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 867 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 868 (all V_a all T_a (class_Rings_Omult__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mult__zero__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 869 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = V_b_2))) # label(fact_right__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 870 (all V_b_2 all V_a_2 all T_b (class_Groups_Oab__group__add(T_b) -> (V_a_2 = V_b_2 <-> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 871 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_diff__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 872 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_diff__0__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 873 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a))) # label(fact_one__neq__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 874 (all T_a (class_Rings_Ozero__neq__one(T_a) -> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a))) # label(fact_zero__neq__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 875 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 876 (all V_nat_H c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H)) # label(fact_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 877 (all V_m hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 878 (all V_nat_H_1 hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 879 (all V_m c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m)) # label(fact_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 880 (all V_m hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 881 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_not__less0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 882 (all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_neq0__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 883 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 884 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_gr__implies__not0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 885 (all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)))) # label(fact_gr0I) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 886 (all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n) # label(fact_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 887 (all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 888 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__is__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 889 (all V_n all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 890 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))) # label(fact_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 891 (all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_le__0__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 892 (all V_n all V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_m = V_n))) # label(fact_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 893 (all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 894 (all V_m hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m) # label(fact_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 895 (all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 896 (all V_n_2 all V_k_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 897 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 898 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__is__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 899 (all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 900 (all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mult__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 901 (all V_n_2 all V_m_2 all V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = V_n_2)) # label(fact_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 902 (all V_n hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_min__0R) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 903 (all V_n hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_min__0L) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 904 (all T_b c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b))) # label(fact_fun__left__comm__idem__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 905 (all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)))) # label(fact_finite__Plus__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 906 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))))) # label(fact_finite__Plus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 907 (all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_finite__PlusD_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 908 (all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)))) # label(fact_finite__PlusD_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 909 (all V_B_2 all T_c all V_A_2 all T_b ((hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) & (-(hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))) -> hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_card__Plus__conv__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 910 (all T_b (class_Lattices_Oab__semigroup__idem__mult(T_b) -> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)))) # label(fact_fun__left__comm__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 911 (all T_b (class_Lattices_Osemilattice__sup(T_b) -> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)))) # label(fact_fun__left__comm__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 912 (all T_b (class_Lattices_Osemilattice__inf(T_b) -> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)))) # label(fact_fun__left__comm__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 913 (all T_b (class_Orderings_Olinorder(T_b) -> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)))) # label(fact_min__max_Ofun__left__comm__idem__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 914 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 915 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 916 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 917 (all V_y_2 all V_x_2 all T_b (class_Groups_Oordered__comm__monoid__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) & V_y_2 = c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 918 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__increasing) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 919 (all V_a all V_b all V_c all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__increasing2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 920 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 921 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))))) # label(fact_zero__le__square) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 922 (all V_b_2 all V_a_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 923 (all V_b_2 all V_a_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))))) # label(fact_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 924 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 925 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 926 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 927 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 928 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 929 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__right__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 930 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 931 (all V_c all V_b all V_a all T_a (class_Rings_Oordered__comm__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 932 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 933 (all V_c all V_a all V_b all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 934 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__mono_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 935 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Oordered__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 936 (all V_b all V_a all T_a (class_Rings_Oordered__ring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))) # label(fact_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 937 (all V_b all V_a all T_a (class_Rings_Oordered__cancel__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 938 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_pos__add__strict) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 939 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 940 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 941 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 942 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 943 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 944 (all V_c all V_a all V_b all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 945 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__comm__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 946 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))))) # label(fact_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 947 (all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))))) # label(fact_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 948 (all V_b all V_a all T_a (class_Rings_Olinordered__ring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 949 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 950 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)))))) # label(fact_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 951 (all V_a all V_b all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)))))) # label(fact_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 952 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)))))) # label(fact_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 953 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 954 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_mult__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 955 (all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))))) # label(fact_mult__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 956 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)))))) # label(fact_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 957 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))))) # label(fact_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 958 (all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))))) # label(fact_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 959 (all V_a all T_a (class_Rings_Olinordered__ring(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__square__less__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 960 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 961 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 962 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) & V_y_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 963 (all V_d all V_c all V_b all V_a all V_r all T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) -> (V_r != c_Groups_Ozero__class_Ozero(T_a) -> (V_a = V_b & V_c != V_d -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)))))) # label(fact_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 964 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__one__le__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 965 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__le__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 966 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_zero__less__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 967 (all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__one__less__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 968 (all V_f_2 all T_c all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b))) # label(fact_setsum__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 969 (all V_g_2 all T_c all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b))) # label(fact_setsum_Oempty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 970 (all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)))) # label(fact_setsum_Oinfinite) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 971 (all V_f_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)))) # label(fact_setsum__infinite) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 972 (all V_f_2 all V_A_2 all T_b all T_c (class_Rings_Ocomm__semiring__1(T_c) & class_Rings_Ono__zero__divisors(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c))))))) # label(fact_setprod__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 973 (all V_f_2 all V_A_2 all T_b all T_c (class_Rings_Ocomm__semiring__1(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c))))) # label(fact_setprod__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 974 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | (exists B_j (V_m_2 = hAPP(c_Nat_OSuc,B_j) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)))))) # label(fact_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 975 (all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_less__Suc0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 976 (all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) <-> (exists B_m V_n_2 = hAPP(c_Nat_OSuc,B_m)))) # label(fact_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 977 (all V_n_2 all V_m_2 (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_one__is__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 978 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_add__is__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 979 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_add__gr__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 980 (all T_b hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_card_Oempty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 981 (all V_A_2 all T_b (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_card__infinite) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 982 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 983 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_zero__less__diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 984 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m))))) # label(fact_diff__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 985 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 986 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 987 (all V_n_2 all V_k_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 988 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))))) # label(fact_mult__less__mono1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 989 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))))) # label(fact_mult__less__mono2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 990 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 991 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) <-> V_m_2 = V_n_2))) # label(fact_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 992 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_diff__add__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 993 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 994 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 995 (all V_n all V_m (V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) -> V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 996 (all V_f_2 all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) -> (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) -> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) # label(fact_setsum__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 997 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 998 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 999 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 1000 (all V_c all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))))) # label(fact_add__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.04 1001 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1002 (all V_b all V_a all T_a (class_Groups_Oordered__comm__monoid__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))))) # label(fact_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1003 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)))))) # label(fact_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1004 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)))))) # label(fact_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1005 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1006 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1007 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1008 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))))) # label(fact_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1009 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1010 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1011 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1012 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1013 (all V_b all V_c all V_a all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)))))) # label(fact_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1014 (all V_b all V_a all V_c all T_a (class_Rings_Olinordered__semiring__strict(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)))))) # label(fact_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1015 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))))) # label(fact_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1016 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) & V_y_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1017 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__ring__strict(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_b) | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1018 (all V_y all V_x all T_a (class_Rings_Olinordered__ring(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1019 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x))))))) # label(fact_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1020 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x))))))) # label(fact_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1021 (all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))))) # label(fact_zero__less__two) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1022 (all V_A_2 all T_b (hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_card__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1023 (all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_card__ge__0__finite) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1024 (all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n)) # label(fact_Suc__pred) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1025 (all V_i all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)))) # label(fact_diff__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1026 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))))) # label(fact_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1027 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))))) # label(fact_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1028 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))))) # label(fact_one__less__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1029 (all V_b_2 all V_a_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) <-> -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) & -hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (exists B_d (V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) & -hBOOL(hAPP(V_Pa_2,B_d))))))) # label(fact_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1030 (all V_b_2 all V_a_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) -> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & (all B_d (V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) -> hBOOL(hAPP(V_Pa_2,B_d)))))) # label(fact_nat__diff__split) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1031 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)))) # label(fact_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1032 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1033 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1034 (all V_n_2 all V_k_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1035 (all V_f_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) -> (B_x != B_xa -> hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))) # label(fact_setsum__eq__Suc0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1036 (all V_f_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) & (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) -> (B_x != B_xa -> hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))) # label(fact_setsum__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1037 (all V_f_2 all V_S_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))))))) # label(fact_setprod__pos__nat__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1038 (all V_v all V_u all V_y all V_a all V_x all T_a (class_Rings_Olinordered__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))))))))) # label(fact_convex__bound__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1039 (all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) <-> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_card__gt__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1040 (all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2)) & (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)))) # label(fact_setsum_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1041 (all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2)))) # label(fact_setsum_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1042 (all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_Suc__pred_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1043 (all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n)) # label(fact_Suc__diff__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1044 (all V_n all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))))) # label(fact_add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1045 (all V_n all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))))) # label(fact_mult__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1046 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_even__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1047 (all V_f_2 all V_A_2 all V_B_2 all T_b all T_c (class_Groups_Oordered__comm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> ((all B_b (hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))))))) # label(fact_setsum__mono2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1048 (all V_fun2_2 all V_com_2 all V_fun1_2 all V_fa_2 all T_b c_Hoare__Mirabelle_Otriple_Otriple__size(T_b,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_triple_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1049 (all V_B_2 all V_A_2 all T_c all T_b (c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_Plus__eq__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1050 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (((exists B_x hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) -> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))))) # label(fact_card_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1051 (all V_g_2 all V_B_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))))))) # label(fact_setsum_Ounion__inter__neutral) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1052 (all V_f_2 all V_T_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) -> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2))))))) # label(fact_setsum__Un__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1053 (all V_f_2 all V_A_2 all V_B_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) & class_Groups_Oordered__ab__semigroup__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))))))) # label(fact_setsum__mono3) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1054 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1055 (all V_fun2_2 all V_com_2 all V_fun1_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_triple_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1056 (all V_k_2 all V_A_2 all T_b (hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) <-> (exists B_b exists B_B (V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) & -hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B)) & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2 & (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_card__Suc__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1057 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))))))) # label(fact_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1058 (all V_com2 all V_com1 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_com_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1059 (all V_com2 all V_com1 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_com_Osize_I12_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1060 (all V_a_2 all V_f_2 all V_A_2 all T_b all T_c (class_Fields_Ofield(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))))) # label(fact_setprod__diff1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1061 (all V_n_2 all V_Pa_2 (-hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) -> (hBOOL(hAPP(V_Pa_2,V_n_2)) -> (exists B_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) & (all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) -> -hBOOL(hAPP(V_Pa_2,B_i)))) & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))) # label(fact_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1062 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__zero__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1063 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1064 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))) # label(fact_add__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1065 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))) # label(fact_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1066 (all V_c all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))) # label(fact_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1067 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_divide__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1068 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Odivision__ring(T_b) -> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) -> (V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2)))) # label(fact_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1069 (all V_a_2 all V_b_2 all V_ca_2 all T_b (class_Rings_Odivision__ring(T_b) -> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2 <-> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))) # label(fact_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1070 (all V_a all V_b all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> (V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a)))) # label(fact_divide__eq__imp) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1071 (all V_b all V_a all V_c all T_a (class_Rings_Odivision__ring(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b -> V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))))) # label(fact_eq__divide__imp) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1072 (all V_a all T_a (class_Rings_Odivision__ring__inverse__zero(T_a) -> (V_a = c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)) & (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_divide__self__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1073 (all V_a all T_a (class_Rings_Odivision__ring(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_divide__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1074 (all V_a_2 all V_b_2 all T_b (class_Rings_Odivision__ring(T_b) -> (V_b_2 != c_Groups_Ozero__class_Ozero(T_b) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b) <-> V_a_2 = V_b_2)))) # label(fact_right__inverse__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1075 (all T_b (class_Rings_Oring__1(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))))) # label(fact_Ints__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1076 (all V_b_2 all V_a_2 all T_b (class_Rings_Oring__1(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))))))) # label(fact_Ints__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1077 (all V_b_2 all V_a_2 all T_b (class_Rings_Oring__1(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))))))) # label(fact_Ints__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1078 (all V_b_2 all V_a_2 all T_b (class_Rings_Oring__1(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))))))) # label(fact_Ints__diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1079 (all T_b (class_Rings_Oring__1(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))))) # label(fact_Ints__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1080 (all V_a_2 all T_b (class_Int_Oring__char__0(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1081 (all V_a_2 all T_b (class_Int_Oring__char__0(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1082 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))))) # label(fact_le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1083 (all V_a_2 all V_ca_2 all V_b_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))))) # label(fact_divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1084 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Fields_Olinordered__field(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)))))) # label(fact_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1085 (all V_a_2 all V_b_2 all V_ca_2 all T_b (class_Fields_Olinordered__field(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))))) # label(fact_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1086 (all V_z all V_x all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)))))) # label(fact_mult__imp__div__pos__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1087 (all V_x all V_z all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))))) # label(fact_mult__imp__le__div__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1088 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Fields_Olinordered__field(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))))) # label(fact_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1089 (all V_w all V_z all V_y all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)))) # label(fact_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1090 (all V_b_2 all V_a_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1091 (all V_b_2 all V_a_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))))) # label(fact_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1092 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))))))) # label(fact_divide__right__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1093 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))))))) # label(fact_divide__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1094 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))))))) # label(fact_divide__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1095 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))))))) # label(fact_divide__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1096 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))))) # label(fact_divide__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1097 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_divide__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1098 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_divide__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1099 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))))) # label(fact_divide__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1100 (all V_b_2 all V_a_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))))) # label(fact_divide__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1101 (all V_b_2 all V_a_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_zero__less__divide__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1102 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Fields_Ofield__inverse__zero(T_b) -> (V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_eq__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1103 (all V_a_2 all V_ca_2 all V_b_2 all T_b (class_Fields_Ofield__inverse__zero(T_b) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2 <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) -> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_divide__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1104 (all V_b all V_a all V_c all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)))) # label(fact_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1105 (all V_b all V_a all V_c all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)))) # label(fact_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1106 (all V_w_2 all V_x_2 all V_z_2 all V_y_2 all T_b (class_Fields_Ofield(T_b) -> (V_y_2 != c_Groups_Ozero__class_Ozero(T_b) -> (V_z_2 != c_Groups_Ozero__class_Ozero(T_b) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)))))) # label(fact_frac__eq__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1107 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))))) # label(fact_divide__nonneg__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1108 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_divide__nonneg__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1109 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))))))))) # label(fact_frac__less2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1110 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))))))))) # label(fact_frac__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1111 (all V_z all V_w all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))))))))) # label(fact_frac__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1112 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))))))) # label(fact_divide__nonpos__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1113 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))))) # label(fact_divide__nonpos__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1114 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))))))) # label(fact_divide__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1115 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))))))) # label(fact_divide__strict__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1116 (all V_a_2 all V_b_2 all V_ca_2 all T_b (class_Fields_Olinordered__field(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)))))) # label(fact_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1117 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Fields_Olinordered__field(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))))) # label(fact_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1118 (all V_x all V_z all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))))) # label(fact_mult__imp__less__div__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1119 (all V_z all V_x all V_y all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)))))) # label(fact_mult__imp__div__pos__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1120 (all V_a_2 all V_b_2 all V_ca_2 all T_b (class_Fields_Olinordered__field(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))))) # label(fact_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1121 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Fields_Olinordered__field(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)))))) # label(fact_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1122 (all V_a_2 all V_ca_2 all V_b_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))))) # label(fact_divide__less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1123 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))))) # label(fact_less__divide__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1124 (all V_x all V_z all V_y all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)))) # label(fact_add__num__frac) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1125 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z)))) # label(fact_add__divide__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1126 (all V_z all V_x all V_y all T_a (class_Fields_Ofield__inverse__zero(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)))) # label(fact_add__frac__num) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1127 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z)))) # label(fact_divide__add__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1128 (all V_w all V_x all V_z all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_add__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1129 (all V_w all V_x all V_z all V_y all T_a (class_Fields_Ofield(T_a) -> (V_y != c_Groups_Ozero__class_Ozero(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_diff__frac__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1130 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z)))) # label(fact_divide__diff__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1131 (all V_y all V_x all V_z all T_a (class_Fields_Ofield(T_a) -> (V_z != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z)))) # label(fact_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1132 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b))))) # label(fact_gt__half__sum) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1133 (all V_b all V_a all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))))))) # label(fact_less__half__sum) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1134 (all V_c all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))))))) # label(fact_divide__left__mono__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1135 (all V_c all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))))))) # label(fact_divide__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1136 (all V_a_2 all V_b_2 all V_ca_2 all T_b (class_Fields_Olinordered__field(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)))))) # label(fact_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1137 (all V_f_2 all V_B_2 all V_A_2 all T_b all T_c (class_Fields_Ofield(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))))))) # label(fact_setprod__Un) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1138 (all V_f_2 all V_S_2 all V_T_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) -> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)))))) # label(fact_setsum__mono__zero__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1139 (all V_f_2 all V_S_2 all V_T_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) -> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)))))) # label(fact_setsum__mono__zero__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1140 (all V_y all V_x all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> ((all B_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))))) # label(fact_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1141 (all V_f_2 all V_S_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))))) # label(fact_setprod__pos__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1142 (all V_n_2 all V_A_2 all V_f_2 all T_b (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) -> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))))))) # label(fact_setsum__SucD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1143 (all V_com2_2 all V_com1_2 all V_fun_2 c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_com_Osize_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1144 (all V_com2_H_2 all V_com1_H_2 all V_fun_H_2 all V_com2_2 all V_com1_2 all V_fun_2 (c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) <-> V_fun_2 = V_fun_H_2 & V_com1_2 = V_com1_H_2 & V_com2_2 = V_com2_H_2)) # label(fact_com_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1145 (all V_com2_2 all V_com1_2 all V_com2_H_2 all V_com1_H_2 all V_fun_H_2 c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) # label(fact_com_Osimps_I45_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1146 (all V_com2_H_2 all V_com1_H_2 all V_fun_H_2 all V_com2_2 all V_com1_2 c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)) # label(fact_com_Osimps_I44_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1147 (all V_com2_H_2 all V_com1_H_2 all V_fun_H_2 c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP) # label(fact_com_Osimps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1148 (all V_com2_H_2 all V_com1_H_2 all V_fun_H_2 c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)) # label(fact_com_Osimps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1149 (all V_com2_2 all V_com1_2 all V_fun_2 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_com_Osize_I13_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1150 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (((exists B_x hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))) -> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) -> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_card_Oneutral) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1151 (all V_ca_2 all V_b_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))))))) # label(fact_min__max_Oinf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1152 (all V_z_2 all V_h_2 all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Oab__semigroup__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x))) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2))))) # label(fact_fold__image__cong) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1153 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_y (hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2))))) # label(fact_Min__eqI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1154 (all V_ca_2 all V_b_2 all V_A_2 all T_b (class_Lattices_Osemilattice__inf(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))))))) # label(fact_inf__le__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1155 (all V_ca_2 all V_b_2 all V_A_2 all T_b (class_Lattices_Osemilattice__sup(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_2))))))) # label(fact_fold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1156 (all V_v (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) -> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_expand__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1157 (all V_y_2 all V_x_2 all T_b (class_Int_Onumber__ring(T_b) & class_Int_Oring__char__0(T_b) -> (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) <-> V_x_2 = V_y_2))) # label(fact_eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1158 (all V_x_2 all V_w_2 all T_b (class_Int_Onumber(T_b) -> (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2 <-> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) # label(fact_number__of__reorient) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1159 (all V_y_2 all V_x_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2))))) # label(fact_le__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1160 (all V_y_2 all V_x_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2))))) # label(fact_less__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1161 (all V_z all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z))) # label(fact_add__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1162 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)))) # label(fact_add__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1163 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)))) # label(fact_number__of__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1164 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)))) # label(fact_number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1165 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)))) # label(fact_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1166 (all V_z all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z))) # label(fact_mult__number__of__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1167 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)))) # label(fact_number__of__diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1168 (all V_w_2 all V_v_2 all T_b (class_Int_Onumber(T_b) & class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) <-> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))))) # label(fact_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.05 1169 (all V_v all V_b all V_a all T_b (class_Int_Onumber(T_b) & class_Rings_Osemiring(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))))) # label(fact_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1170 (all V_c all V_b all V_v all T_b (class_Int_Onumber(T_b) & class_Rings_Osemiring(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)))) # label(fact_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1171 (all V_c all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c))) # label(fact_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1172 (all V_c all V_b all V_v all T_b (class_Int_Onumber(T_b) & class_Rings_Oring(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)))) # label(fact_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1173 (all V_v all V_b all V_a all T_b (class_Int_Onumber(T_b) & class_Rings_Oring(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))))) # label(fact_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1174 (all V_v all V_u all T_b (class_Int_Onumber(T_b) & class_Orderings_Oord(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))) # label(fact_min__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1175 (all V_w_2 all T_b (class_Int_Onumber__ring(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))))) # label(fact_Ints__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1176 (all V_a_2 all V_w_2 all V_b_2 all T_b (class_Fields_Ofield__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2 <-> (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) -> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) & (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_divide__eq__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1177 (all V_w_2 all V_ca_2 all V_b_2 all T_b (class_Fields_Ofield__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) -> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) -> hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_divide__eq__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1178 (all V_ca_2 all V_b_2 all V_w_2 all T_b (class_Fields_Ofield__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) <-> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_b_2) & (V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) -> hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_eq__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1179 (all V_w_2 all V_b_2 all V_a_2 all T_b (class_Fields_Ofield__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) <-> (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2) & (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) -> V_a_2 = c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_eq__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1180 (all V_a_2 all V_w_2 all V_b_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))))) # label(fact_divide__less__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1181 (all V_w_2 all V_ca_2 all V_b_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))))))) # label(fact_divide__less__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1182 (all V_ca_2 all V_b_2 all V_w_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))))))) # label(fact_less__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1183 (all V_w_2 all V_b_2 all V_a_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))))) # label(fact_less__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1184 (all V_w_2 all V_b_2 all V_a_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))))) # label(fact_le__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1185 (all V_ca_2 all V_b_2 all V_w_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))))))) # label(fact_le__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1186 (all V_w_2 all V_ca_2 all V_b_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))))))) # label(fact_divide__le__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1187 (all V_a_2 all V_w_2 all V_b_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))))) # label(fact_divide__le__eq__number__of1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1188 (all V_com_2 all V_fun_2 all V_loc_2 c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_com_Osize_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1189 (all V_com_2 all V_fun_2 all V_loc_2 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_com_Osize_I11_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1190 (all V_C_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) -> -(all B_X (hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) -> -hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)))))) # label(fact_UnionE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1191 (all V_f_2 all V_A_2 all T_b all T_c (class_Rings_Olinordered__semidom(T_c) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))))) # label(fact_setprod__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1192 (all V_f_2 all V_A_2 all T_b all T_c (class_Rings_Olinordered__semidom(T_c) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))))) # label(fact_setprod__nonneg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1193 (all V_k all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)))) # label(fact_number__of__succ) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1194 (all V_y all V_x all T_a (class_Fields_Olinordered__field(T_a) -> ((all B_e (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))))) # label(fact_field__le__epsilon) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1195 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1196 (all V_w all V_v hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))) # label(fact_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1197 (all V_w all V_v hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))) # label(fact_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1198 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1199 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_odd__nonzero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1200 (all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_odd__less__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1201 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1202 (all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)))) # label(fact_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1203 (all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))))) # label(fact_le__imp__0__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1204 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z) # label(fact_zadd__0__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1205 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z) # label(fact_zadd__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1206 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))))) # label(fact_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1207 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_less__bin__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1208 (all V_z all V_z_H all V_w all V_w_H (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)))))) # label(fact_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1209 (all V_w_2 all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) & V_z_2 != V_w_2)) # label(fact_zless__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1210 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))) # label(fact_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1211 (all V_z2 all V_z1 all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))) # label(fact_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1212 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) | V_x = V_y | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)))) # label(fact_zless__linear) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1213 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) # label(fact_zmult__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1214 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))) # label(fact_zmult__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1215 (all V_z2 all V_z1 all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))) # label(fact_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1216 (all V_w all V_z2 all V_z1 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))) # label(fact_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1217 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))))) # label(fact_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1218 (all V_w all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) # label(fact_zadd__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1219 (all V_z all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z))) # label(fact_zadd__left__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1220 (all V_z3 all V_z2 all V_z1 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3))) # label(fact_zadd__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1221 (all V_w hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w))) # label(fact_zle__refl) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1222 (all V_w all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)))) # label(fact_zle__linear) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1223 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k))))) # label(fact_zle__trans) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1224 (all V_w all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) -> V_z = V_w))) # label(fact_zle__antisym) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1225 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))))) # label(fact_zadd__left__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1226 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)))) # label(fact_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1227 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)))) # label(fact_add1__zle__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1228 (all V_z all V_w (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)))) # label(fact_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1229 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)))) # label(fact_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1230 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z) # label(fact_zmult__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1231 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z) # label(fact_zmult__1__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1232 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) | V_w_2 = V_z_2)) # label(fact_zless__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1233 (all V_k c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_succ__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1234 (all V_com_H_2 all V_fun_H_2 all V_loc_H_2 all V_com_2 all V_fun_2 all V_loc_2 (c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) <-> V_loc_2 = V_loc_H_2 & V_fun_2 = V_fun_H_2 & V_com_2 = V_com_H_2)) # label(fact_com_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1235 (all V_com_2 all V_fun_2 all V_loc_2 all V_com2_H_2 all V_com1_H_2 all V_fun_H_2 c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) # label(fact_com_Osimps_I37_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1236 (all V_com2_H_2 all V_com1_H_2 all V_fun_H_2 all V_com_2 all V_fun_2 all V_loc_2 c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)) # label(fact_com_Osimps_I36_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1237 (all V_com2_H_2 all V_com1_H_2 all V_com_2 all V_fun_2 all V_loc_2 c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)) # label(fact_com_Osimps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1238 (all V_com_2 all V_fun_2 all V_loc_2 all V_com2_H_2 all V_com1_H_2 c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) # label(fact_com_Osimps_I35_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1239 (all V_com_H_2 all V_fun_H_2 all V_loc_H_2 c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP) # label(fact_com_Osimps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1240 (all V_com_H_2 all V_fun_H_2 all V_loc_H_2 c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)) # label(fact_com_Osimps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1241 (all V_q all V_r all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)))))) # label(fact_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1242 (all V_q all V_r all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) # label(fact_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1243 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q))))))))) # label(fact_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1244 (all V_r all V_q all V_r_H all V_q_H all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H))))))) # label(fact_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1245 (all V_r_H all V_q_H all V_b_H all V_r all V_q all V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H))))))))) # label(fact_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1246 (all V_r all V_q all V_r_H all V_q_H all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q))))))) # label(fact_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1247 (all V_r_H all V_q_H all V_b_H (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) # label(fact_q__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1248 (all V_k hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k) # label(fact_number__of__is__id) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1249 (all V_r_H all V_q_H all V_b_H (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)))))) # label(fact_q__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1250 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1251 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1252 (all V_n all V_v ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n)))) # label(fact_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1253 (all V_v ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))))) # label(fact_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1254 (all V_v all T_a (class_Int_Onumber__ring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_of__nat__number__of__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1255 (all V_n_2 all V_m_2 all T_b (class_Nat_Osemiring__char__0(T_b) -> (hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) <-> V_m_2 = V_n_2))) # label(fact_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1256 (all V_n -hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)))) # label(fact_not__neg__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1257 (all V_z hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1258 (all V_Pa_2 ((exists B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> (exists B_x hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))))) # label(fact_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1259 (all V_Pa_2 ((all B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> (all B_x hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))))) # label(fact_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1260 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)))) # label(fact_transfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1261 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)))) # label(fact_transfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1262 (all V_y all V_x hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y))) # label(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1263 (all V_y all V_x hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y))) # label(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1264 (all V_v ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) # label(fact_int__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1265 (all V_n_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1266 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)))) # label(fact_zero__zle__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1267 (all V_k -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_int__less__0__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1268 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_zless__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1269 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_zle__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1270 (all V_z all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z)) # label(fact_zadd__int__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1271 (all V_n all V_m hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) # label(fact_zadd__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1272 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) <-> (exists B_n V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n))))) # label(fact_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1273 (all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))))) # label(fact_of__nat__0__le__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1274 (all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))))) # label(fact_zero__le__imp__of__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1275 (all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_of__nat__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1276 (all V_v all T_a (class_Int_Onumber__ring(T_a) -> (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)))) # label(fact_of__nat__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1277 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) # label(fact_zmult__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1278 (all V_n all V_m hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) # label(fact_int__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1279 (all T_a (class_Rings_Osemiring__1(T_a) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_of__nat__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1280 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1281 (all V_n all V_m all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))))) # label(fact_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1282 (all V_n_2 all V_m_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1283 (all V_n_2 all V_m_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1284 (all V_n all V_m all T_a (class_Rings_Osemiring__1(T_a) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))) # label(fact_of__nat__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1285 (all V_n all V_m all T_a (class_Rings_Osemiring__1(T_a) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))) # label(fact_of__nat__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1286 (all T_a (class_Rings_Osemiring__1(T_a) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_of__nat__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1287 (all V_n_2 all T_b (class_Rings_Oring__1(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))))) # label(fact_Ints__of__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1288 (all V_x_2 (-hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)))) # label(fact_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1289 (all V_Z_2 (hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_neg__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1290 (all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_int__le__0__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1291 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) <-> (exists B_n V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n)))))) # label(fact_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1292 (all V_m hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) # label(fact_int__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1293 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))) # label(fact_zdiff__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1294 (all V_m all T_a (class_Rings_Osemiring__1(T_a) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)))) # label(fact_of__nat__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1295 (all V_m all V_n all T_a (class_Rings_Oring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))))) # label(fact_of__nat__diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1296 (all V_v (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1297 (all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))) # label(fact_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1298 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j)))))) # label(fact_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1299 (all V_n_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))))) # label(fact_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1300 (all V_v_H_2 all V_v_2 (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2) <-> (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) -> (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) -> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) -> V_v_2 = V_v_H_2)))) # label(fact_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1301 (all V_k all V_v_H all V_v ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k))))) # label(fact_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1302 (all V_y_2 all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) -> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_zdiff__int__split) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1303 (all V_K_2 all V_f_2 all V_A_2 all T_b all T_c (class_Groups_Oordered__ab__semigroup__add(T_c) & class_Rings_Osemiring__1(T_c) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2)))))) # label(fact_setsum__bounded) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1304 (all V_x all V_y ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) -> c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) -> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_tsub__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1305 (all V_v ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))))) # label(fact_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1306 (all V_v ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))))) # label(fact_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1307 (all V_v_2 (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) <-> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1308 (all V_v_H all V_v ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))))) # label(fact_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1309 (all V_n_2 all V_m_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) <-> V_m_2 = V_n_2)) # label(fact_int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1310 (all V_y_2 all V_x_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) <-> V_x_2 = V_y_2)) # label(fact_transfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1311 (all V_k hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k) # label(fact_add__Pls__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1312 (all V_k hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k) # label(fact_add__Pls) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1313 (all V_w hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls) # label(fact_mult__Pls) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1314 (all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k) # label(fact_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1315 (all V_x c_Int_Osucc(c_Int_Opred(V_x)) = V_x) # label(fact_succ__pred) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1316 (all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls))) # label(fact_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1317 (all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_number__of__Pls) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1318 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a)) # label(fact_add__numeral__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1319 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a)) # label(fact_add__numeral__0__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1320 (all V_m all V_v (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))))) # label(fact_Suc__diff__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1321 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)))) # label(fact_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1322 (all V_k c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_pred__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1323 (all V_y all V_x c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y))) # label(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1324 (all V_v ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))))) # label(fact_nat__number__of__diff__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1325 (all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_divide__Numeral0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1326 (all V_v_2 (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)))) # label(fact_eq__number__of__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1327 (all V_v_2 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)))) # label(fact_eq__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1328 (all V_v_H_2 all V_v_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)))) # label(fact_less__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1329 (all V_v_H_2 all V_v_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) <-> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))))) # label(fact_le__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1330 (all V_x_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls))))) # label(fact_le__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1331 (all V_y_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2))))) # label(fact_le__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1332 (all V_y_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2))))) # label(fact_less__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1333 (all V_x_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls))))) # label(fact_less__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1334 (all V_v_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)))) # label(fact_less__0__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1335 (all V_v_H all V_v ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)))))) # label(fact_add__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1336 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y)))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1337 (all V_x all V_y (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) -> c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y))) # label(fact_tsub__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1338 (all V_k all V_v_H all V_v ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k)))) # label(fact_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1339 (all V_w_2 all T_b (class_Int_Onumber__ring(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b)))))) # label(fact_Nats__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1340 (all V_k_2 all V_Pa_2 all V_d_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) -> ((all B_x (hBOOL(hAPP(V_Pa_2,B_x)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (all B_x (hBOOL(hAPP(V_Pa_2,B_x)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))))))))) # label(fact_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1341 (all V_k_2 all V_Pa_2 all V_d_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) -> ((all B_x (hBOOL(hAPP(V_Pa_2,B_x)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (all B_x (hBOOL(hAPP(V_Pa_2,B_x)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))))))))) # label(fact_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1342 (all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> (exists B_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n))))) # label(fact_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1343 (all V_x all V_z all V_d (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))))) # label(fact_incr__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1344 (all V_z all V_x all V_d (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)))) # label(fact_decr__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1345 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) # label(fact_abs__idempotent) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1346 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))))) # label(fact_abs__le__D1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1347 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))))) # label(fact_abs__ge__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1348 (all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_abs__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1349 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add__abs(T_b) -> (hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_abs__eq__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1350 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) # label(fact_abs__add__abs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1351 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) # label(fact_abs__mult__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1352 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) # label(fact_abs__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1353 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) # label(fact_abs__minus__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1354 (all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_abs__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1355 (all V_n all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) # label(fact_abs__of__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1356 (all V_b all V_a all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) # label(fact_abs__divide) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1357 (all V_m hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) # label(fact_abs__int__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1358 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))))) # label(fact_abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.06 1359 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add__abs(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1360 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a))) # label(fact_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1361 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1362 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add__abs(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2))) <-> V_a_2 != c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1363 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a))) # label(fact_abs__of__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1364 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))))) # label(fact_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1365 (all V_d all V_b all V_c all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))))))) # label(fact_abs__mult__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1366 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))))) # label(fact_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1367 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))))) # label(fact_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1368 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))))) # label(fact_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1369 (all V_a all V_b all T_a (class_Fields_Olinordered__field(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))) # label(fact_nonzero__abs__divide) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1370 (all V_n all V_m (hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint) -> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1371 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x))))) # label(fact_abs__mult__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1372 (all V_b all V_a all T_a (class_Rings_Oordered__ring__abs(T_a) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))) # label(fact_abs__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1373 (all V_d all V_c all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))))) # label(fact_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1374 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))))) # label(fact_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1375 (all V_x all V_y all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))) # label(fact_abs__div__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1376 (all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) <-> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1377 (all T_b (class_Rings_Osemiring__1(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))))) # label(fact_Nats__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1378 (all V_b_2 all V_a_2 all T_b (class_Rings_Osemiring__1(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))))))) # label(fact_Nats__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1379 (all V_b_2 all V_a_2 all T_b (class_Rings_Osemiring__1(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))))))) # label(fact_Nats__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1380 (all T_b (class_Rings_Osemiring__1(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))))) # label(fact_Nats__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1381 (all V_n_2 all T_b (class_Rings_Osemiring__1(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))))) # label(fact_of__nat__in__Nats) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1382 (all V_k_2 all V_f_2 all V_n_2 ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) -> (exists B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) & hAPP(V_f_2,B_i) = V_k_2)))))) # label(fact_int__val__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1383 (all V_k_2 all V_f_2 all V_n_2 ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) -> (exists B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) & hAPP(V_f_2,B_i) = V_k_2)))))) # label(fact_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1384 (all V_k_2 all V_f_2 all V_n_2 all V_m_2 ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) -> (exists B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) & hAPP(V_f_2,B_i) = V_k_2))))))) # label(fact_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1385 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))))) # label(fact_Suc__diff__eq__diff__pred) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1386 (all V_y all V_q_1 all V_b_1 all V_a_1 (V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> (V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y)))) # label(fact_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1387 (all V_q all V_r all V_b all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) # label(fact_zmult2__lemma__aux2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1388 (all V_l_2 all V_k_2 (c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) <-> V_k_2 = V_l_2)) # label(fact_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1389 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1390 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1391 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a)) # label(fact_mod__by__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1392 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1393 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1394 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__add__self1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1395 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1396 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c))) # label(fact_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1397 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__add__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1398 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c))) # label(fact_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1399 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c))) # label(fact_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1400 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c))))) # label(fact_mod__add__cong) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1401 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c))))) # label(fact_mod__mult__cong) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1402 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c))) # label(fact_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1403 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c))) # label(fact_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1404 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)))) # label(fact_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1405 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__mult__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1406 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c))) # label(fact_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1407 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1408 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__diff__right__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1409 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c))) # label(fact_mod__diff__left__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1410 (all V_c all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c))) # label(fact_mod__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1411 (all V_b_H all V_b all V_a_H all V_c all V_a all T_a (class_Divides_Oring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) -> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c))))) # label(fact_mod__diff__cong) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1412 (all V_b c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1413 (all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1414 (all V_k2_2 all V_k1_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)))) # label(fact_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1415 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1416 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1417 (all V_k2_2 all V_k1_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)))) # label(fact_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1418 (all V_k c_Int_OBit1(V_k) != c_Int_OPls) # label(fact_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1419 (all V_l c_Int_OPls != c_Int_OBit1(V_l)) # label(fact_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1420 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)) # label(fact_zmod__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1421 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)) # label(fact_zmod__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1422 (all V_m all V_y all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m)) # label(fact_zdiff__zmod__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1423 (all V_y all V_m all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m)) # label(fact_zdiff__zmod__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1424 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1425 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1426 (all V_b all V_c all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1427 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b))) # label(fact_mod__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1428 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__by__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1429 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)))))) # label(fact_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1430 (all V_k all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)))) # label(fact_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1431 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)))) # label(fact_pos__mod__bound) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1432 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))) # label(fact_neg__mod__bound) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1433 (all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1434 (all V_d_2 all V_m_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> (exists B_q V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q)))) # label(fact_zmod__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1435 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)))) # label(fact_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1436 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)))) # label(fact_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1437 (all V_k c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k)) # label(fact_Bit1__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1438 (all V_w_2 (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) <-> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))))) # label(fact_neg__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1439 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)))) # label(fact_number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1440 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a)) # label(fact_mult__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1441 (all V_a all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a)) # label(fact_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1442 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a))) # label(fact_mod__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1443 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))) # label(fact_neg__mod__conj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1444 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_neg__mod__sign) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1445 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a))) # label(fact_mod__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1446 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)))) # label(fact_pos__mod__conj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1447 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))) # label(fact_pos__mod__sign) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1448 (all T_a (class_Int_Onumber__ring(T_a) -> c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)))) # label(fact_semiring__norm_I110_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1449 (all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1450 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)))) # label(fact_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1451 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)))) # label(fact_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1452 (all V_a all T_a (class_Fields_Ofield(T_a) & class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a)) # label(fact_divide__numeral__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1453 (all V_x all T_a (class_Fields_Ofield(T_a) & class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x)) # label(fact_divide__Numeral1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1454 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))) # label(fact_mod__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1455 (all V_n hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)) # label(fact_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1456 (all V_x_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))))) # label(fact_le__special_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1457 (all V_y_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))))) # label(fact_le__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1458 (all V_y_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))))) # label(fact_less__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1459 (all V_x_2 all T_b (class_Int_Onumber__ring(T_b) & class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))))) # label(fact_less__special_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1460 (all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))))) # label(fact_add__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1461 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)))) # label(fact_add__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1462 (all V_k_2 all V_n_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(V_Pa_2,V_n_2))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) -> hBOOL(hAPP(V_Pa_2,B_j))))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) -> hBOOL(hAPP(V_Pa_2,B_j))))))) # label(fact_split__zmod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1463 (all V_q all V_b all V_r all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))))))) # label(fact_zmult2__lemma__aux3) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1464 (all V_q all V_b all V_r all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))))))) # label(fact_zmult2__lemma__aux4) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1465 (all V_q all V_r all V_b all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))))))) # label(fact_zmult2__lemma__aux1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1466 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_neg__zmod__mult__2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1467 (all V_v all V_w ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))) # label(fact_zmod__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1468 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))))) # label(fact_pos__zmod__mult__2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1469 (all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_zmod__minus1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1470 (all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))) # label(fact_diff__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1471 (all V_m all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) # label(fact_negative__zle) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1472 (all V_m all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))) # label(fact_negative__zless) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1473 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z))) # label(fact_mult__minus1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1474 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z))) # label(fact_mult__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1475 (all V_z all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z))) # label(fact_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1476 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)))) # label(fact_number__of__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1477 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))) # label(fact_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1478 (all V_z hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z) # label(fact_zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1479 (all V_k hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))) # label(fact_minus__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1480 (all V_l c_Int_OMin != c_Int_OBit0(V_l)) # label(fact_rel__simps_I42_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1481 (all V_k c_Int_OBit0(V_k) != c_Int_OMin) # label(fact_rel__simps_I45_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1482 (all V_l_2 all V_k_2 (c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) <-> V_k_2 = V_l_2)) # label(fact_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1483 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a)) # label(fact_minus__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1484 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) <-> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))) # label(fact_equation__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1485 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2 <-> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2))) # label(fact_minus__equation__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1486 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) <-> V_a_2 = V_b_2))) # label(fact_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1487 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x)) # label(fact_double__compl) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1488 (all V_x_2 all V_A_2 all T_c all T_b (class_Groups_Ouminus(T_b) -> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)))) # label(fact_uminus__apply) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1489 (all V_y_2 all V_x_2 all T_b (class_Lattices_Oboolean__algebra(T_b) -> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) <-> V_x_2 = V_y_2))) # label(fact_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1490 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)))) # label(fact_rel__simps_I28_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1491 (all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)) # label(fact_mult__Min) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1492 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)))) # label(fact_rel__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1493 (all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin))) # label(fact_arith__simps_I31_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1494 (all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_number__of__Min) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1495 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)))) # label(fact_rel__simps_I11_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1496 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)))) # label(fact_rel__simps_I25_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1497 (all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) # label(fact_divide__minus1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1498 (all V_l hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l))) # label(fact_diff__bin__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1499 (all V_l hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l))) # label(fact_diff__bin__simps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1500 (all V_y all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)))))) # label(fact_compl__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1501 (all V_y_2 all V_x_2 all T_b (class_Lattices_Oboolean__algebra(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))))) # label(fact_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1502 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))))) # label(fact_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1503 (all V_a_2 all V_b_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))))) # label(fact_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1504 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))))) # label(fact_minus__le__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1505 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))))) # label(fact_le__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1506 (all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_minus__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1507 (all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) <-> c_Groups_Ozero__class_Ozero(T_b) = V_a_2))) # label(fact_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1508 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_equal__neg__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1509 (all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1510 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2 <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_neg__equal__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1511 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))))) # label(fact_less__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1512 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))))) # label(fact_minus__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1513 (all V_a_2 all V_b_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))))) # label(fact_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1514 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_minus__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1515 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))) # label(fact_minus__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1516 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b)) # label(fact_add__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1517 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b)) # label(fact_minus__add__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1518 (all V_b_2 all V_a_2 all T_b (class_Rings_Oidom(T_b) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2) <-> V_a_2 = V_b_2 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))) # label(fact_square__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1519 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) # label(fact_minus__mult__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1520 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_minus__mult__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1521 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))) # label(fact_minus__mult__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1522 (all V_b all V_a all T_a (class_Rings_Oring(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_minus__mult__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1523 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))) # label(fact_minus__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1524 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) # label(fact_mod__Suc__eq__Suc__mod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1525 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m)) # label(fact_mod__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1526 (all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b))) # label(fact_mod__minus__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1527 (all V_a_H all V_b all V_a all T_a (class_Divides_Oring__div(T_a) -> (c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) -> c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b)))) # label(fact_mod__minus__cong) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1528 (all V_n all V_m hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m))) # label(fact_mod__less__eq__dividend) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1529 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1530 (all V_k2_2 all V_k1_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)))) # label(fact_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1531 (all V_k2_2 all V_k1_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)))) # label(fact_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1532 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1533 (all V_l_2 (c_Int_OPls = c_Int_OBit0(V_l_2) <-> c_Int_OPls = V_l_2)) # label(fact_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1534 (all V_k_2 (c_Int_OBit0(V_k_2) = c_Int_OPls <-> V_k_2 = c_Int_OPls)) # label(fact_rel__simps_I44_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1535 (all V_l all V_k c_Int_OBit0(V_k) != c_Int_OBit1(V_l)) # label(fact_rel__simps_I49_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1536 (all V_l all V_k c_Int_OBit1(V_k) != c_Int_OBit0(V_l)) # label(fact_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1537 (all V_n all V_m all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) # label(fact_mod__mult__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1538 (all V_k all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))) # label(fact_mod__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1539 (all V_k c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k)) # label(fact_Bit0__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1540 (all V_l all V_k hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l))) # label(fact_add__Bit0__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1541 (all V_b all V_a all T_a (class_Rings_Odivision__ring(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))) # label(fact_minus__divide__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1542 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_minus__divide__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1543 (all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))) # label(fact_minus__divide__divide) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1544 (all V_l all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))) # label(fact_mult__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1545 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) # label(fact_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1546 (all V_l_2 (c_Int_OMin = c_Int_OBit1(V_l_2) <-> c_Int_OMin = V_l_2)) # label(fact_rel__simps_I43_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1547 (all V_k_2 (c_Int_OBit1(V_k_2) = c_Int_OMin <-> V_k_2 = c_Int_OMin)) # label(fact_rel__simps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1548 (all V_w all V_z hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) # label(fact_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1549 (all V_w hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) # label(fact_minus__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1550 (all V_l all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l))) # label(fact_diff__bin__simps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1551 (all V_w all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w))) # label(fact_zmult__zminus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1552 (all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b))) # label(fact_zmod__zminus2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1553 (all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) # label(fact_zmod__zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1554 (all V_m all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m)) # label(fact_zminus__zmod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1555 (all V_x all T_a (class_Fields_Ofield__inverse__zero(T_a) & class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)))) # label(fact_minus1__divide) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1556 (all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_mod2__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1557 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1558 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1559 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1560 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1561 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1562 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1563 (all V_a_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1564 (all V_a_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1565 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_right__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1566 (all V_b_2 all V_a_2 all T_b (class_Groups_Ogroup__add(T_b) -> (V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1567 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_left__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1568 (all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_ab__left__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1569 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b))) # label(fact_minus__unique) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1570 (all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) # label(fact_diff__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1571 (all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1572 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_diff__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1573 (all V_b all V_a all T_a (class_Groups_Oab__group__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))) # label(fact_ab__diff__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1574 (all V_b all V_a all T_a (class_Groups_Ogroup__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) # label(fact_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1575 (all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x))) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1576 (all V_x_2 all T_b (class_Rings_Oring__1__no__zero__divisors(T_b) -> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b) <-> V_x_2 = c_Groups_Oone__class_Oone(T_b) | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))))) # label(fact_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1577 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_compl__inf__bot) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1578 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_inf__compl__bot) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1579 (all V_y all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)))) # label(fact_diff__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1580 (all V_n all V_m ((hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))))) # label(fact_mod__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1581 (all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_mod__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1582 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)))) # label(fact_mod__less__divisor) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1583 (all V_y all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)))) # label(fact_compl__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1584 (all V_y all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)))) # label(fact_compl__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1585 (all V_a all V_b all T_a (class_Rings_Odivision__ring(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))))) # label(fact_nonzero__minus__divide__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1586 (all V_a all V_b all T_a (class_Rings_Odivision__ring(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)))) # label(fact_nonzero__minus__divide__divide) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1587 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))))) # label(fact_abs__le__D2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1588 (all V_b all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)))))) # label(fact_abs__leI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1589 (all V_b_2 all V_a_2 all T_b (class_Groups_Oordered__ab__group__add__abs(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))))) # label(fact_abs__le__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1590 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))))) # label(fact_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1591 (all V_b_2 all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))))) # label(fact_abs__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1592 (all V_d_2 all V_m_2 (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> (exists B_q V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q)))) # label(fact_mod__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.07 1593 (all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1594 (all V_n all V_m ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)))) # label(fact_mod__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1595 (all V_n all V_m (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))) # label(fact_mod__geq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1596 (all V_m all V_n all V_k c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) # label(fact_mod__mult__self3) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1597 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)))) # label(fact_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1598 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)))) # label(fact_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1599 (all V_k2_2 all V_k1_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)))) # label(fact_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1600 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1601 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))) # label(fact_le__mod__geq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1602 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)))) # label(fact_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1603 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)))) # label(fact_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1604 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1605 (all V_k2_2 all V_k1_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)))) # label(fact_less__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1606 (all V_l all V_k hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l))) # label(fact_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1607 (all V_l all V_k hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l))) # label(fact_add__Bit0__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1608 (all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1609 (all V_m_2 all V_n_2 (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_negative__eq__positive) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1610 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)))) # label(fact_rel__simps_I30_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1611 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)))) # label(fact_rel__simps_I26_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1612 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)))) # label(fact_rel__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1613 (all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)))) # label(fact_rel__simps_I13_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1614 (all V_l hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l))) # label(fact_diff__bin__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1615 (all V_l all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l))) # label(fact_diff__bin__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1616 (all V_l all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l))) # label(fact_diff__bin__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1617 (all V_b all V_a hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b))) # label(fact_zmod__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1618 (all V_y all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y))) # label(fact_Divides_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1619 (all V_m all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))))) # label(fact_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1620 (all V_l all V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zmod__zminus2__not__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1621 (all V_l all V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_zmod__zminus1__not__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1622 (all V_w all V_z hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) # label(fact_diff__int__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1623 (all V_w all V_z hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w)) # label(fact_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1624 (all V_a_2 all T_b (class_Rings_Oring__1(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b)))))) # label(fact_Ints__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1625 (all V_w_2 (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) <-> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))))) # label(fact_neg__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1626 (all V_k c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k))) # label(fact_pred__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1627 (all V_k c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k)) # label(fact_pred__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1628 (all V_k hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) # label(fact_minus__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1629 (all V_k hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k)) # label(fact_add__Min__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1630 (all V_k hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k)) # label(fact_add__Min) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1631 (all V_k c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k))) # label(fact_succ__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1632 (all V_k c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k)) # label(fact_succ__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1633 (all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k)) # label(fact_diff__bin__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1634 (all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) <-> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_mod2__gr__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1635 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)))) # label(fact_number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1636 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))) # label(fact_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1637 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1638 (all V_a all T_a (class_Groups_Oabs__if(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a))) # label(fact_abs__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1639 (all V_a all T_a (class_Groups_Oordered__ab__group__add__abs(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))) # label(fact_abs__of__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1640 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)))) # label(fact_mod__le__divisor) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1641 (all V_m all V_n all V_k c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)) # label(fact_mod__mult__self4) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1642 (all V_k2_2 all V_k1_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)))) # label(fact_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1643 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1644 (all V_k2_2 all V_k1_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)))) # label(fact_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1645 (all V_l_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)))) # label(fact_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1646 (all V_w all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))))) # label(fact_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1647 (all V_l all V_k hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l)) # label(fact_mult__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1648 (all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_abs__minus__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1649 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_int__zle__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1650 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_negative__zle__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1651 (all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1652 (all V_l hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l))) # label(fact_diff__bin__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1653 (all V_n all V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) -> V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) # label(fact_pos__zmult__eq__1__iff__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1654 (all V_n_2 all V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) <-> V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) | V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) # label(fact_zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1655 (all V_w all V_v hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))) # label(fact_minus__numeral__code_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1656 (all V_b all V_a ((c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))) # label(fact_zmod__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1657 (all V_b all V_a ((c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)))) # label(fact_zmod__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1658 (all V_i ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i))) # label(fact_zabs__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1659 (all V_n hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))))) # label(fact_neg__zminus__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1660 (all V_l all V_k hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l))) # label(fact_diff__bin__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1661 (all V_l all V_k hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l)))) # label(fact_add__Bit1__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1662 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)))) # label(fact_double__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1663 (all V_x all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)))) # label(fact_abs__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1664 (all V_k_2 all V_n_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(V_Pa_2,V_n_2))) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) -> (V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) -> hBOOL(hAPP(V_Pa_2,B_j)))))))) # label(fact_split__mod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1665 (all V_q all V_b all V_r all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)))))) # label(fact_mod__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1666 (all V_w all V_c all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c))) # label(fact_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1667 (all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n)))))) # label(fact_number__of1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1668 (all V_m all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_Suc__times__mod__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1669 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)))) # label(fact_number__of__pred) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1670 (all V_n -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))))) # label(fact_not__zle__0__negative) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1671 (all V_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_negative__zless__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1672 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z))) # label(fact_mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1673 (all V_z all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z))) # label(fact_mult__2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1674 (all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_one__add__one__is__two) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1675 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n))) # label(fact_mod__Suc__eq__mod__add3) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1676 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n)) # label(fact_Suc__mod__eq__add3__mod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1677 (all V_v all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) # label(fact_Suc__mod__eq__add3__mod__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1678 (all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) # label(fact_add__2__eq__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1679 (all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) # label(fact_add__2__eq__Suc_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1680 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z)) # label(fact_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1681 (all V_z hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z)) # label(fact_nat__mult__2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1682 (all V_w all V_v c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) # label(fact_zmod__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1683 (all V_r all T_a (class_Fields_Olinordered__field__inverse__zero(T_a) & class_Int_Onumber__ring(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))) # label(fact_half__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1684 (all V_r_2 all T_b (class_Fields_Olinordered__field__inverse__zero(T_b) & class_Int_Onumber__ring(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2))))) # label(fact_half__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1685 (all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) -> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_less__2__cases) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1686 (all V_w all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))))) # label(fact_diff__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1687 (all V_x_2 all T_b (class_Int_Onumber__ring(T_b) -> (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b) <-> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))))) # label(fact_eq__special_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1688 (all V_y_2 all T_b (class_Int_Onumber__ring(T_b) -> (c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) <-> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))))) # label(fact_eq__special_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1689 (all V_k all V_l ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) -> c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) -> c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))))) # label(fact_z3mod__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1690 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a))) # label(fact_neg__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1691 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a))) # label(fact_pos__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1692 (all V_x all T_a (class_Rings_Osemiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x)))))) # label(fact_of__nat__double) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1693 (all V_A_2 all V_ca_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))))) # label(fact_ComplI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1694 (all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)))) # label(fact_ComplE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1695 (all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)))) # label(fact_ComplD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1696 (all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) <-> -hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)))) # label(fact_Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1697 (all V_b hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zdiv__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1698 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))))) # label(fact_Compl__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1699 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))) # label(fact_Compl__subset__Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1700 (all V_n hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n) # label(fact_nat__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1701 (all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) # label(fact_zdiv__zminus__zminus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1702 (all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b)) # label(fact_zdiv__zminus2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1703 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_div__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1704 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_div__by__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1705 (all V_A_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) # label(fact_vimage__Compl) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1706 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a)) # label(fact_div__by__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1707 (all T_a (class_Rings_Osemiring__1(T_a) -> c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_iszero__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1708 (all V_z_2 all T_b (class_Rings_Osemiring__1(T_b) -> (c_Int_Oiszero(T_b,V_z_2) <-> V_z_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_iszero__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1709 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)))))) # label(fact_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1710 (all T_a (class_Rings_Osemiring__1(T_a) -> -c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)))) # label(fact_not__iszero__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1711 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1712 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))))) # label(fact_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1713 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_div__neg__pos__less0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1714 (all V_z_H_2 all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) -> (hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) <-> V_z_2 = V_z_H_2)))) # label(fact_eq__nat__nat__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1715 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) -> (hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_transfer__nat__int__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1716 (all V_Pa_2 ((all B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) <-> (all B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) -> hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))))))) # label(fact_all__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1717 (all V_Pa_2 ((exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))))))) # label(fact_ex__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1718 (all V_a (V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint))) # label(fact_zdiv__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1719 (all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_subset__Compl__self__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1720 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Compl__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1721 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Compl__disjoint2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1722 (all V_w all V_v hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) # label(fact_zdiv__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1723 (all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_zmod__zdiv__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1724 (all V_a (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a)) # label(fact_DIVISION__BY__ZERO) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1725 (all V_v hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) # label(fact_nat__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1726 (all V_w hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) # label(fact_nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1727 (all V_B_2 all V_A_2 all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) # label(fact_Compl__Un) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1728 (all V_B_2 all V_A_2 all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) # label(fact_Compl__Int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1729 (all V_c all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c))) # label(fact_zdiv__zadd1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1730 (all V_B_2 all V_A_2 all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) # label(fact_Compl__Diff__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1731 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Diff__Compl) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1732 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) # label(fact_Diff__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1733 (all V_z (hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) -> hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_neg__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1734 (all V_z (-hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z)) # label(fact_not__neg__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1735 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c = c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a)) & (V_c != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)))) # label(fact_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1736 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a))) # label(fact_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1737 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a))) # label(fact_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1738 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)))) # label(fact_div__mult__mult2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1739 (all V_b all V_a all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (V_c != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)))) # label(fact_div__mult__mult1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1740 (all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_div__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1741 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_mod__div__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1742 (all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__le__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1743 (all V_i_2 (hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_nat__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1744 (all V_b all V_a_H all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)))))) # label(fact_zdiv__mono1__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1745 (all V_b all V_a_H all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)))))) # label(fact_zdiv__mono1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1746 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_div__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1747 (all V_b all V_b_H all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))))))) # label(fact_zdiv__mono2__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1748 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_div__nonpos__pos__le0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1749 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1750 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_div__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1751 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_div__nonneg__neg__le0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1752 (all V_b all V_b_H all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))))))) # label(fact_zdiv__mono2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1753 (all V_b_2 all V_a_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))))) # label(fact_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1754 (all V_i_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2))))) # label(fact_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1755 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))))) # label(fact_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1756 (all V_k_2 all V_i_2 (hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)))) # label(fact_zdiv__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1757 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)))) # label(fact_zless__nat__conj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1758 (all V_w_2 all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))))) # label(fact_nat__mono__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1759 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)))))) # label(fact_transfer__nat__int__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1760 (all V_k all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x))))) # label(fact_int__div__less__self) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1761 (all V_b all V_a all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c))) # label(fact_zdiv__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1762 (all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z)) # label(fact_nat__0__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1763 (all V_z_2 all V_m_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 <-> V_m_2 = hAPP(c_Int_Onat,V_z_2) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)))) # label(fact_int__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1764 (all V_z ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_int__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1765 (all V_z_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)))) # label(fact_zless__nat__eq__int__zless) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1766 (all V_B_2 all V_A_2 all T_b (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) # label(fact_disjoint__eq__subset__Compl) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1767 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))))) # label(fact_nat__mod__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1768 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))))) # label(fact_Divides_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1769 (all V_n hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_nat__zminus__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1770 (all V_k all V_b all V_a hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)) # label(fact_zdiv__zmod__equality2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1771 (all V_k all V_a all V_b hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)) # label(fact_zdiv__zmod__equality) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1772 (all V_c all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c))) # label(fact_zdiv__zmult1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1773 (all V_b all V_a V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) # label(fact_zmod__zdiv__equality) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1774 (all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)) # label(fact_zdiv__minus1__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1775 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n))) # label(fact_zmod__zdiv__equality_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1776 (all V_m all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) # label(fact_zmult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1777 (all V_z all V_w hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z)))) # label(fact_nat__abs__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1778 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))))) # label(fact_div__mult__self1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1779 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))))) # label(fact_div__mult__self2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1780 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_div__add__self2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1781 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a))))) # label(fact_div__add__self1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1782 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) # label(fact_div__mod__equality) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1783 (all V_c all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) # label(fact_div__mod__equality2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1784 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a)) # label(fact_mod__div__equality) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1785 (all V_a all V_b all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a)) # label(fact_mod__div__equality2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1786 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a)) # label(fact_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1787 (all T_a (class_Int_Onumber__ring(T_a) -> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)))) # label(fact_iszero__Numeral0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1788 (all V_w all T_a (class_Int_Onumber__ring(T_a) & class_Int_Oring__char__0(T_a) -> -c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))))) # label(fact_iszero__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1789 (all V_w_2 all T_b (class_Int_Onumber__ring(T_b) & class_Int_Oring__char__0(T_b) -> (c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) <-> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))) # label(fact_iszero__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1790 (all T_a (class_Int_Onumber__ring(T_a) -> -c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)))) # label(fact_nonzero__number__of__Min) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1791 (all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)))) # label(fact_zero__less__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1792 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))))) # label(fact_nat__less__eq__zless) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1793 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)))))) # label(fact_transfer__nat__int__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1794 (all V_w_2 all V_m_2 (V_m_2 = hAPP(c_Int_Onat,V_w_2) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__eq__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1795 (all V_m_2 all V_w_2 (hAPP(c_Int_Onat,V_w_2) = V_m_2 <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1796 (all V_z_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))))) # label(fact_nat__le__eq__zle) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1797 (all V_i_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) <-> (all B_n (V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) -> hBOOL(hAPP(V_Pa_2,B_n)))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) # label(fact_split__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1798 (all V_z_H all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))))) # label(fact_nat__add__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1799 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1800 (all V_v_2 all V_m_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) <-> V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))))) # label(fact_int__eq__iff__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1801 (all V_z_H all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)))) # label(fact_nat__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1802 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1803 (all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) # label(fact_div__eq__minus1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1804 (all V_z all V_z_H (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))))) # label(fact_nat__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1805 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y))))) # label(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1806 (all V_z_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)))) # label(fact_one__less__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1807 (all V_k_2 all V_n_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (all B_i ((exists B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j))) -> hBOOL(hAPP(V_Pa_2,B_i))))) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (all B_i ((exists B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j))) -> hBOOL(hAPP(V_Pa_2,B_i))))))) # label(fact_split__zdiv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1808 (all V_r_1 all V_y all V_b_1 all V_a_1 (V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> (V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y)))) # label(fact_divmod__int__rel__div__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1809 (all V_m_2 all V_w_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))))) # label(fact_nat__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1810 (all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)))) # label(fact_Suc__nat__eq__nat__zadd1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1811 (all V_b all V_a all V_c (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) # label(fact_zmod__zmult2__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1812 (all V_z_H all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))))) # label(fact_nat__mult__distrib__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1813 (all V_a all V_b (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) & (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint))))) # label(fact_zdiv__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1814 (all V_a all V_b (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) & (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint))))) # label(fact_zdiv__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1815 (all V_v_H all V_v ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> (hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))))))) # label(fact_mod__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1816 (all T_a (class_Int_Onumber__ring(T_a) -> -c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))))) # label(fact_not__iszero__Numeral1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1817 (all V_y_2 all V_x_2 all T_b (class_Int_Onumber__ring(T_b) -> (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) <-> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))))) # label(fact_eq__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1818 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))) # label(fact_div__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.08 1819 (all V_n_2 all V_Pa_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) -> (hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) -> hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))))))) # label(fact_split__pos__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1820 (all V_n_2 all V_Pa_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) <-> (all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) -> hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))))))) # label(fact_split__neg__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1821 (all V_v all V_w ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) # label(fact_zdiv__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1822 (all V_v_H ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))))) # label(fact_one__mod__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1823 (all V_x_2 all T_b (class_Int_Onumber__ring(T_b) -> (hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b) <-> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))))) # label(fact_eq__special_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1824 (all V_y_2 all T_b (class_Int_Onumber__ring(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) <-> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))))) # label(fact_eq__special_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1825 (all V_k all V_l ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) -> c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) -> c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)))))) # label(fact_z3div__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1826 (all V_n all V_i c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n)) # label(fact_nat__aux__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1827 (all V_n all V_i ((V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n) & (V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n))))) # label(fact_nat__of__aux__code) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1828 (all V_n all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin))) # label(fact_power__m1__odd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1829 (all V_A_2 all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2) # label(fact_double__complement) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1830 (all V_B_2 all V_A_2 all T_b (hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) <-> V_A_2 = V_B_2)) # label(fact_Compl__eq__Compl__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1831 (all V_q all V_y all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1832 (all V_k all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))))) # label(fact_div__le__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1833 (all V_n all V_m hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m))) # label(fact_div__le__dividend) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1834 (all V_n all V_m hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n)) # label(fact_int__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1835 (all V_n all V_m hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))) # label(fact_zpower__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1836 (all V_n all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n))) # label(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1837 (all V_c all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c)) # label(fact_div__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1838 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1839 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))) # label(fact_zpower__zpower) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1840 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1841 (all V_y all V_m all V_x c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m)) # label(fact_zpower__zmod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1842 (all V_n all V_z (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n))) # label(fact_nat__power__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1843 (all V_n all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))) # label(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1844 (all V_m hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m) # label(fact_div__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1845 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_div__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1846 (all V_n all V_m all V_k ((V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)))) # label(fact_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1847 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1848 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1849 (all V_q all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1850 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1851 (all V_q all V_p all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1852 (all V_n all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))))) # label(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1853 (all V_c all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c))) # label(fact_div__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1854 (all V_b all V_a hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b))) # label(fact_zdiv__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1855 (all V_y all V_x hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y))) # label(fact_Divides_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1856 (all V_z all V_y all V_x hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))) # label(fact_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1857 (all V_n_2 all V_a_2 all T_b (class_Rings_Oring__1(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b)))))) # label(fact_Ints__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1858 (all V_w all V_v ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)))))) # label(fact_power__nat__number__of__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1859 (all V_n all V_v ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n))))) # label(fact_power__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1860 (all V_k all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m)))))) # label(fact_div__le__mono2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1861 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n))) # label(fact_nat__mult__div__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1862 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m)) # label(fact_div__mult__self1__is__m) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1863 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m)) # label(fact_div__mult__self__is__m) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1864 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m))))) # label(fact_div__less__dividend) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1865 (all V_c all V_b all V_a c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b))) # label(fact_mod__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1866 (all V_c all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c))) # label(fact_div__mult1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1867 (all V_n all V_m hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))) # label(fact_div__mod__equality_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1868 (all V_m all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))) # label(fact_mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1869 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n))) # label(fact_Divides_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1870 (all V_n all V_x hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n)))) # label(fact_zero__le__zpower__abs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1871 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))))) # label(fact_div__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1872 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))))) # label(fact_div__geq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1873 (all V_k_2 all V_n_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) <-> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) -> (V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) -> hBOOL(hAPP(V_Pa_2,B_i)))))))) # label(fact_split__div) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1874 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))))) # label(fact_Divides_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1875 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) -> hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)))) # label(fact_nat__div__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1876 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a))) # label(fact_power3__eq__cube) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1877 (all V_n all T_a (class_Int_Onumber__ring(T_a) & class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_abs__power__minus__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1878 (all V_p all V_m ((V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat)) & (V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) # label(fact_power__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1879 (all V_n_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1880 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))))) # label(fact_le__div__geq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1881 (all V_m_2 all V_q_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) <-> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_split__div__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1882 (all V_n_2 all V_m_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (exists B_q (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q)))) & hBOOL(hAPP(V_Pa_2,B_q)))))) # label(fact_split__div_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1883 (all V_n all V_m hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n))) # label(fact_div__Suc__eq__div__add3) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1884 (all V_n all V_m hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n)) # label(fact_Suc__div__eq__add3__div) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1885 (all V_v all V_m hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) # label(fact_Suc__div__eq__add3__div__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1886 (all V_m hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_div2__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1887 (all V_m hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m) # label(fact_add__self__div__2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1888 (all T_a (class_Rings_Osemiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_zero__power2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1889 (all V_a_2 all T_b (class_Rings_Oring__1__no__zero__divisors(T_b) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_zero__eq__power2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1890 (all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1891 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) # label(fact_power2__eq__square) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1892 (all T_a (class_Rings_Osemiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a))) # label(fact_one__power2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1893 (all V_a all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_power2__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1894 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_power__even__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1895 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_abs__power2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1896 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_power2__abs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1897 (all V_y all V_x all T_a (class_Rings_Olinordered__semidom(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> V_x = V_y))))) # label(fact_power2__eq__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1898 (all V_y all V_x all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)))))) # label(fact_power2__le__imp__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1899 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_zero__le__power2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1900 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_power2__less__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1901 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) <-> V_a_2 != c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_zero__less__power2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1902 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) & V_y_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1903 (all V_w all T_b (class_Groups_Omonoid__mult(T_b) & class_Int_Onumber(T_b) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)))) # label(fact_power2__eq__square__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1904 (all V_a_2 all T_b (class_Rings_Oring__1__no__zero__divisors(T_b) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b) <-> V_a_2 = c_Groups_Oone__class_Oone(T_b) | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))))) # label(fact_power2__eq__1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1905 (all V_v_H all V_v ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))))) # label(fact_div__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1906 (all V_n all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1907 (all V_n all V_a all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) # label(fact_power__minus__even) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1908 (all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_div__2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1909 (all V_y all V_x all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)))))) # label(fact_power2__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1910 (all V_v_H hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))) # label(fact_one__div__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1911 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b))) <-> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) & V_y_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__power2__le__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1912 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))) # label(fact_sum__power2__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1913 (all V_y_2 all V_x_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) <-> V_x_2 != c_Groups_Ozero__class_Ozero(T_b) | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1914 (all V_y all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_not__sum__power2__lt__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1915 (all V_y all V_x all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)))) # label(fact_power2__sum) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1916 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))) # label(fact_zero__le__even__power_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1917 (all V_n all V_x all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1918 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_power__odd__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1919 (all V_n all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__minus1__even) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1920 (all V_k all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) # label(fact_int__power__div__base) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1921 (all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_Suc__n__div__2__gt__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1922 (all V_y all V_x all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)))) # label(fact_power2__diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1923 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))))) # label(fact_odd__0__le__power__imp__0__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1924 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a)))))) # label(fact_odd__power__less__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1925 (all V_n all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)))) # label(fact_power__minus1__odd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1926 (all V_n all T_a (class_Int_Onumber__ring(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__m1__even) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1927 (all V_k ((V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & (V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> (c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) & (c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) # label(fact_int__of__code) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1928 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))))) # label(fact_power__strict__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1929 (all V_m all V_n all V_a all T_a (class_Fields_Ofield(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_power__diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1930 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_one__less__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1931 (all V_y_2 all V_x_2 all V_b_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)))))) # label(fact_power__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1932 (all V_n all V_a all T_a (class_Rings_Oring__1__no__zero__divisors(T_a) -> (V_a != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_field__power__not__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1933 (all V_n hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_power__Suc__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1934 (all V_m_2 all V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1935 (all V_n_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1936 (all V_n all V_m all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))))) # label(fact_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1937 (all V_n all V_b all V_a all T_a (class_Groups_Ocomm__monoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))) # label(fact_power__mult__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1938 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__commutes) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1939 (all V_n all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1940 (all V_n all V_m all T_a (class_Rings_Osemiring__1(T_a) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n))) # label(fact_of__nat__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1941 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n))) # label(fact_power__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1942 (all V_n all V_b all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))) # label(fact_power__divide) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1943 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) # label(fact_power__abs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1944 (all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a)) # label(fact_power__one__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1945 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_zero__le__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1946 (all V_n all V_b all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))))) # label(fact_power__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1947 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_zero__less__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1948 (all V_n_2 all V_a_2 all T_b (class_Power_Opower(T_b) & class_Rings_Omult__zero(T_b) & class_Rings_Ono__zero__divisors(T_b) & class_Rings_Ozero__neq__one(T_b) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_power__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1949 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))) # label(fact_one__le__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1950 (all V_n all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_power__0__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1951 (all V_n_2 all V_m_2 all V_a_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) <-> V_m_2 = V_n_2)))) # label(fact_power__inject__exp) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1952 (all V_n all V_a all T_a (class_Power_Opower(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1953 (all V_n all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a))) # label(fact_power__Suc2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1954 (all V_n all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))))) # label(fact_nat__one__le__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1955 (all V_a all T_a (class_Power_Opower(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_power__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1956 (all V_n all V_m all V_a all T_a (class_Groups_Omonoid__mult(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1957 (all V_n all V_a all V_b all T_a (class_Fields_Ofield(T_a) -> (V_b != c_Groups_Ozero__class_Ozero(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))) # label(fact_nonzero__power__divide) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1958 (all V_n all V_a all T_a (class_Fields_Ofield__inverse__zero(T_a) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n))) # label(fact_power__one__over) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1959 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_abs__power__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1960 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)))))) # label(fact_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1961 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> V_a = V_b))))) # label(fact_power__inject__base) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1962 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)))))) # label(fact_power__le__imp__le__base) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1963 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1964 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1965 (all V_n all T_a (class_Power_Opower(T_a) & class_Rings_Osemiring__0(T_a) -> (V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_power__0__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1966 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))))))) # label(fact_power__gt1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1967 (all V_y_2 all V_x_2 all V_b_2 all T_b (class_Rings_Olinordered__semidom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)))))) # label(fact_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1968 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)))))) # label(fact_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1969 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))))) # label(fact_power__strict__increasing) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1970 (all V_n all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))))) # label(fact_zero__le__power__abs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1971 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))))) # label(fact_power__increasing) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1972 (all V_n all V_a all T_a (class_Rings_Oring__1(T_a) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) # label(fact_power__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1973 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))) # label(fact_power__Suc__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1974 (all V_b all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> V_a = V_b)))))) # label(fact_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1975 (all V_n all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))))))) # label(fact_power__Suc__less__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1976 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))))) # label(fact_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1977 (all V_a all V_N all V_n all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))))) # label(fact_power__decreasing) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1978 (all V_n all V_m all V_a all T_a (class_Rings_Olinordered__semidom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)))))) # label(fact_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1979 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))) # label(fact_card__Pow) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1980 (all T_b (class_Power_Opower(T_b) -> c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)))) # label(fact_power__power__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1981 (all V_k all T_a (class_Rings_Oring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k))))) # label(fact_of__int__of__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1982 (all V_y all V_x c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y))))) # label(fact_Nitpick_Oint__lcm__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1983 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))))) # label(fact_PowI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1984 (all V_z_2 all V_w_2 all T_b (class_Int_Oring__char__0(T_b) -> (hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) <-> V_w_2 = V_z_2))) # label(fact_of__int__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1985 (all V_k all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k))) # label(fact_number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1986 (all V_w hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w)) # label(fact_int__number__of__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1987 (all V_n hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) # label(fact_of__int__int__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1988 (all V_A_2 all T_b hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2)))) # label(fact_Pow__top) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1989 (all V_A_2 all T_b c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2) # label(fact_Union__Pow__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1990 (all V_A_2 all T_b hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) # label(fact_Pow__not__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1991 (all T_a (class_Rings_Oring__1(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_of__int__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1992 (all V_z_2 all T_b (class_Int_Oring__char__0(T_b) -> (c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) <-> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_of__int__0__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1993 (all V_z_2 all T_b (class_Int_Oring__char__0(T_b) -> (hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_of__int__eq__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1994 (all V_z_2 all V_w_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))))) # label(fact_of__int__le__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1995 (all V_z_2 all V_w_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))))) # label(fact_of__int__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1996 (all V_z all V_w all T_a (class_Rings_Oring__1(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)))) # label(fact_of__int__add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1997 (all V_v all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v))) # label(fact_of__int__number__of__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1998 (all V_z all V_w all T_a (class_Rings_Oring__1(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)))) # label(fact_of__int__mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 1999 (all T_a (class_Rings_Oring__1(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a))) # label(fact_of__int__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2000 (all V_z all V_w all T_a (class_Rings_Oring__1(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)))) # label(fact_of__int__diff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2001 (all V_n all T_a (class_Rings_Oring__1(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) # label(fact_of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2002 (all V_z all T_a (class_Rings_Oring__1(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)))) # label(fact_of__int__minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2003 (all V_B_2 all T_b hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2)))) # label(fact_Pow__bottom) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2004 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_Pow__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2005 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_PowD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2006 (all V_z_2 all T_b (class_Rings_Oring__1(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))))) # label(fact_Ints__of__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2007 (all V_n all V_z all T_a (class_Rings_Oring__1(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n))) # label(fact_of__int__power) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2008 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))))) # label(fact_Pow__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2009 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_finite__Pow__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2010 (all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))))) # label(fact_subset__Pow__Union) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2011 (all V_a_2 all V_times_2 all V_one_2 all T_b hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2) # label(fact_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2012 (all V_n_2 all V_a_2 all V_times_2 all V_one_2 all T_b hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2))) # label(fact_power_Opower_Opower__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2013 (all V_B_2 all V_A_2 all T_b hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) # label(fact_Pow__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2014 (all T_a (class_Int_Onumber__ring(T_a) -> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin))) # label(fact_of__int__m1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2015 (all T_b hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) # label(fact_Pow__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2016 (all V_z_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_of__int__le__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2017 (all V_z_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))))) # label(fact_of__int__0__le__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2018 (all V_z_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))))) # label(fact_of__int__0__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2019 (all V_z_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_of__int__less__0__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2020 (all V_z all T_a (class_Rings_Oring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)))) # label(fact_of__nat__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2021 (all V_B_2 all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Un__Pow__subset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2022 (all V_y all V_x c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y))) # label(fact_Nitpick_Onat__lcm__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2023 (all V_code__numeral c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_code__numeral_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2024 (all V_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (exists B_n V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n)))))) # label(fact_negD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2025 (all V_x all T_a (class_Groups_Osgn__if(T_a) -> (V_x = c_Groups_Ozero__class_Ozero(T_a) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a)) & (V_x != c_Groups_Ozero__class_Ozero(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) -> c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)))))) # label(fact_sgn__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2026 (all V_code__numeral_H_2 all V_code__numeral_2 (c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) <-> V_code__numeral_2 = V_code__numeral_H_2)) # label(fact_code__numeral_Oinject) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2027 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a))) # label(fact_sgn__sgn) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2028 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) <-> V_a_2 = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_sgn__0__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2029 (all T_a (class_Groups_Osgn__if(T_a) -> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_sgn0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2030 (all V_b all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)))) # label(fact_sgn__times) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2031 (all V_code__numeral_H c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H)) # label(fact_code__numeral_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2032 (all V_code__numeral_H_1 c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) # label(fact_code__numeral_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.09 2033 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_sgn__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2034 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_sgn__greater) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2035 (all V_code__numeral hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_code__numeral_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2036 (all V_x all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x)) # label(fact_mult__sgn__abs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2037 (all V_k all T_a (class_Rings_Olinordered__idom(T_a) -> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)))) # label(fact_abs__sgn) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2038 (all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n) # label(fact_Suc__code__numeral__minus__one) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2039 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))))) # label(fact_sgn__1__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2040 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) -> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)))) # label(fact_sgn__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2041 (all V_x all V_y ((V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Nitpick_Onat__gcd(V_x,V_y) = V_x) & (V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y))))) # label(fact_nat__gcd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2042 (all V_i ((V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) & (V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) -> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) -> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) # label(fact_zsgn__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2043 (all V_a all T_a (class_Rings_Olinordered__idom(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) -> c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))))) # label(fact_sgn__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2044 (all V_a_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))))) # label(fact_sgn__1__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2045 (all V_y all V_x hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y))))) # label(fact_Nitpick_Oint__gcd__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2046 (all V_code__numeral_2 all V_f2_2 all V_f1_2 all T_b c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2)) # label(fact_code__numeral_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2047 (all V_y all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) -> (hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y)))) # label(fact_compl__unique) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2048 (all V_f2_2 all V_f1_2 all T_b c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2) # label(fact_code__numeral_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2049 (all V_x_2 all T_b hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2050 (all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))) # label(fact_finite__fun__UNIVD2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2051 (all T_b c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_UNIV__not__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2052 (all T_b (class_Finite__Set_Ofinite(T_b) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_finite__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2053 (all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_subset__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2054 (all T_c all T_b c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))) # label(fact_UNIV__Plus__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2055 (all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_finite__option__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2056 (all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))))) # label(fact_finite__Prod__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2057 (all T_b c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Union__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2058 (all V_x_2 all T_c all T_b (class_Orderings_Otop(T_b) -> hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b))) # label(fact_top__apply) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2059 (all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b))) # label(fact_Sup__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2060 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2) # label(fact_Int__UNIV__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2061 (all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2) # label(fact_Int__UNIV__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2062 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Un__UNIV__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2063 (all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Un__UNIV__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2064 (all T_b hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) # label(fact_Pow__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2065 (all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))) # label(fact_finite__Plus__UNIV__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2066 (all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_vimage__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2067 (all V_y all V_x (c_Nat__Transfer_Ois__nat(V_x) -> (c_Nat__Transfer_Ois__nat(V_y) -> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))))) # label(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2068 (all V_z c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))) # label(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2069 (all V_y all V_x (c_Nat__Transfer_Ois__nat(V_x) -> (c_Nat__Transfer_Ois__nat(V_y) -> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))))) # label(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2070 (all V_y all V_x (c_Nat__Transfer_Ois__nat(V_x) -> (c_Nat__Transfer_Ois__nat(V_y) -> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))))) # label(fact_Divides_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2071 (all V_y all V_x (c_Nat__Transfer_Ois__nat(V_x) -> (c_Nat__Transfer_Ois__nat(V_y) -> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))))) # label(fact_Divides_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2072 (all V_x all T_a (class_Orderings_Otop(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))))) # label(fact_top__greatest) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2073 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_sup__top__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2074 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_sup__top__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2075 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x)) # label(fact_inf__top__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2076 (all V_x all T_a (class_Lattices_Obounded__lattice__top(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x)) # label(fact_inf__top__right) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2077 (all V_y_2 all V_x_2 all T_b (class_Lattices_Obounded__lattice__top(T_b) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b) <-> V_x_2 = c_Orderings_Otop__class_Otop(T_b) & V_y_2 = c_Orderings_Otop__class_Otop(T_b)))) # label(fact_inf__eq__top__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2078 (all V_n all V_x (c_Nat__Transfer_Ois__nat(V_x) -> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))) # label(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2079 (all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Diff__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2080 (all V_y all V_x (c_Nat__Transfer_Ois__nat(V_x) -> (c_Nat__Transfer_Ois__nat(V_y) -> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y))))) # label(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2081 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) -> (hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_card__eq__UNIV__imp__eq__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2082 (all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Compl__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2083 (all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Compl__UNIV__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2084 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_finite__compl) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2085 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Compl__partition2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2086 (all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Compl__partition) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2087 (all V_A_2 all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) # label(fact_Compl__eq__Diff__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2088 (all V_x_2 (c_Nat__Transfer_Ois__nat(V_x_2) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)))) # label(fact_is__nat__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2089 (all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_compl__bot__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2090 (all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a))) # label(fact_compl__top__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2091 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_sup__compl__top) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2092 (all V_x all T_a (class_Lattices_Oboolean__algebra(T_a) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a))) # label(fact_compl__sup__top) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2093 (all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_finite__UNIV__card__ge__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2094 (all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) -> (hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_finite__fun__UNIVD1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2095 (all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2)))) # label(fact_Inf__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2096 (all V_y all V_n all V_x (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) -> (exists B_q V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)))))) # label(fact_nat__mod__eq__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2097 (all V_i_2 all V_Pa_2 all V_p_2 ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) -> (hBOOL(hAPP(V_Pa_2,B_i)) -> hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))))) -> (hBOOL(hAPP(V_Pa_2,V_i_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) -> hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) # label(fact_mod__induct__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2098 (all V_i all V_b ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) -> c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) & (-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) -> c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b)))))) # label(fact_log_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2099 (all V_M_2 all T_b ((exists B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))))) # label(fact_finite__Inter) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2100 (all V_x_2 all T_b hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2))) # label(fact_top1I) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2101 (all V_X_2 all V_C_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))))) # label(fact_InterD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2102 (all V_X_2 all V_C_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))))) # label(fact_InterE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2103 (all T_b c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Inter__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2104 (all T_b c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Inter__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2105 (all V_A_2 all V_b_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))))))) # label(fact_le__Inf__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2106 (all V_a_2 all V_S_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) & class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))))))) # label(fact_Inf__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2107 (all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b))) # label(fact_Inf__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2108 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)))) # label(fact_Inter__lower) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2109 (all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))))) # label(fact_Inter__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2110 (all V_B_2 all V_a_2 all T_b c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) # label(fact_Inter__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2111 (all V_A_2 all V_x_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2))))) # label(fact_Inf__lower) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2112 (all V_B_2 all V_A_2 all T_b c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) # label(fact_Inter__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2113 (all V_a_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2)) # label(fact_Inf__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2114 (all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b))) # label(fact_Inf__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2115 (all V_A_2 all V_a_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))) # label(fact_Inf__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2116 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))))) # label(fact_Int__eq__Inter) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2117 (all V_B_2 all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Inter__Un__subset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2118 (all V_b_2 all V_a_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) # label(fact_Inf__binary) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2119 (all V_B_2 all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2)))) # label(fact_inf__Inf__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2120 (all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))))) # label(fact_Inf__fin__Inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2121 (all V_r all V_l all V_k ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) -> c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) -> c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l)))) # label(fact_minus__shift__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2122 (all V_k all V_v ((V_v = V_k -> c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) & (V_v != V_k -> c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))) # label(fact_inc__shift__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2123 (all V_x_2 all T_b hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_iso__tuple__UNIV__I) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2124 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)))) # label(fact_mod__div__decomp) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2125 (all V_B_2 all V_A_2 all T_b ((all B_X (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)))) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2))))) # label(fact_Inter__subset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2126 (all V_A_2 all V_C_2 all T_b ((all B_X (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))))) # label(fact_InterI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2127 (all V_com_2 all V_fun_2 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_com_Osize_I14_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2128 (all V_com_2 all V_fun_2 c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_com_Osize_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2129 (all V_com_H_2 all V_fun_H_2 all V_com_2 all V_fun_2 (c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) <-> V_fun_2 = V_fun_H_2 & V_com_2 = V_com_H_2)) # label(fact_com_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2130 (all V_com_H_2 all V_fun_H_2 all V_com2_2 all V_com1_2 all V_fun_2 c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)) # label(fact_com_Osimps_I52_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2131 (all V_com2_2 all V_com1_2 all V_fun_2 all V_com_H_2 all V_fun_H_2 c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) # label(fact_com_Osimps_I53_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2132 (all V_com_H_2 all V_fun_H_2 all V_com2_2 all V_com1_2 c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)) # label(fact_com_Osimps_I46_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2133 (all V_com2_2 all V_com1_2 all V_com_H_2 all V_fun_H_2 c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) # label(fact_com_Osimps_I47_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2134 (all V_com_H_2 all V_fun_H_2 all V_com_2 all V_fun_2 all V_loc_2 c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)) # label(fact_com_Osimps_I38_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2135 (all V_com_2 all V_fun_2 all V_loc_2 all V_com_H_2 all V_fun_H_2 c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) # label(fact_com_Osimps_I39_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2136 (all V_com_H_2 all V_fun_H_2 c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)) # label(fact_com_Osimps_I16_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2137 (all V_com_H_2 all V_fun_H_2 c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP) # label(fact_com_Osimps_I17_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2138 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m)) # label(fact_minus__code__numeral__code) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2139 (all V_b_2 all V_a_2 all V_fb_2 all V_fa_2 all T_c all T_b c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_pair__box_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2140 (all V_w (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) -> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) -> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))))) # label(fact_negDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2141 (all V_b_H_2 all V_a_H_2 all V_b_2 all V_a_2 all T_c all T_b (c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) <-> V_a_2 = V_a_H_2 & V_b_2 = V_b_H_2)) # label(fact_pair__box_Oinject) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2142 (all V_l all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) -> c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l))))) # label(fact_negDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2143 (all V_b c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_negDivAlg__minus1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2144 (all V_b all V_a ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) & (-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))))) # label(fact_negDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2145 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) -> c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) -> c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))))) # label(fact_negDivAlg__eqn) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2146 (all V_w all V_v (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) -> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) -> c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))))) # label(fact_negDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2147 (all V_w (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))))) # label(fact_posDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2148 (all V_b all V_a ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) & (-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))))) # label(fact_posDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2149 (all V_y_2 all V_x_2 all V_R_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)))) # label(fact_in__rel__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2150 (all V_w all V_v (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) -> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))))) # label(fact_posDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2151 (all V_b c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_posDivAlg__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2152 (all V_l all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) -> c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l))))) # label(fact_posDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2153 (all V_a all V_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) -> c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) -> c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))))) # label(fact_posDivAlg__eqn) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2154 (all V_m all V_n c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m))) # label(fact_div__mod__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2155 (all V_r_2 all T_b (c_Nitpick_Orefl_H(T_b,V_r_2) <-> (all B_x hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))))) # label(fact_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2156 (all V_m all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) -> c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))))) # label(fact_divmod__nat__step) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2157 (all V_b all V_a all T_b all T_a hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_pair__box_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2158 (all V_m c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) # label(fact_divmod__nat__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2159 (all V_n all V_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) -> c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))) # label(fact_divmod__nat__base) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2160 (all V_n all V_m c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))) # label(fact_divmod__nat__div__mod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2161 (all V_a all V_r all V_q all V_c all V_b (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) -> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c))))))) # label(fact_divmod__nat__rel__mult1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2162 (all V_c all V_r all V_q all V_b all V_a (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) -> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))))))) # label(fact_divmod__nat__rel__mult2__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2163 (all V_b_2 all V_a_2 all V_f1_2 all T_b all T_d all T_c c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) # label(fact_pair__box_Orecs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2164 (all V_b_2 all V_a_2 all V_f1_2 all T_b all T_d all T_c c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) # label(fact_pair__box_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2165 (all V_qr_H all V_qr all V_n all V_m (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) -> (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) -> V_qr = V_qr_H))) # label(fact_divmod__nat__rel__unique) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2166 (all V_qr all V_n all V_m (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) -> c_Divides_Odivmod__nat(V_m,V_n) = V_qr)) # label(fact_divmod__nat__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2167 (all V_n all V_m hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n)))) # label(fact_divmod__nat__rel__divmod__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2168 (all V_r all V_q all V_n all V_m (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) -> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r)) # label(fact_mod__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2169 (all V_r all V_q all V_n all V_m (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q)) # label(fact_div__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2170 (all V_n all V_m hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))))) # label(fact_divmod__nat__rel) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2171 (all V_br all V_bq all V_b all V_ar all V_aq all V_c all V_a (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar))) -> (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) -> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))))))) # label(fact_divmod__nat__rel__add1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2172 (all V_b_2 all V_a_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) & (-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2)))))) # label(fact_negDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2173 (all V_k all V_l ((V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k))) & (V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))))) # label(fact_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2174 (all V_l all V_k c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)))) # label(fact_pdivmod__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2175 (all V_c all V_r all V_q all V_b all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) -> (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))))))) # label(fact_zmult2__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2176 (all V_r_H all V_q_H all V_r all V_q all V_b all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) -> (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) -> (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> V_r = V_r_H)))) # label(fact_unique__remainder) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2177 (all V_r_H all V_q_H all V_r all V_q all V_b all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) -> (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H))) -> (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> V_q = V_q_H)))) # label(fact_unique__quotient) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2178 (all V_r all V_q all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) -> (V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) # label(fact_self__remainder) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2179 (all V_b (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))) # label(fact_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2180 (all V_r all V_q all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) -> (V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> V_q = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_self__quotient) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2181 (all V_r all V_q all V_b all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) -> (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r))) # label(fact_divmod__int__rel__mod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2182 (all V_r all V_q all V_b all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) -> (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q))) # label(fact_divmod__int__rel__div) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2183 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b)))))) # label(fact_negDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2184 (all V_a all V_b (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))))) # label(fact_divmod__int__rel__div__mod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2185 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b)))))) # label(fact_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2186 (all V_br all V_bq all V_b all V_ar all V_aq all V_c all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar))) -> (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br))) -> (V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))))))) # label(fact_zadd1__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2187 (all V_r_2 all V_q_2 all V_b_2 all V_a_2 (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))))) # label(fact_zminus1__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2188 (all V_r all V_q all V_b all V_a (V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))))) # label(fact_divmod__int__relI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2189 (all V_a all V_r all V_q all V_c all V_b (hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) -> (V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c))))))) # label(fact_zmult1__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2190 (all V_b_2 all V_a_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) & (-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2)))))) # label(fact_posDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2191 (all V_Pa_2 all V_a1_2 all V_a0_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) -> ((all B_a all B_b (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) -> ((-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))) -> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))))) # label(fact_negDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2192 (all V_Pa_2 all V_a1_2 all V_a0_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) -> ((all B_a all B_b (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) -> ((-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) -> hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))) -> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))))) # label(fact_posDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2193 (all V_R2_2 all V_R1_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))))) # label(fact_accp__subset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2194 (all V_y_2 all V_x_2 all V_Q_2 all V_Pa_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,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].
% 6.04/6.10 2195 (all V_Q_2 all T_c all T_b all V_y_2 all V_x_2 all V_Pa_2 (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,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].
% 6.04/6.10 2196 (all V_a_2 all V_r_2 all T_b (hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) <-> (all B_x (hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)))))) # label(fact_accp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2197 (all V_a_2 all V_r_2 all T_b (hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) <-> (all B_x (hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)))))) # label(fact_accp_Oequations) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2198 (all V_a_2 all V_b_2 all V_r_2 all T_b (hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) -> (hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))))) # label(fact_accp__downward) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2199 (all V_y_2 all V_x_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2))) -> (V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2) & (V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2))))) # label(fact_nat__gcd_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2200 (all V_nat c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2201 (all V_f_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))))) # label(fact_in__measure) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2202 (all V_R_2 all T_b all V_y_2 all V_x_2 all V_f_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)))))) # label(fact_mlex__leq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2203 (all V_R_2 all T_b all V_y_2 all V_x_2 all V_f_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))))) # label(fact_mlex__less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2204 (all V_Pa_2 all V_a1_2 all V_a0_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) -> ((all B_x all B_y (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) -> ((B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y)))) -> hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))))) # label(fact_nat__gcd_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2205 (all V_nat hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2206 (all V_b all V_a ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> (V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & (V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))))) # label(fact_divmod__int__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2207 (all V_w (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) # label(fact_mod__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2208 (all V_b all V_a c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b))) # label(fact_mod__int__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2209 (all V_n hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n) # label(fact_nat__size) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2210 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))))) # label(fact_mod__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2211 (all V_r all V_q hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r))) # label(fact_negateSnd__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2212 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))))) # label(fact_mod__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2213 (all V_qr all V_b all V_a (hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr)) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))))) # label(fact_divmod__int__rel__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2214 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b))))) # label(fact_mod__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2215 (all V_a all V_b (V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))))) # label(fact_divmod__int__correct) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2216 (all V_w (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))))) # label(fact_mod__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2217 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b))))) # label(fact_mod__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2218 (all V_q all V_p c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q))) # label(fact_divmod__int__mod__div) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2219 (all V_w (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))))) # label(fact_div__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2220 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))))) # label(fact_div__neg__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2221 (all V_a all V_y all V_x all T_a all T_b (hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a -> V_y = V_a)) # label(fact_snd__eqD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2222 (all V_b all V_a all T_a all T_b hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b) # label(fact_snd__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2223 (all T_c all T_b all V_t_2 all V_s_2 (V_s_2 = V_t_2 <-> hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2))) # label(fact_Pair__fst__snd__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2224 (all V_q all V_p all T_b all T_a (hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) -> (hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) -> V_p = V_q))) # label(fact_prod__eqI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2225 (all V_b all V_a all T_b all T_a hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a) # label(fact_fst__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2226 (all V_a all V_y all V_x all T_b all T_a (hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a -> V_x = V_a)) # label(fact_fst__eqD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2227 (all T_b all T_a all V_t V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t))) # label(fact_surjective__pairing) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2228 (all V_p all T_b all T_a hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p) # label(fact_pair__collapse) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2229 (all V_b all V_a hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b))) # label(fact_div__int__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2230 (all V_n all V_m c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n))) # label(fact_mod__nat__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2231 (all V_b_H all V_a_H all V_b all V_a all T_b all T_a (hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(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].
% 6.04/6.10 2232 (all V_b_H_2 all V_a_H_2 all V_b_2 all V_a_2 all T_c all T_b (hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) <-> V_a_2 = V_a_H_2 & V_b_2 = V_b_H_2)) # label(fact_Pair__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2233 (all T_c all T_b 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,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)))))) # label(fact_split__paired__All) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2234 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b))))) # label(fact_div__neg__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2235 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b))))) # label(fact_div__pos__pos) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2236 (all V_w (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) # label(fact_div__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2237 (all V_b all V_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))))) # label(fact_div__pos__neg) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2238 (all V_p_2 all V_g_2 all V_f_2 all T_c all T_b c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_prod__size__simp) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2239 (all T_c all T_b all V_q_2 all V_Q_2 all V_p_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_p_2)) -> (hBOOL(hAPP(V_Q_2,V_q_2)) -> hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))))) # label(fact_conjI__realizer) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2240 (all T_b all T_c all V_x_2 all V_y_2 all V_Pa_2 (hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2)) -> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))))) # label(fact_exI__realizer) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2241 (all V_b_2 all V_a_2 all V_f1_2 all T_b all T_d all T_c c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) # label(fact_prod_Orecs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2242 (all V_n all V_m hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n))) # label(fact_div__nat__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2243 (all V_qr_2 all V_n_2 all V_m_2 (hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) <-> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) & (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) # label(fact_divmod__nat__rel__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2244 (all V_s all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)))) # label(fact_range) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2245 (all V_s_2 all V_r_2 all V_b_H_2 all V_a_H_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) | V_a_2 = V_a_H_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)))) # label(fact_in__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2246 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)))) # label(fact_in__finite__psubset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.10 2247 (all V_t_2 all V_s_2 all V_b_2 all V_a_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less))))) # label(fact_pair__lessI2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2248 (all V_t_2 all V_s_2 all V_b_2 all V_a_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)))) # label(fact_pair__lessI1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2249 (all T_b all V_R_2 all V_y_2 all V_y_H_2 all T_c all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)))))) # label(fact_same__fstI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2250 (all V_t_2 all V_s_2 all V_b_2 all V_a_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq))))) # label(fact_pair__leqI2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2251 (all V_X_2 all V_x_2 all V_Y_2 all V_y_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)))))) # label(fact_smax__insertI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2252 (all V_YS_2 all V_y_2 all V_XS_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)))))) # label(fact_smin__insertI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2253 (all V_X_2 (V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)))) # label(fact_smin__emptyI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2254 (all V_Y_2 (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) -> (V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict))))) # label(fact_smax__emptyI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2255 (all V_t_2 all V_s_2 all V_b_2 all V_a_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)))) # label(fact_pair__leqI1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2256 (all V_YS_2 all V_y_2 all V_XS_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)))))) # label(fact_wmin__insertI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2257 (all V_XS_2 all V_x_2 all V_YS_2 all V_y_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)))))) # label(fact_wmax__insertI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2258 (all V_X_2 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak))) # label(fact_wmin__emptyI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2259 (all V_X_2 (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)))) # label(fact_wmax__emptyI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2260 (all V_B_2 all T_b all V_A_2 (V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_less__by__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2261 (all V_D_2 all V_C_2 all V_R_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2)))))) # label(fact_max__ext__additive) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2262 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)))) # label(fact_less__than__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2263 (all V_v_2 all V_u_2 all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel)) <-> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) # label(fact_intrel__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2264 (all V_f_2 all T_c all V_Pa_2 all T_b (c_FunDef_Oreduction__pair(T_b,V_Pa_2) -> c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)))) # label(fact_rp__inv__image__rp) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2265 (all V_R_2 all V_Y_2 all V_X_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) -> (V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) -> (exists B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)))))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))))))) # label(fact_max__ext_Ointros) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2266 (all V_y_2 all V_x_2 (hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)))) # label(fact_equiv__intrel__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2267 (all T_a c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_Nitpick_Ozero__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2268 (all T_b c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than)) # label(fact_measure__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2269 (all V_r_2 all V_q_2 all V_b_2 hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2)))) # label(fact_adjust__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2270 (all V_A_2 all V_f_2 all T_c all T_b (class_Groups_Oordered__ab__group__add__abs(T_b) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))))) # label(fact_setsum__abs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2271 (all V_A_2 all V_f_2 all T_c all T_b (class_Groups_Oordered__ab__group__add__abs(T_b) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))))) # label(fact_setsum__abs__ge__zero) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2272 (all V_h_2 all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2))))) # label(fact_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2273 (all V_h_2 all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2))))) # label(fact_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2274 (all V_g_2 all V_f_2 all V_A_2 all T_b all T_c (class_Fields_Ofield__inverse__zero(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2))))) # label(fact_setprod__dividef) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2275 (all V_w_2 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) # label(fact_nat__number__of__Bit0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2276 (all V_A_2 all V_f_2 all T_c all T_b (class_Groups_Oab__group__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)))) # label(fact_setsum__negf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2277 (all V_x_2 all V_A_2 all T_c all T_b (class_Groups_Ouminus(T_b) -> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)))) # label(fact_fun__Compl__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2278 (all V_A_2 all V_f_2 all T_b hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) # label(fact_int__setprod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2279 (all V_A_2 all T_c all T_b (class_Groups_Ocomm__monoid__mult(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b))) # label(fact_setprod__1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2280 (all V_A_2 all V_f_2 all T_c all T_b (class_Groups_Oordered__ab__group__add__abs(T_b) -> hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) # label(fact_abs__setsum__abs) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2281 (all V_A_2 all V_f_2 all T_c all T_b (class_Fields_Olinordered__field(T_b) -> hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) # label(fact_abs__setprod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2282 (all V_A_2 all V_f_2 all T_c all V_r_2 all T_b (class_Rings_Osemiring__0(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2))) # label(fact_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2283 (all V_r_2 all V_A_2 all V_f_2 all T_c all T_b (class_Rings_Osemiring__0(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2))) # label(fact_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2284 (all V_B_2 all V_g_2 all T_d all V_A_2 all V_f_2 all T_c all T_b (class_Rings_Osemiring__0(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2))) # label(fact_setsum__product) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2285 (all V_x_2 all V_g_2 all V_f_2 all T_c all T_b (class_Lattices_Olattice(T_b) -> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))) # label(fact_inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2286 (all V_A_2 all V_g_2 all V_f_2 all T_c all T_b (class_Groups_Ocomm__monoid__mult(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)))) # label(fact_setprod__timesf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2287 (all V_g_2 all T_d all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)))) # label(fact_fun__left__comm_Ofun__left__comm__apply) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2288 (all V_A_2 all V_B_2 all V_f_2 all T_d all T_c all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2))) # label(fact_setsum__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2289 (all V_g_2 all T_d all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) -> c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)))) # label(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2290 (all V_r_2 all V_A_2 all V_f_2 all T_c all T_b (class_Fields_Ofield(T_b) -> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2))) # label(fact_setsum__divide__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2291 (all V_g_2 all V_f_2 all T_c all T_b hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2))) # label(fact_fold__image__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2292 (all V_A_2 all V_f_2 all T_b hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) # label(fact_int__setsum) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2293 (all V_A_2 all T_c all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b))) # label(fact_setsum__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2294 (all V_x_2 all V_B_2 all V_A_2 all T_c all T_b (class_Groups_Ominus(T_b) -> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)))) # label(fact_fun__diff__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2295 (all V_A_2 all V_g_2 all V_f_2 all T_c all T_b (class_Groups_Oab__group__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)))) # label(fact_setsum__subtractf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2296 (all V_A_2 all V_f_2 all T_c all T_b (class_Groups_Ocomm__monoid__mult(T_b) & class_Rings_Oring__1(T_b) -> hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2))) # label(fact_of__int__setprod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2297 (all V_A_2 all V_f_2 all T_c all T_b (class_Rings_Oring__1(T_b) -> hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2))) # label(fact_of__int__setsum) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2298 (all V_A_2 all V_g_2 all V_f_2 all T_c all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)))) # label(fact_setsum__addf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2299 (all V_x_2 all V_S_2 all V_R_2 all T_b (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))))) # label(fact_inf__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2300 (all V_S_2 all V_R_2 all T_b (hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2) <-> V_R_2 = V_S_2)) # label(fact_pred__equals__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2301 (all V_S_2 all V_R_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)))) # label(fact_pred__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2302 (all V_x_2 all V_S_2 all V_R_2 all T_b (hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))))) # label(fact_sup__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2303 (all V_y_2 all V_x_2 all V_S_2 all V_R_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))))) # label(fact_sup__Un__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2304 (all V_y_2 all V_x_2 all V_S_2 all V_R_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))))) # label(fact_inf__Int__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2305 (all V_S_2 all V_R_2 all T_c all T_b (hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2) <-> V_R_2 = V_S_2)) # label(fact_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2306 (all V_n_2 hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) # label(fact_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2307 (all V_x_2 all V_g_2 all V_f_2 all T_c all T_b (class_Lattices_Olattice(T_b) -> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))) # label(fact_sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2308 (all V_x_2 all T_c all T_b (class_Orderings_Obot(T_b) -> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b))) # label(fact_bot__fun__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2309 (all V_y_2 all V_x_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))))) # label(fact_bot__empty__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2310 (all V_x_2 all T_b (hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_bot__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2311 (all V_A_2 all V_f_2 all T_c all T_b (class_Rings_Osemiring__1(T_b) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2))) # label(fact_of__nat__setsum) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2312 (all V_A_2 all V_f_2 all T_b hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2))) # label(fact_transfer__nat__int__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2313 (all V_A_2 all T_b hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2)) # label(fact_card__eq__setsum) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2314 (all V_A_2 all V_f_2 all T_c all T_b (class_Groups_Ocomm__monoid__mult(T_b) & class_Rings_Osemiring__1(T_b) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2))) # label(fact_of__nat__setprod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2315 (all V_A_2 all V_f_2 all T_b hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2))) # label(fact_transfer__nat__int__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2316 (all V_b_2 all V_a_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c))))) # label(fact_setsum__delta_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2317 (all V_b_2 all V_a_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c))))) # label(fact_setsum__delta) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2318 (all V_b_2 all V_a_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c))))) # label(fact_setprod__delta_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2319 (all V_b_2 all V_a_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c))))) # label(fact_setprod__delta) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2320 (all T_c all V_A_2 all V_ca_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) # label(fact_vimage__const) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2321 (all V_A_2 all V_y_2 all T_c all T_b (class_Rings_Osemiring__1(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2))) # label(fact_setsum__constant) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2322 (all V_w_2 all V_z_2 all T_b (class_Int_Onumber__ring(T_b) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))))) # label(fact_power__number__of__even) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2323 (all V_h_2 all V_g_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2))))) # label(fact_fold__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2324 (all V_y_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))))) # label(fact_setprod__constant) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2325 (all V_w_2 all V_z_2 hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint)))) # label(fact_zpower__number__of__even) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2326 (all V_S_2 all V_R_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))) # label(fact_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2327 (all V_Q_2 all V_ca_2 all V_Ga_2 all T_b c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))) # label(fact_falseE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2328 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))))) # label(fact_Powp__Pow__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2329 (all V_B_2 all V_f_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2)))) # label(fact_setsum__restrict__set) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2330 (all V_w_2 all V_v_2 all T_b (class_Int_Onumber__ring(T_b) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))))) # label(fact_power__number__of__even__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2331 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))) # label(fact_card_Oeq__fold__g) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2332 (all V_A_2 all T_b ((hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) & (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_card__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2333 (all T_b c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_fun__left__comm__idem__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2334 (all V_B_2 all T_c all V_d_2 all V_A_2 all V_ca_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) -> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) -> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) -> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) -> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) # label(fact_vimage__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2335 (all V_z_2 all V_z_H_2 ((hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))))) # label(fact_diff__nat__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2336 (all V_ca_2 all V_b_2 all V_Pa_2 all V_Ga_2 all T_b c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_Pa_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))) # label(fact_LoopF) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2337 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2))) # label(fact_minus__fold__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2338 (all V_n_2 all V_v_2 (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) <-> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))))) # label(fact_eq__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2339 (all V_v_2 all V_n_2 (hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) <-> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))))) # label(fact_Suc__eq__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2340 (all V_w_2 ((hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) -> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (-hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) -> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))))) # label(fact_nat__number__of__Bit1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2341 (all V_v_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) <-> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))))) # label(fact_less__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2342 (all V_n_2 all V_v_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))))) # label(fact_less__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2343 (all V_n_2 all V_v_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) <-> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))))) # label(fact_le__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2344 (all V_v_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) <-> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))))) # label(fact_le__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2345 (all V_z_2 all V_w_2 all T_b (class_Int_Onumber__ring(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)))) # label(fact_power__number__of__odd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2346 (all V_ca_2 all V_b_2 all V_a_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)))))) # label(fact_setprod__gen__delta) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2347 (all V_z_2 all V_w_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) -> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_zpower__number__of__odd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2348 (all V_v_2 all V_n_2 hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) # label(fact_min__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2349 (all V_n_2 all V_v_2 hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) # label(fact_min__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2350 (all V_v_2 all V_w_2 all T_b (class_Int_Onumber__ring(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) -> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)))) # label(fact_power__number__of__odd__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2351 (all V_v_2 all V_v_H_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))))) # label(fact_diff__nat__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2352 (all T_a c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_Nitpick_Oone__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2353 (all V_n all T_a c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_Nitpick_Onumber__of__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2354 (all V_a_2 all V_r_2 all T_c all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)))) # label(fact_Image__singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2355 (all V_a_2 all V_b_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) & (-(V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))))))) # label(fact_norm__frac_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2356 (all T_c all T_b all V_A_2 all V_y_2 all V_x_2 all V_B_2 ((-hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)))) # label(fact_sup2CI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2357 (all V_y_2 all V_x_2 all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) -> (-hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))))) # label(fact_sup2E) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2358 (all T_c all T_b all V_B_2 all V_y_2 all V_x_2 all V_A_2 (hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))))) # label(fact_inf2I) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2359 (all V_y_2 all V_x_2 all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) -> -(hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) -> -hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))))) # label(fact_inf2E) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2360 (all V_y_2 all V_x_2 all T_c all T_b -hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))) # label(fact_bot2E) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2361 (all V_A_2 all T_c all T_b all V_y_2 all V_x_2 all V_B_2 (hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)))) # label(fact_sup2I2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2362 (all V_B_2 all T_c all T_b all V_y_2 all V_x_2 all V_A_2 (hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)))) # label(fact_sup2I1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2363 (all V_y_2 all V_x_2 all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)))) # label(fact_inf2D1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2364 (all V_y_2 all V_x_2 all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)))) # label(fact_inf2D2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2365 (all V_R_2 all T_b all T_c hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Image__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2366 (all V_B_2 all V_A_2 all V_R_2 all T_b all T_c hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2))) # label(fact_Image__Un) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2367 (all V_B_2 all V_A_2 all V_R_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2))))) # label(fact_Image__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2368 (all V_A_2 all V_A_H_2 all V_r_2 all V_r_H_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))))) # label(fact_Image__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2369 (all V_A_2 all V_S_2 all V_R_2 all T_b all T_c hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2))) # label(fact_Un__Image) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2370 (all V_f_2 all V_r_2 all T_c all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)))) # label(fact_in__inv__image) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2371 (all V_A_2 all V_r_2 all T_c all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)))))) # label(fact_Image__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2372 (all V_r_2 all V_b_2 all T_c all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))))) # label(fact_rev__ImageI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2373 (all V_b_2 all V_a_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> (V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) & (-(V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)) -> c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))))))) # label(fact_norm__frac_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2374 (all V_k_2 all T_b (class_Rings_Oring__1(T_b) -> (V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b)) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))) # label(fact_of__int__num) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2375 (all V_xa_2 all V_x_2 all V_R_2 all T_b (c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))))) # label(fact_max__extp__max__ext__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2376 (all V_n_2 all V_v_2 all V_f_2 all V_a_2 all T_b c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) # label(fact_nat__case__add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2377 (all V_ca_2 all T_d all T_c all T_b all V_q_2 all V_p_2 (V_p_2 = V_q_2 -> hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2))) # label(fact_split__weak__cong) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2378 (all V_b_2 all V_a_2 all V_f1_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) # label(fact_prod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2379 (all V_b_2 all V_a_2 all V_f_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2)) # label(fact_split__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2380 (all V_p_2 all V_g_2 all T_f all T_e all V_f_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2)) # label(fact_split__twice) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2381 (all V_f_2 all T_d all T_c all T_b hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2) # label(fact_split__eta) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2382 (all V_p_2 all T_c all T_b hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2)) # label(fact_fst__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2383 (all V_p_2 all T_b all T_c hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2)) # label(fact_snd__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2384 (all V_f2_2 all V_f1_2 all T_b c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2) # label(fact_nat__case__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2385 (all V_nat_2 all V_f2_2 all V_f1_2 all T_b c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2)) # label(fact_nat__case__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2386 (all V_p_2 all V_f_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2))) # label(fact_prod__case__beta) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2387 (all V_g_2 all V_f_2 all T_e all T_d all T_c all T_b hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2))) # label(fact_split__comp__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2388 (all V_z_2 all V_Pa_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2))) # label(fact_split__beta) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2389 (all V_p_2 all V_ca_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2))) # label(fact_split__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2390 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) <-> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2391 (all V_n_2 all V_m_2 hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2))) # label(fact_diff__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2392 (all V_m_2 all V_n_2 hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2)) # label(fact_min__Suc1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2393 (all V_n_2 all V_m_2 hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2)) # label(fact_min__Suc2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2394 (all V_b_2 all V_a_2 c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))))) # label(fact_divmod__int__rel__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2395 (all V_R_2 all V_f_2 all T_b c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b)))) # label(fact_mlex__prod__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2396 (all V_v_2 all V_f_2 all V_a_2 all T_b c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)))) # label(fact_nat__case__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.11 2397 (all V_b_2 c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))) # label(fact_adjust__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2398 (all V_l_2 all V_k_2 ((V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) & (V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))))))) # label(fact_divmod__int__pdivmod) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2399 (all V_l_2 all V_k_2 ((V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> (V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) & (V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) -> c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))))))) # label(fact_divmod__int__code) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2400 (all V_j_2 all V_i_2 all T_b (class_Rings_Oring__1(T_b) -> hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)))) # label(fact_of__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2401 (all T_d all T_c all V_b_2 all V_a_2 all V_ca_2 all V_z_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))))) # label(fact_mem__splitI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2402 (all T_c all T_b all V_b_2 all V_a_2 all V_f1_2 (hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))))) # label(fact_prod__caseI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2403 (all T_c all T_b all V_b_2 all V_a_2 all V_f_2 (hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))))) # label(fact_splitI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2404 (all V_ca_2 all V_b_2 all V_a_2 all V_R_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_ca_2)) -> hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)))) # label(fact_splitD_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2405 (all V_b_2 all V_a_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) -> hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)))) # label(fact_splitD) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2406 (all V_y_2 all V_x_2 all V_f_2 all T_b all T_c all T_d hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2))) # label(fact_apsnd__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2407 (all V_x_2 all V_f_2 all T_d all T_c all T_b hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2)) # label(fact_fst__apsnd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2408 (all V_x_2 all V_f_2 all T_d all T_b all T_c hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))) # label(fact_snd__apsnd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2409 (all V_g_2 all V_x_2 all V_f_2 all T_b all T_c all T_d (hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2) <-> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)))) # label(fact_apsnd__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2410 (all T_c all T_b c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c)))) # label(fact_rp__inv__image__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2411 (all V_m_2 all V_n_2 ((V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) -> c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) & (-(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))) -> c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2))))) # label(fact_divmod__nat__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2412 (all V_y_2 all V_x_2 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) # label(fact_minus) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2413 (all V_m_2 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) # label(fact_int__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2414 (all V_v_2 all V_u_2 all V_y_2 all V_x_2 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) # label(fact_add) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2415 (all V_y_2 all V_x_2 hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)) # label(fact_nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2416 (all V_v_2 all V_u_2 all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))))) # label(fact_less) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2417 (all V_v_2 all V_u_2 all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))))) # label(fact_le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2418 (all V_v_2 all V_u_2 all V_y_2 all V_x_2 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) # label(fact_mult) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2419 (all V_n_2 all V_v_2 all V_f_2 all V_a_2 all T_b hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))))) # label(fact_nat__rec__add__eq__if) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2420 (all V_n_2 all T_b (class_Rings_Osemiring__1(T_b) -> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_semiring__1__class_Oof__nat__code) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2421 (all V_v_2 all V_f_2 all V_a_2 all T_b hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat))))) # label(fact_nat__rec__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2422 (all T_b (class_Orderings_Olinorder(T_b) -> c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b))) # label(fact_dual__max) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2423 (all V_f2_2 all V_f1_2 all T_b hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2) # label(fact_nat__rec__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2424 (all V_nat_2 all V_f2_2 all V_f1_2 all T_b hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2))) # label(fact_nat__rec__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2425 (all V_i_2 all V_inc_2 all T_b (class_Rings_Osemiring__1(T_b) -> c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2)) # label(fact_of__nat__aux_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2426 (all V_i_2 all V_n_2 all V_inc_2 all T_b (class_Rings_Osemiring__1(T_b) -> c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)))) # label(fact_of__nat__aux_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2427 (all V_f_2 all V_A_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)))) # label(fact_transfer__int__nat__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2428 (all V_r_2 all T_b (c_Relation_Oirrefl(T_b,V_r_2) <-> (all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))))) # label(fact_irrefl__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2429 (all V_f_2 all V_A_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)))) # label(fact_transfer__int__nat__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2430 (all V_Pa_2 all V_a1_2 all V_a0_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) -> ((all B_a all B_b (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) -> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b)))) -> hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))))) # label(fact_norm__frac_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2431 (all V_b all V_a all T_a hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b))) # label(fact_Nitpick_Ofrac__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2432 (all V_z_2 -(all B_x all B_y V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) # label(fact_eq__Abs__Integ) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2433 (all V_n_2 all V_d_2 all V_a_2 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2))))) # label(fact_arith__series__int) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2434 (all V_r_2 all V_b_2 all V_a_2 all T_b hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2))) # label(fact_Field__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2435 (all V_k_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)))) # label(fact_finite__lessThan) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2436 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) <-> V_x_2 = V_y_2))) # label(fact_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2437 (all V_u_2 hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2) # label(fact_card__lessThan) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2438 (all V_k_2 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) # label(fact_lessThan__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2439 (all V_k_2 all V_i_2 all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2))))) # label(fact_lessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2440 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))))) # label(fact_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2441 (all V_n_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)))) # label(fact_setsum__lessThan__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2442 (all V_n_2 all V_m_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2))))) # label(fact_lessThan__strict__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2443 (all V_k_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_single__Diff__lessThan) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2444 (all V_N_2 (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) <-> (exists B_m all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)))))) # label(fact_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2445 (all T_b hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Field__empty) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2446 (all V_s_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))))) # label(fact_mono__Field) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2447 (all V_N_2 (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) <-> (exists B_m all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)))))) # label(fact_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2448 (all V_s_2 all V_r_2 all T_b hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) # label(fact_Field__Un) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2449 (all V_r_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) # label(fact_finite__Field) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2450 (all V_n_2 all V_d_2 all V_a_2 all T_b (class_Rings_Ocomm__semiring__1(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))))) # label(fact_arith__series__general) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2451 (all V_n_2 all V_d_2 all V_a_2 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2))))) # label(fact_arith__series__nat) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2452 (all V_k_2 all V_less__eq_2 all V_i_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) <-> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)))) # label(fact_ord_OatMost__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2453 (all V_k_2 all V_less__eq_2 all V_i_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) <-> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)))) # label(fact_ord_OatLeast__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2454 (all V_k_2 all V_less_2 all V_i_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) <-> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)))) # label(fact_ord_OlessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2455 (all V_k_2 all V_less_2 all V_i_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) <-> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)))) # label(fact_ord_OgreaterThan__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2456 (all V_u_2 all V_l_2 all V_less_2 all V_less__eq_2 all V_i_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) <-> hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))) # label(fact_ord_OgreaterThanAtMost__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2457 (all V_u_2 all V_l_2 all V_less_2 all V_less__eq_2 all V_i_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) <-> hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))) # label(fact_ord_OatLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2458 (all V_u_2 all V_l_2 all V_less_2 all V_i_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2))) <-> hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)))) # label(fact_ord_OgreaterThanLessThan__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2459 (all V_u_2 all V_l_2 all V_less__eq_2 all V_i_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2))) <-> hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)))) # label(fact_ord_OatLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2460 (all V_i_2 all V_f_2 all V_s_2 all T_b all T_c (class_Groups_Oordered__ab__group__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))))) -> (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) -> hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c))))))) # label(fact_setsum__nonneg__0) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2461 (all V_i_2 all V_B_2 all V_f_2 all V_s_2 all T_b all T_c (class_Groups_Oordered__ab__group__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))))) -> (hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)))))))) # label(fact_setsum__nonneg__leq__bound) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2462 (all V_v_2 all V_n_2 hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) # label(fact_max__number__of__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2463 (all V_n_2 all V_v_2 hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) # label(fact_max__Suc__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2464 (all V_y_2 all V_x_2 all V_z_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))))) # label(fact_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2465 (all V_x all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) -> -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) -> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)))))) # label(fact_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2466 (all V_d all V_b all V_c all V_a all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))))))) # label(fact_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2467 (all V_z all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)))))) # label(fact_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2468 (all V_b all V_x all V_a all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)))))) # label(fact_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2469 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x))) # label(fact_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2470 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y))) # label(fact_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2471 (all V_a all V_b all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))))) # label(fact_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2472 (all V_b all V_a all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))))) # label(fact_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2473 (all V_z_2 all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))))) # label(fact_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2474 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) <-> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2))) # label(fact_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2475 (all V_x all V_y all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))))) # label(fact_le__maxI2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2476 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))))) # label(fact_le__maxI1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2477 (all T_b (class_Orderings_Olinorder(T_b) -> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)))) # label(fact_min__max_Ofun__left__comm__idem__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2478 (all V_z all V_y all V_x all T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)))) # label(fact_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2479 (all V_b all V_a all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))))) # label(fact_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2480 (all V_a all V_b all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))))) # label(fact_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2481 (all V_y_2 all V_x_2 all V_z_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))))) # label(fact_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2482 (all V_z_2 all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))))) # label(fact_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2483 (all V_z all V_y all V_x all T_a (class_Groups_Oordered__ab__group__add(T_a) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)))) # label(fact_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2484 (all V_a all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a)) # label(fact_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2485 (all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a))) # label(fact_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2486 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x))) # label(fact_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2487 (all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) # label(fact_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2488 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) # label(fact_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2489 (all V_c all V_a all V_b all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)))) # label(fact_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2490 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) # label(fact_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2491 (all V_c all V_b all V_a all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)))) # label(fact_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2492 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) # label(fact_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2493 (all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x)) # label(fact_Max_Oidem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2494 (all V_x all V_z all V_y all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)))) # label(fact_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2495 (all V_x all V_z all V_y all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)))) # label(fact_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2496 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)))) # label(fact_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2497 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) # label(fact_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2498 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x)) # label(fact_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2499 (all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x)) # label(fact_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2500 (all V_n all V_m hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n))) # label(fact_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2501 (all V_n hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n) # label(fact_max__0L) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2502 (all V_n hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n) # label(fact_max__0R) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2503 (all T_b (class_Lattices_Osemilattice__sup(T_b) & class_Orderings_Olinorder(T_b) -> c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b))) # label(fact_sup__max) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2504 (all V_v all V_u all T_b (class_Int_Onumber(T_b) & class_Orderings_Oord(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)))) # label(fact_max__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2505 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))))) # label(fact_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2506 (all V_z all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))))) # label(fact_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2507 (all V_y all V_x all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)))) # label(fact_minus__max__eq__min) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2508 (all V_y all V_x all T_a (class_Groups_Olinordered__ab__group__add(T_a) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)))) # label(fact_minus__min__eq__max) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2509 (all V_m all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m)) # label(fact_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2510 (all V_m_2 all V_n_2 hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2)) # label(fact_max__Suc1) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2511 (all V_n_2 all V_m_2 hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2)) # label(fact_max__Suc2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2512 (all T_b (class_Orderings_Oord(T_b) -> c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)))) # label(fact_max__ord__max) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2513 (all V_a_2 all V_b_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))))) # label(fact_min__max_Ofold__sup__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2514 (all T_b (class_Orderings_Olinorder(T_b) -> c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b))) # label(fact_dual__min) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2515 (all V_b_2 all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))))))) # label(fact_min__max_Osup__le__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2516 (all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2)))) # label(fact_min__max_Osup__Inf__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2517 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))))) # label(fact_Max_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2518 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))))))) # label(fact_min__max_OInf__le__Sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2519 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))))) # label(fact_min__max_OSup__fin_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2520 (all V_n_2 all V_Pa_2 all V_Q_2 ((all B_x hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_Pa_2,B_x)))) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)))) # label(fact_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2521 (all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2)) # label(fact_Max_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2522 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))))) # label(fact_min__max_OSup__fin_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2523 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))))))) # label(fact_Max__ge) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2524 (all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2)) # label(fact_min__max_OSup__fin_Osingleton) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2525 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)))))) # label(fact_Max__in) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2526 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))))) # label(fact_Max_Oin__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2527 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2)))) # label(fact_min__max_OSup__fin_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2528 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2)))) # label(fact_Max_OF__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2529 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)))))) # label(fact_min__max_OSup__fin_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2530 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)))))) # label(fact_min__max_OSup__fin_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2531 (all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2)))) # label(fact_min__max_Oinf__Sup__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2532 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)))))))) # label(fact_min__max_OSup__fin_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2533 (all V_N_2 all V_M_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2)) -> (V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)))))))) # label(fact_Max__mono) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2534 (all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2)))) # label(fact_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2535 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)))))) # label(fact_Max__insert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2536 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)))))) # label(fact_Max_Osubset__idem) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2537 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)))))))) # label(fact_Max__Un) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2538 (all V_a_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2)))) # label(fact_Max_Oeq__fold__idem_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2539 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))))))) # label(fact_min__max_OSup__fin_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2540 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_min__max_OSup__fin_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2541 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))))))))) # label(fact_min__max_OSup__fin_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2542 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))))))) # label(fact_min__max_OSup__fin_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2543 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2))))) # label(fact_min__max_OSup__fin_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2544 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))))))) # label(fact_Max_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2545 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2) & (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))))) # label(fact_Max_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2546 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))))))))) # label(fact_Max_Ounion__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2547 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))))))) # label(fact_Max_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2548 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2))))) # label(fact_Max_Oeq__fold_H) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2549 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x all B_y hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2))))))) # label(fact_min__max_OSup__fin_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2550 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x all B_y hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))))))) # label(fact_Max_Oclosed) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2551 (all V_x_2 all V_g_2 all T_e all V_f_2 all T_c all T_b all T_d hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)))) # label(fact_apfst__apsnd) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2552 (all V_x_2 all V_g_2 all T_e all V_f_2 all T_b all T_c all T_d hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2)))) # label(fact_apsnd__apfst) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2553 (all V_y_2 all V_x_2 all V_f_2 all T_c all T_b all T_d hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2)) # label(fact_apfst__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2554 (all V_g_2 all V_x_2 all V_f_2 all T_c all T_b all T_d (hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2) <-> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)))) # label(fact_apfst__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2555 (all V_x_2 all V_f_2 all T_d all T_c all T_b hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))) # label(fact_fst__apfst) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2556 (all V_x_2 all V_f_2 all T_d all T_b all T_c hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2)) # label(fact_snd__apfst) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2557 (all V_p_2 all V_g_2 all T_e all V_f_2 all T_b all T_c all T_d hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2))) # label(fact_apsnd__apfst__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.12 2558 (all V_f_2 all V_n_2 all V_m_2 all T_b (class_Groups_Oab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_setsum__natinterval__difff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2559 (all V_n_2 all T_b (class_Rings_Ocomm__semiring__1(T_b) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))))) # label(fact_gauss__sum) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2560 (all V_f_2 all V_A_2 all T_b all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2)))) # label(fact_INFI__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2561 (all V_f_2 all V_A_2 all T_b all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2)))) # label(fact_SUPR__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2562 (all T_c all V_b_2 all V_B_2 all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> (hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) -> hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))))) # label(fact_SUP1__I) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2563 (all V_B_2 all V_b_2 all T_c all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) -> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_UN__I) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2564 (all V_a_2 all V_b_2 all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) -> (-hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))))) # label(fact_INF1__E) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2565 (all V_a_2 all V_b_2 all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))))) # label(fact_INF1__D) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2566 (all V_a_2 all V_B_2 all V_A_2 all T_c all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))))) # label(fact_INT__D) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2567 (all V_a_2 all V_B_2 all V_A_2 all T_c all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) -> -hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))))) # label(fact_INT__E) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2568 (all T_d all T_c all V_ca_2 all V_b_2 all V_B_2 all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> (hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))))) # label(fact_SUP2__I) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2569 (all V_a_2 all V_ca_2 all V_b_2 all V_B_2 all V_A_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))))) # label(fact_INF2__D) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2570 (all V_a_2 all V_ca_2 all V_b_2 all V_B_2 all V_A_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) -> (-hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))))) # label(fact_INF2__E) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2571 (all V_A_2 all T_c all V_I_2 all T_b ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))))) # label(fact_finite__INT) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2572 (all V_u_2 all V_l_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)))) # label(fact_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2573 (all V_B_2 all V_C_2 all T_c all V_a_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2))) # label(fact_INT__extend__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2574 (all V_B_2 all V_a_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))) # label(fact_INT__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2575 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))))))) # label(fact_finite__UN) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2576 (all V_B_2 all V_A_2 all T_b all T_c (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_UNION__empty__conv_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2577 (all V_ca_2 all T_c all T_b all V_A_2 ((V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) & (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2))) # label(fact_UN__constant) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2578 (all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_UN__empty2) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2579 (all V_B_2 all V_A_2 all T_c all T_b (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_UNION__empty__conv_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2580 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))))) # label(fact_INT__extend__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2581 (all V_S_2 all T_b c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_Union__def) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2582 (all V_B_2 all V_A_2 all T_c all T_b hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))) # label(fact_Pow__INT__eq) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2583 (all V_B_2 all V_A_2 all T_c all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2))) # label(fact_Compl__INT) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2584 (all V_B_2 all V_A_2 all T_c all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2))) # label(fact_Compl__UN) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2585 (all V_x_2 all V_f_2 all V_A_2 all T_d all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)))) # label(fact_SUPR__apply) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2586 (all V_x_2 all V_f_2 all V_A_2 all T_d all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)))) # label(fact_INFI__apply) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2587 (all V_f_2 all V_B_2 all T_d all V_A_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))))) # label(fact_SUP__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2588 (all V_f_2 all V_B_2 all T_d all V_A_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))))) # label(fact_INF__commute) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2589 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2)) # label(fact_INT__extend__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2590 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2)) # label(fact_UN__extend__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2591 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2))) # label(fact_INT__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2592 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2))) # label(fact_UN__simps_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2593 (all V_B_2 all V_A_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))) # label(fact_UN__simps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2594 (all V_B_2 all V_A_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)) # label(fact_UN__simps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2595 (all V_B_2 all V_C_2 all T_c all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2))) # label(fact_UN__extend__simps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2596 (all V_B_2 all V_A_2 all V_C_2 all T_c all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2))) # label(fact_UN__extend__simps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2597 (all V_B_2 all V_A_2 all T_c all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))))))) # label(fact_UN__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2598 (all V_B_2 all V_A_2 all T_c all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))))))) # label(fact_INT__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2599 (all V_B_2 all V_A_2 all V_I_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)))))) # label(fact_UN__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2600 (all V_A_2 all V_I_2 all T_c all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))))))) # label(fact_INT__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2601 (all V_B_2 all V_A_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_UN__Pow__subset) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2602 (all V_B_2 all V_A_2 all T_d all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2))) # label(fact_vimage__UN) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2603 (all V_B_2 all V_A_2 all T_d all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2))) # label(fact_vimage__INT) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2604 (all V_B_2 all V_A_2 all T_d all V_r_2 all T_b all T_c hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2))) # label(fact_Image__UN) # label(axiom) # label(non_clause). [assumption].
% 6.04/6.13 2605 (all V_B_2 all V_A_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))) # label(fact_UN__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2606 (all V_B_2 all V_A_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)) # label(fact_UN__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2607 (all V_B_2 all V_A_2 all V_I_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2))) # label(fact_INT__Int__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2608 (all V_B_2 all V_C_2 all T_c all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2))) # label(fact_UN__extend__simps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2609 (all V_A_2 all V_I_2 all T_c all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2))) # label(fact_Int__UN__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2610 (all V_B_2 all V_A_2 all V_C_2 all T_c all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2))) # label(fact_UN__extend__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2611 (all V_B_2 all V_J_2 all T_d all V_A_2 all V_I_2 all T_c all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2)))) # label(fact_Int__UN__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2612 (all V_S_2 all T_b c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_Inter__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2613 (all V_B_2 all V_A_2 all T_c all T_b (c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_INTER__UNIV__conv_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2614 (all V_B_2 all V_A_2 all T_b all T_c (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_INTER__UNIV__conv_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2615 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))))) # label(fact_INT__simps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2616 (all V_B_2 all V_J_2 all T_d all V_A_2 all V_I_2 all T_c all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2)))) # label(fact_Un__INT__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2617 (all V_B_2 all V_A_2 all V_C_2 all T_c all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2))) # label(fact_INT__extend__simps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2618 (all V_M_2 all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2))) # label(fact_UN__Un) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2619 (all V_A_2 all V_I_2 all T_c all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2))) # label(fact_Un__INT__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2620 (all V_B_2 all V_C_2 all T_c all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2))) # label(fact_INT__extend__simps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2621 (all V_B_2 all V_A_2 all V_I_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2))) # label(fact_UN__Un__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2622 (all V_B_2 all V_A_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)) # label(fact_INT__simps_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2623 (all V_B_2 all V_A_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))) # label(fact_INT__simps_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2624 (all V_y_2 all V_x_2 all V_r_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))))) # label(fact_INF__INT__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2625 (all V_y_2 all V_x_2 all V_r_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))))) # label(fact_SUP__UN__eq2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2626 (all V_u_2 all V_M_2 all V_A_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))))))) # label(fact_SUP__le__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2627 (all V_M_2 all V_A_2 all T_c all V_u_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))))))) # label(fact_le__INF__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2628 (all V_f_2 all V_A_2 all T_c all V_a_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) & class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))))))) # label(fact_less__SUP__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2629 (all V_a_2 all V_f_2 all V_A_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) & class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2)) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))))))) # label(fact_INF__less__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2630 (all V_B_2 all V_a_2 all T_c all V_A_2 all V_u_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_INT__insert__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2631 (all V_B_2 all T_c all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))))) # label(fact_INT__lower) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2632 (all V_x_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))))) # label(fact_INF__INT__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2633 (all V_A_2 all T_c all V_I_2 all V_k_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) # label(fact_INT__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2634 (all V_M_2 all T_b all V_A_2 all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2))) # label(fact_SUP__const) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2635 (all V_M_2 all T_b all V_A_2 all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2))) # label(fact_INF__const) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2636 (all V_B_2 all V_a_2 all T_c all V_A_2 all V_u_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_UN__insert__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2637 (all V_ca_2 all T_c all T_b all V_A_2 ((V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) & (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2))) # label(fact_INT__constant) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2638 (all V_B_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_INT__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2639 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))))) # label(fact_INT__extend__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2640 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))))) # label(fact_INT__extend__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2641 (all V_B_2 all T_c all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_UN__upper) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2642 (all V_x_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))))) # label(fact_SUP__UN__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2643 (all V_A_2 all T_c all V_I_2 all V_k_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) # label(fact_UN__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2644 (all V_B_2 all V_A_2 all V_a_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_INT__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2645 (all V_B_2 all V_a_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))))) # label(fact_UN__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2646 (all V_A_2 all T_b hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2) # label(fact_UN__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2647 (all V_B_2 all V_a_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2))))) # label(fact_UN__extend__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2648 (all V_M_2 all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2))) # label(fact_INT__Un) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2649 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))))) # label(fact_UN__extend__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2650 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))))) # label(fact_UN__extend__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2651 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)))) # label(fact_UN__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2652 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))))) # label(fact_UN__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2653 (all V_B_2 all V_A_2 all V_a_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) # label(fact_UN__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2654 (all V_B_2 all V_A_2 all T_d all V_r_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2))))) # label(fact_Image__INT__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2655 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) # label(fact_Int__Union) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2656 (all V_A_2 all V_B_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))) # label(fact_Int__Union2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2657 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) # label(fact_Un__Inter) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2658 (all V_b_2 all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) <-> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))))) # label(fact_atLeastatMost__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2659 (all V_b_2 all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> (c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))))) # label(fact_atLeastatMost__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2660 (all V_a_2 all V_b_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) -> c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_atLeastatMost__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2661 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2))) <-> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))))) # label(fact_atLeastatMost__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2662 (all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_atLeastAtMost__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2663 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> (c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) <-> V_a_2 = V_b_2 & V_b_2 = V_ca_2))) # label(fact_atLeastAtMost__singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2664 (all V_b_2 all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> (V_a_2 = V_b_2 -> c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_atLeastAtMost__singleton_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2665 (all V_A_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2))) # label(fact_vimage__Union) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2666 (all V_n_2 all V_m_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_setsum__shift__bounds__cl__Suc__ivl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2667 (all V_n_2 all V_k_2 all V_m_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2668 (all V_f_2 all V_B_2 all V_A_2 all T_b all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)))))) # label(fact_INF__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2669 (all V_f_2 all V_B_2 all V_A_2 all T_b all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2)))))) # label(fact_SUP__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2670 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))))) # label(fact_INT__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2671 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)))) # label(fact_INT__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2672 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)))) # label(fact_INT__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2673 (all V_B_2 all V_A_2 all T_c all T_b all V_C_2 ((V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2)) & (V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))))) # label(fact_INT__extend__simps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2674 (all V_B_2 all V_r_2 all T_b all T_c hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) # label(fact_Image__eq__UN) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2675 (all V_B_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) # label(fact_vimage__eq__UN) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2676 (all V_u_2 all V_l_2 hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2)) # label(fact_card__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2677 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) -> c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)))) # label(fact_atLeastAtMostSuc__conv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2678 (all V_M_2 all V_A_2 all V_i_2 all T_b all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2)))))) # label(fact_INF__leI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2679 (all V_M_2 all V_A_2 all V_i_2 all T_b all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2)))))) # label(fact_le__SUPI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2680 (all V_k_2 all V_f_2 (hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)))) # label(fact_setsum__shift__lb__Suc0__0) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2681 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)))) # label(fact_Int__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2682 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2))) <-> (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) & (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)))) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2))))) # label(fact_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2683 (all V_u_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2684 (all V_f_2 all V_n_2 all V_m_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2)))))) # label(fact_setsum__head__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2685 (all V_f_2 all V_m_2 all V_n_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)))))) # label(fact_setsum__cl__ivl__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2686 (all V_f_2 all V_B_2 all V_A_2 all T_b all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2)))) # label(fact_sup__SUPR__fold__sup) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2687 (all V_f_2 all V_B_2 all V_A_2 all T_b all T_c (class_Complete__Lattice_Ocomplete__lattice(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2)))) # label(fact_inf__INFI__fold__inf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2688 (all V_p_2 all V_f_2 all V_n_2 all V_m_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))))))) # label(fact_setsum__ub__add__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2689 (all V_z_2 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))) # label(fact_minus__int__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2690 (all V_Pa_2 all V_n_2 ((exists B_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) & hBOOL(hAPP(V_Pa_2,B_m)))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ex__nat__less) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2691 (all V_Pa_2 all V_n_2 ((all B_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) -> hBOOL(hAPP(V_Pa_2,B_m)))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_all__nat__less) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2692 (all V_z_2 hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))) # label(fact_nat__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2693 (all V_ca_2 all V_b_2 all V_B_2 all V_A_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)))))) # label(fact_SUP2__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2694 (all V_ca_2 all V_b_2 all V_B_2 all V_A_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)))))) # label(fact_INF2__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2695 (all V_b_2 all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)))))) # label(fact_SUP1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2696 (all V_b_2 all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)))))) # label(fact_INF1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2697 (all V_C_2 all V_B_2 all V_A_2 all T_d all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2))) # label(fact_UN__UN__flatten) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2698 (all V_C_2 all V_B_2 all V_A_2 all T_d all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2))) # label(fact_UN__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2699 (all V_C_2 all V_B_2 all V_A_2 all T_d all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2))) # label(fact_INT__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2700 (all V_C_2 all V_B_2 all T_d all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) # label(fact_UN__extend__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2701 (all V_C_2 all V_B_2 all T_d all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) # label(fact_INT__extend__simps_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2702 (all V_Pa_2 all V_B_2 all V_A_2 all T_c all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) -> hBOOL(hAPP(V_Pa_2,B_xa)))))))) # label(fact_ball__UN) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2703 (all V_y_2 all V_x_2 (hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) <-> V_x_2 = V_y_2)) # label(fact_Rep__Integ__inject) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2704 (all V_x_2 hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2) # label(fact_Rep__Integ__inverse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2705 (all V_i_2 all V_j_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) -> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) -> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2))))) # label(fact_simp__from__to) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.13 2706 (all V_u_2 all V_l_2 hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))) # label(fact_card__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2707 (all V_A_2 all V_t_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) -> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))))))) # label(fact_aset_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2708 (all V_B_2 all V_t_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) -> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))))))))) # label(fact_bset_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2709 (all V_t_2 all V_A_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) -> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)))))))) # label(fact_aset_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2710 (all V_u_2 all V_l_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)))) # label(fact_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2711 (all V_A_2 all V_t_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) -> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa))))) -> (B_x != V_t_2 -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2)))))) # label(fact_aset_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2712 (all V_B_2 all V_t_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) -> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa))))) -> (B_x != V_t_2 -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2)))))) # label(fact_bset_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2713 (all V_B_2 all V_t_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) -> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))))))))) # label(fact_bset_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2714 (all V_B_2 all V_t_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) -> V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x))))) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2)))) # label(fact_bset_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2715 (all V_A_2 all V_t_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) -> V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x))))) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2)))) # label(fact_aset_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2716 (all V_A_2 all V_t_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) -> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))))))) # label(fact_aset_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2717 (all V_t_2 all V_B_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) -> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))))))) # label(fact_bset_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2718 (all V_Pa_2 all V_d_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) -> ((all B_x all B_k (hBOOL(hAPP(V_Pa_2,B_x)) <-> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))))) -> ((exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) & hBOOL(hAPP(V_Pa_2,B_x)))))))) # label(fact_periodic__finite__ex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2719 (all V_t_2 all V_A_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) -> B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)))))))) # label(fact_aset_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2720 (all V_t_2 all V_B_2 all V_D_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) -> (all B_x ((all B_xa (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) -> (all B_xb (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) -> B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))))))) # label(fact_bset_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2721 (all V_u_2 all V_l_2 hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))) # label(fact_card__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2722 (all V_A_2 all T_b c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))) # label(fact_Id__on__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2723 (all V_u_2 all V_l_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)))) # label(fact_finite__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2724 (all V_A_2 all T_b c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2))) # label(fact_Id__on__def_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2725 (all V_k_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) -> c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_greaterThanLessThan__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2726 (all T_b c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) # label(fact_Id__on__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2727 (all V_B_2 all V_A_2 all T_b hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Image__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2728 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I13_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2729 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I12_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2730 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)))) # label(fact_Int__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2731 (all V_A_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2))) <-> V_x_2 = V_y_2 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)))) # label(fact_Id__on__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2732 (all V_A_2 all T_b all V_b_2 all V_a_2 (V_a_2 = V_b_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2)))))) # label(fact_Id__on__eqI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2733 (all V_M_2 all V_n_2 all T_b hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_UN__le__eq__Un0) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2734 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I19_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2735 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)))) # label(fact_ivl__disj__un_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2736 (all V_u_2 all V_l_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)))) # label(fact_finite__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2737 (all V_u_2 all V_l_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)))) # label(fact_finite__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2738 (all V_u_2 all V_l_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)))) # label(fact_finite__greaterThanAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2739 (all V_k_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)))) # label(fact_finite__atMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2740 (all V_u_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2741 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)))) # label(fact_ivl__disj__un_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2742 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) <-> V_x_2 = V_y_2))) # label(fact_atMost__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2743 (all V_k_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2)) -> c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_greaterThanAtMost__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2744 (all V_l_2 all V_k_2 all T_b (class_Orderings_Oorder(T_b) -> (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) <-> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))))) # label(fact_greaterThanAtMost__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2745 (all V_l_2 all V_k_2 all T_b (class_Orderings_Oorder(T_b) -> (c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))))) # label(fact_greaterThanAtMost__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2746 (all V_n_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)) # label(fact_atLeast0AtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2747 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I20_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2748 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I14_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2749 (all V_k_2 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) # label(fact_lessThan__Suc__atMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2750 (all V_u_2 all V_l_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) # label(fact_atLeastSucAtMost__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2751 (all V_u_2 hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2)) # label(fact_card__atMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2752 (all V_k_2 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) # label(fact_atMost__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2753 (all V_k_2 all V_i_2 all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2))))) # label(fact_atMost__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2754 (all V_y_2 all V_x_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))))) # label(fact_atMost__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2755 (all V_u_2 all V_l_2 hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2)) # label(fact_card__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2756 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I22_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2757 (all V_u_2 all V_l_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) # label(fact_atLeastPlusOneAtMost__greaterThanAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2758 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I16_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2759 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)))) # label(fact_Int__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2760 (all V_n_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))))) # label(fact_setsum__atMost__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2761 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2762 (all V_u_2 all V_l_2 hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2))) # label(fact_card__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2763 (all V_d_2 all V_ca_2 all V_b_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)))) # label(fact_Int__atLeastAtMostR1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2764 (all V_d_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)))) # label(fact_Int__atLeastAtMostL1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2765 (all V_u_2 all V_l_2 hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) # label(fact_card__greaterThanAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2766 (all V_k_2 all V_M_2 all V_n_2 all T_b hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2)) # label(fact_UN__le__add__shift) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2767 (all V_u_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2768 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I16_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2769 (all V_Pa_2 all V_n_2 all V_m_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2)))))) # label(fact_setsum__head) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2770 (all V_u_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2))) # label(fact_ivl__disj__un_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2771 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)))) # label(fact_ivl__disj__un_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2772 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)))) # label(fact_ivl__disj__un_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2773 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)))) # label(fact_ivl__disj__un_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2774 (all V_r_2 all V_A_2 all T_b hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) # label(fact_quotient__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2775 (all V_A_2 all V_ca_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2))) -> -(all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x))))) # label(fact_Id__onE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2776 (all V_A_2 all V_r_2 all T_c all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) -> -(all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)))))) # label(fact_ImageE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2777 (all V_r_2 all V_A_2 all T_b (hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_quotient__is__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2778 (all V_r_2 all V_A_2 all T_b (c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_quotient__is__empty2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2779 (all V_r_2 all T_b hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) # label(fact_quotient__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2780 (all V_r_2 all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))))) # label(fact_quotientI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2781 (all V_r_2 all V_x_2 all T_b hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) # label(fact_singleton__quotient) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2782 (all V_b_2 all V_a_2 all V_x_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))))) # label(fact_equiv__class__nondisjoint) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2783 (all V_a_2 all V_b_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)))))) # label(fact_subset__equiv__class) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2784 (all V_r_2 all V_A_2 all V_X_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> -(all B_x (V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) -> -hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)))))) # label(fact_quotientE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2785 (all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2)) # label(fact_Union__quotient) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2786 (all V_a_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_equiv__class__self) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2787 (all V_Y_2 all V_X_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> V_X_2 = V_Y_2 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_quotient__disj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2788 (all V_b_2 all V_a_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_equiv__class__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2789 (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_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) -> (V_X_2 = V_Y_2 <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))))))))) # label(fact_quotient__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2790 (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_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),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].
% 6.16/6.14 2791 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) <-> hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))))) # label(fact_equiv__class__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2792 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) -> (hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))))))) # label(fact_eq__equiv__class__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2793 (all V_A_2 all V_b_2 all V_a_2 all V_r_2 all T_b (hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) -> (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)))))) # label(fact_eq__equiv__class) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2794 (all V_b_2 all V_a_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_equiv__class__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2795 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) -> (hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))))))) # label(fact_eq__equiv__class__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2796 (all V_a2_2 all V_a1_2 all V_f_2 all T_d all V_r2_2 all V_A2_2 all T_c all V_r1_2 all V_A1_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) -> (c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) -> (c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2)) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2))))))) # label(fact_UN__equiv__class2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2797 (all V_a_2 all V_f_2 all T_c all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2))))) # label(fact_UN__equiv__class) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2798 (all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) <-> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)))) # label(fact_equivp__equiv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2799 (all V_z_2 all V_y_2 all V_x_2 all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) -> (hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) -> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)))))) # label(fact_equivp__transp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2800 (all V_y_2 all V_x_2 all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) -> (hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2))))) # label(fact_equivp__symp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2801 (all V_x_2 all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) -> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)))) # label(fact_equivp__reflp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2802 (all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) <-> (all B_x all B_y (hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) <-> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y))))) # label(fact_equivp__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2803 (all T_b c_Equiv__Relations_Oequivp(T_b,c_fequal)) # label(fact_identity__equivp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2804 (all V_a_2 all V_f_2 all V_r2_2 all T_d all T_c all V_r1_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) -> (c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)))))) # label(fact_congruent2__implies__congruent) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2805 (all V_z2_2 all V_y2_2 all V_z1_2 all V_y1_2 all V_f_2 all V_r2_2 all V_r1_2 all T_d all T_c all T_b (c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2)) -> hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2))))) # label(fact_congruent2D) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2806 (all V_z_2 all V_y_2 all V_f_2 all V_r_2 all T_c all T_b (c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2)) -> hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2)))) # label(fact_congruentD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2807 (all V_a_2 all V_f_2 all T_d all V_r2_2 all V_A2_2 all T_c all V_r1_2 all V_A1_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) -> (c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) -> (c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2)) -> c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2))))))) # label(fact_congruent2__implies__congruent__UN) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2808 (all V_Y_2 all V_X_2 all V_f_2 all T_c all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) -> (hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> (all B_y (hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) -> (hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))))))) -> V_X_2 = V_Y_2))))))) # label(fact_UN__equiv__class__inject) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2809 (all V_B_2 all V_X2_2 all V_X1_2 all V_f_2 all T_d all V_r2_2 all V_A2_2 all T_c all V_r1_2 all V_A1_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) -> (c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2) -> (c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2))) -> ((all B_x1 (hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) -> (all B_x2 (hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)))))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2))))))))) # label(fact_UN__equiv__class__type2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2810 (all V_B_2 all V_X_2 all V_f_2 all T_c all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> (c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2))))))) # label(fact_UN__equiv__class__type) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2811 (all V_r_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2) -> hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))) # label(fact_card__quotient__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2812 (all V_n_2 all V_x_2 all T_b (class_Fields_Ofield(T_b) -> (V_x_2 != c_Groups_Oone__class_Oone(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b)))))) # label(fact_geometric__sum) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2813 (all V_u_2 all V_l_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)))) # label(fact_finite__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2814 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) -> (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) <-> V_a_2 = V_ca_2 & V_b_2 = V_d_2))))) # label(fact_atLeastLessThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2815 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) -> V_a_2 = V_ca_2))))) # label(fact_atLeastLessThan__inj_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2816 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) -> V_b_2 = V_d_2))))) # label(fact_atLeastLessThan__inj_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2817 (all V_Pa_2 all V_n_2 ((exists B_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) & hBOOL(hAPP(V_Pa_2,B_m)))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_ex__nat__less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2818 (all V_Pa_2 all V_n_2 ((all B_m (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) -> hBOOL(hAPP(V_Pa_2,B_m)))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_all__nat__less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2819 (all V_k_2 all V_j_2 all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) -> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))))) # label(fact_atLeastLessThan__add__Un) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2820 (all V_u_2 all V_l_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) # label(fact_atLeastLessThanSuc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2821 (all V_m_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) # label(fact_atLeastLessThan0) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2822 (all V_n_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) # label(fact_atLeast0LessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2823 (all V_k_2 all V_A_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) -> V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) # label(fact_subset__card__intvl__is__intvl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2824 (all V_u_2 all V_l_2 hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2)) # label(fact_card__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2825 (all V_a_2 all V_b_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) -> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_atLeastLessThan__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2826 (all V_b_2 all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) <-> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))))) # label(fact_atLeastLessThan__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2827 (all V_b_2 all V_a_2 all T_b (class_Orderings_Oorder(T_b) -> (hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))))) # label(fact_atLeastLessThan__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2828 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))))) # label(fact_atLeastLessThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2829 (all V_n_2 all V_m_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_setsum__shift__bounds__Suc__ivl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2830 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2))))) # label(fact_ivl__disj__un_I17_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2831 (all V_n_2 all V_k_2 all V_m_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)))) # label(fact_setsum__shift__bounds__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2832 (all V_m_2 all V_n_2 all V_i_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2)))) # label(fact_ivl__diff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2833 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I11_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2834 (all V_u_2 all V_l_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) # label(fact_atLeastSucLessThan__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2835 (all V_h_2 all T_c all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) -> (c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2)))))) # label(fact_finite__vimageI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2836 (all V_f_2 all V_p_2 all V_n_2 all V_m_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)))))) # label(fact_setsum__add__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2837 (all V_f_2 all V_p_2 all V_n_2 all V_m_2 all T_b (class_Groups_Oab__group__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) -> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)))))) # label(fact_setsum__diff__nat__ivl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2838 (all V_m_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) # label(fact_atLeastLessThan__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2839 (all V_x_2 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg))) # label(fact_Rep__Integ) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2840 (all V_A_2 all T_b hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)) # label(fact_UN__UN__finite__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2841 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I21_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2842 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I15_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2843 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)))) # label(fact_Int__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2844 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)))) # label(fact_ivl__disj__un_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2845 (all V_u_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2846 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I9_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2847 (all V_k_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))))) # label(fact_setsum__shift__lb__Suc0__0__upt) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2848 (all V_f_2 all V_n_2 all V_m_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2)))))) # label(fact_setsum__head__upt__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2849 (all V_n_2 all V_m_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_atLeastLessThanSuc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2850 (all V_f_2 all V_m_2 all V_n_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2))))) # label(fact_setsum__op__ivl__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2851 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2))))) # label(fact_ivl__disj__un_I15_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2852 (all V_a_2 all V_A_2 all V_r_2 all T_b (c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2))))) # label(fact_quotient__diff1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2853 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)))) # label(fact_ivl__disj__un_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2854 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)))) # label(fact_ivl__disj__un_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2855 (all V_u_2 all V_m_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2))))) # label(fact_ivl__disj__un_I18_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2856 (all V_A_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2))) # label(fact_inj__uminus) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2857 (all V_f_2 all T_c all T_b c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_inj__on__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2858 (all T_b c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_inj__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2859 (all V_u_2 all V_l_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)))) # label(fact_finite__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2860 (all V_N_2 all V_k_2 c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2)) # label(fact_inj__on__add__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2861 (all V_N_2 c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2)) # label(fact_inj__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2862 (all T_b (class_Nat_Osemiring__char__0(T_b) -> c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_inj__of__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2863 (all V_A_2 all T_c all T_b c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2)) # label(fact_swap__inj__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2864 (all V_u_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)))) # label(fact_finite__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2865 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) -> (hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) -> B_x = B_xa))))))) # label(fact_inj__on__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2866 (all V_u_2 all V_l_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) # label(fact_atLeastLessThanPlusOne__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2867 (all V_u_2 hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2)) # label(fact_card__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2868 (all V_u_2 all V_l_2 hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) # label(fact_card__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2869 (all V_u_2 all V_l_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) # label(fact_atLeastPlusOneLessThan__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2870 (all V_A_2 all T_b c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2)) # label(fact_inj__on__id2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2871 (all V_Y_2 all T_b hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2) # label(fact_vimage__ident) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2872 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) -> V_x_2 = V_y_2))))) # label(fact_inj__onD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2873 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) -> (hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) <-> V_x_2 = V_y_2))))) # label(fact_inj__on__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2874 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (V_x_2 != V_y_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) -> hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)))))) # label(fact_inj__on__contraD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2875 (all V_A_2 all V_B_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)))) # label(fact_subset__inj__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2876 (all V_y_2 all V_x_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_inj__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2877 (all V_y_2 all V_x_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) -> V_x_2 = V_y_2))) # label(fact_injD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2878 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_inj__on__Int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2879 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) # label(fact_inj__on__diff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2880 (all T_d all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_inj__fun) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2881 (all V_a_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_inj__vimage__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2882 (all V_B_2 all V_k_2 all V_A_2 all T_b ((all B_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))))) # label(fact_UN__finite2__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2883 (all V_B_2 all V_k_2 all V_A_2 all T_b ((all B_n hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) # label(fact_UN__finite2__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2884 (all V_y_2 all V_x_2 all T_c all T_b c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)) # label(fact_The__split__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2885 (all V_Pa_2 all T_c all T_b c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) # label(fact_split__paired__The) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2886 (all V_A_2 all V_z_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2))) # label(fact_fold__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2887 (all V_n_2 all V_m_2 c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2))) # label(fact_divmod__nat__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2888 (all V_A_2 all V_f_2 all T_b hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2))) # label(fact_fold1__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2889 (all V_Pa_2 all T_c all T_b c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c)))) # label(fact_The__split) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2890 (all V_X_2 all T_b c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_the__elem__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2891 (all V_b_2 all V_A_2 all T_b ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) -> c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) -> c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_flat__lub__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.14 2892 (all V_C_2 all V_A_2 all T_b ((all B_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)))) # label(fact_UN__finite__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2893 (all V_y_2 all V_x_2 all V_A_2 all V_Abs_2 all V_Rep_2 all T_c all T_b (c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) -> (hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) <-> V_x_2 = V_y_2))))) # label(fact_type__definition_OAbs__inject) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2894 (all V_y_2 all V_A_2 all V_Abs_2 all V_Rep_2 all T_c all T_b (c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) -> hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2))) # label(fact_type__definition_OAbs__inverse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2895 (all V_x_2 all V_A_2 all V_Abs_2 all V_Rep_2 all T_c all T_b (c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) -> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)))) # label(fact_type__definition_ORep) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2896 (all V_x_2 all V_A_2 all V_Abs_2 all V_Rep_2 all T_c all T_b (c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) -> hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2)) # label(fact_type__definition_ORep__inverse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2897 (all V_y_2 all V_x_2 all V_A_2 all V_Abs_2 all V_Rep_2 all T_c all T_b (c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) -> (hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) <-> V_x_2 = V_y_2))) # label(fact_type__definition_ORep__inject) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2898 (all V_x_2 all V_y_2 all V_ca_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) -> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) -> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) -> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) # label(fact_image__minus__const__atLeastLessThan__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2899 (all V_u_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) -> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))))) # label(fact_image__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2900 (all V_n_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_atMost__Int__atLeast) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2901 (all T_b all V_A_2 all T_c all V_x_2 all V_f_2 all V_b_2 (V_b_2 = hAPP(V_f_2,V_x_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))))) # label(fact_image__eqI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2902 (all V_h_2 all T_c all V_F_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))))) # label(fact_finite__imageI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2903 (all V_g_2 all V_f_2 all T_d all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) # label(fact_range__composition) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2904 (all V_x_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)))) # label(fact_image__uminus__atLeast) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2905 (all V_x_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)))) # label(fact_image__uminus__atMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2906 (all V_B_2 all V_a_2 all V_f_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))) # label(fact_image__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2907 (all V_A_2 all V_f_2 all T_c all T_b (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_empty__is__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2908 (all V_f_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_image__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2909 (all V_A_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_image__is__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2910 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) <-> V_x_2 = V_y_2))) # label(fact_atLeast__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2911 (all V_B_2 all V_A_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))))) # label(fact_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2912 (all V_B_2 all V_A_2 (V_A_2 = V_B_2 <-> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) # label(fact_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2913 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2 -> hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2))) # label(fact_image__Pow__surj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2914 (all V_A_2 all V_g_2 all T_d all V_f_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2)) # label(fact_image__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2915 (all V_f_2 all V_B_2 all T_d all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2)) # label(fact_INT__extend__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2916 (all V_B_2 all V_A_2 all V_f_2 all T_d all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2))) # label(fact_INT__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2917 (all V_B_2 all V_A_2 all V_f_2 all T_d all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2))) # label(fact_UN__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2918 (all V_B_2 all V_A_2 all T_d all V_f_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2))) # label(fact_image__UN) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2919 (all V_f_2 all V_B_2 all T_d all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2)) # label(fact_UN__extend__simps_I10_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2920 (all V_Y_2 all T_b hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2) # label(fact_image__ident) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2921 (all V_f_2 all T_c all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))))) # label(fact_image__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2922 (all V_A_2 all V_f_2 all T_c all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) <-> (exists B_AA (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA))))) # label(fact_subset__image__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2923 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))))) # label(fact_image__Pow__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2924 (all V_B_2 all V_A_2 all V_f_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))) # label(fact_image__Un) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2925 (all V_A_2 all V_f_2 all T_c all V_z_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) & V_z_2 = hAPP(V_f_2,B_x))))) # label(fact_image__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2926 (all V_f_2 all T_c all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))))) # label(fact_imageI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2927 (all T_c all V_f_2 all V_b_2 all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (V_b_2 = hAPP(V_f_2,V_x_2) -> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))))) # label(fact_rev__image__eqI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2928 (all V_f_2 all T_c all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) # label(fact_insert__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2929 (all T_c all T_b all V_x_2 all V_f_2 all V_b_2 (V_b_2 = hAPP(V_f_2,V_x_2) -> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))))) # label(fact_range__eqI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2930 (all T_c all V_x_2 all V_f_2 all T_b hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))) # label(fact_rangeI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2931 (all V_f_2 all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))))) # label(fact_finite__surj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2932 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))))) # label(fact_image__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2933 (all V_A_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) -> (c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))))) # label(fact_finite__imageD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2934 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_image__diff__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2935 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) <-> V_A_2 = V_B_2))) # label(fact_inj__image__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2936 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> (hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) <-> V_A_2 = V_B_2))) # label(fact_inj__on__Un__image__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2937 (all V_y_2 all V_x_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)))) # label(fact_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2938 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) # label(fact_card__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2939 (all V_A_2 all V_f_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2))) # label(fact_image__vimage__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2940 (all V_A_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2)) # label(fact_surj__image__vimage__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2941 (all V_j_2 all V_i_2 hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2))) # label(fact_image__Suc__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2942 (all V_A_2 all V_Abs_2 all V_Rep_2 all T_c all T_b (c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) -> hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_type__definition_OAbs__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2943 (all V_A_2 all V_Abs_2 all V_Rep_2 all T_c all T_b (c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) -> hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2)) # label(fact_type__definition_ORep__range) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2944 (all V_j_2 all V_i_2 hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2))) # label(fact_image__Suc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2945 (all V_y_2 all V_x_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)))) # label(fact_image__uminus__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2946 (all V_A_2 all V_B_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))))) # label(fact_inj__on__strict__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2947 (all V_ca_2 all T_c all T_b all V_A_2 ((V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) & (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) # label(fact_image__constant__conv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2948 (all V_f_2 all T_d all V_g_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))))) # label(fact_finite__range__imageI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2949 (all V_A_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))))) # label(fact_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2950 (all V_A_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) & class_Groups_Ocomm__monoid__mult(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)))) # label(fact_transfer__nat__int__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2951 (all V_j_2 all V_i_2 all V_k_2 hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) # label(fact_image__add__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2952 (all V_j_2 all V_i_2 all V_k_2 hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) # label(fact_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2953 (all V_B_2 all V_A_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))))) # label(fact_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2954 (all V_S_2 all V_f_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2))) # label(fact_image__Union) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2955 (all V_b_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) <-> (exists B_x (V_b_2 = hAPP(V_f_2,B_x) & (all B_y (V_b_2 = hAPP(V_f_2,B_y) -> B_y = B_x))))))) # label(fact_range__ex1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2956 (all V_A_2 all V_a_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))))) # label(fact_inj__image__mem__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2957 (all V_A_H_2 all T_c all T_b all V_A_2 (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((exists B_f (c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)))) <-> (exists B_g hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2)))) # label(fact_inj__on__iff__surj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2958 (all V_f_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2))) -> c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)))) # label(fact_finite__surj__inj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2959 (all V_f_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2)) -> (c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) -> hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2)))) # label(fact_endo__inj__surj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2960 (all V_f_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) -> (hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_finite__UNIV__surj__inj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2961 (all V_f_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) -> (c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_finite__UNIV__inj__surj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2962 (all V_f_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))))) # label(fact_card__image__le) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2963 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_inj__image__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2964 (all V_B_2 all V_A_2 all V_C_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))))) # label(fact_inj__on__image__Int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2965 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))) # label(fact_image__Int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2966 (all V_f_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)))) # label(fact_eq__card__imp__inj__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2967 (all V_f_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) <-> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))) # label(fact_inj__on__iff__eq__card) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2968 (all V_B_2 all V_A_2 all V_C_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))))) # label(fact_inj__on__image__set__diff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2969 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))) # label(fact_image__set__diff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2970 (all V_A_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) -> -c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2))) # label(fact_pigeonhole) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2971 (all V_F_2 all V_h_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) -> (hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))))) # label(fact_finite__vimageD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2972 (all V_k_2 all V_i_2 all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2))))) # label(fact_atLeast__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2973 (all V_A_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))))) # label(fact_surj__Compl__image__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2974 (all V_A_2 all V_B_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))))) # label(fact_vimage__subsetD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2975 (all V_A_2 all V_f_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) # label(fact_image__vimage__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2976 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2)) # label(fact_inj__vimage__image__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2977 (all V_y_2 all V_x_2 all T_b (class_Orderings_Oorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))))) # label(fact_atLeast__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2978 (all V_y_2 all V_x_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)))) # label(fact_image__uminus__greaterThanAtMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2979 (all V_y_2 all V_x_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)))) # label(fact_image__uminus__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2980 (all V_ca_2 all T_c all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) # label(fact_image__constant) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2981 (all V_A_2 all V_f_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_image__eq__UN) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2982 (all V_A_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) & class_Groups_Ocomm__monoid__mult(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)))) # label(fact_transfer__nat__int__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2983 (all V_k_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) # label(fact_Compl__atLeast) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2984 (all V_k_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) # label(fact_Compl__lessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2985 (all V_A_2 (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))))) # label(fact_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2986 (all V_A_2 hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) # label(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2987 (all V_g_2 all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) -> (c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))))))) # label(fact_card__bij__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2988 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))))) # label(fact_inj__image__Compl__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2989 (all V_A_2 all V_B_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))))) # label(fact_vimage__subsetI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2990 (all V_f_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2))) # label(fact_image__eq__fold__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2991 (all V_n_2 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)))) # label(fact_lessThan__Suc__eq__insert__0) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2992 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)))) # label(fact_ivl__disj__un_I14_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2993 (all V_u_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I8_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2994 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2))) # label(fact_Int__atLeastAtMostL2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2995 (all V_d_2 all V_ca_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2))) # label(fact_Int__atLeastAtMostR2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2996 (all V_A_2 all V_a_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) <-> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) & -hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_inj__on__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2997 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) <-> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_inj__on__Un) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2998 (all V_u_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 2999 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))))))) # label(fact_card__inj__on__le) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3000 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> ((exists B_f (c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))))))) # label(fact_inj__on__iff__card__le) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3001 (all V_k_2 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_atLeast__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3002 (all V_S_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)))))) # label(fact_minus__Min__eq__Max) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3003 (all V_S_2 all T_b (class_Groups_Olinordered__ab__group__add(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)))))) # label(fact_minus__Max__eq__Min) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3004 (all V_n_2 all V_m_2 (c_Nat__Transfer_Ois__nat(V_m_2) -> (c_Nat__Transfer_Ois__nat(V_n_2) -> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2)))))) # label(fact_SetInterval_Otransfer__int__nat__set__functions) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3005 (all V_j_2 all V_B_2 all V_A_2 all T_d all V_C_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)))) -> (hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2)) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)))))) # label(fact_image__INT) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3006 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)))) # label(fact_ivl__disj__un_I12_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3007 (all V_y_2 all V_f_2 all T_c all V_A_2 all V_x_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) # label(fact_fun__upd__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3008 (all V_x_2 all V_f_2 all T_c all T_b c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2) # label(fact_fun__upd__triv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3009 (all V_f_2 all T_d all V_A_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))))) # label(fact_pair__imageI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3010 (all V_k_2 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)) # label(fact_atLeast__Suc__greaterThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3011 (all V_A_2 all T_b -(exists B_f hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2))) # label(fact_Cantors__paradox) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3012 (all T_b all T_c all V_y_2 all V_x_2 all V_f_2 (hAPP(V_f_2,V_x_2) = V_y_2 -> c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2)) # label(fact_fun__upd__idem) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3013 (all V_y_2 all V_f_2 all T_c all T_b all V_x_2 all V_z_2 (V_z_2 != V_x_2 -> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2))) # label(fact_fun__upd__other) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3014 (all V_d_2 all V_b_2 all V_m_2 all T_c all T_b all V_ca_2 all V_a_2 (V_a_2 != V_ca_2 -> c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2))) # label(fact_fun__upd__twist) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3015 (all V_y_2 all V_f_2 all T_c all T_b all V_x_2 all V_z_2 ((V_z_2 = V_x_2 -> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2) & (V_z_2 != V_x_2 -> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2)))) # label(fact_fun__upd__apply) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3016 (all V_y_2 all V_x_2 all V_f_2 all T_b all T_c hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2) # label(fact_fun__upd__same) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3017 (all V_z_2 all V_y_2 all V_x_2 all V_f_2 all T_c all T_b c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2)) # label(fact_fun__upd__upd) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3018 (all V_y_2 all V_x_2 all V_f_2 all T_c all T_b (c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2 <-> hAPP(V_f_2,V_x_2) = V_y_2)) # label(fact_fun__upd__idem__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3019 (all V_b_2 all V_f_2 all T_c all T_b all V_a_2 all V_x_2 ((V_x_2 = V_a_2 -> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2) & (V_x_2 != V_a_2 -> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2)))) # label(fact_fun__upd__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3020 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) <-> V_x_2 = V_y_2))) # label(fact_greaterThan__eq__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3021 (all V_R_2 all T_b hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2))) # label(fact_Field__Union) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3022 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2))) # label(fact_UNION__eq__Union__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3023 (all V_A_2 all V_B_2 all T_c all T_b c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Union__image__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3024 (all V_A_2 all V_B_2 all T_c all T_b c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) # label(fact_Inter__image__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3025 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2))) # label(fact_INTER__eq__Inter__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3026 (all V_B_2 all V_A_2 hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2)))) # label(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3027 (all V_A_2 hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2) # label(fact_transfer__int__nat__set__return__embed) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3028 (all V_k_2 all V_i_2 all T_b (class_Orderings_Oord(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2))))) # label(fact_greaterThan__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3029 (all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))))) # label(fact_greaterThan__subset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3030 (all V_B_2 all V_A_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2)))) # label(fact_Un__Union__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3031 (all V_B_2 all V_A_2 all V_C_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2)))) # label(fact_Int__Inter__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3032 (all V_A_2 all V_a_2 all T_b hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2)))) # label(fact_Pow__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3033 (all V_k_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) # label(fact_Compl__atMost) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3034 (all V_k_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) # label(fact_Compl__greaterThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3035 (all V_x_2 all V_y_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (-hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) -> c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2)))) # label(fact_inj__on__fun__updI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3036 (all V_n_2 all V_m_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))) # label(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3037 (all V_u_2 all V_l_2 hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) # label(fact_image__add__int__atLeastLessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3038 (all V_B_2 all V_A_2 hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2)))) # label(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3039 (all V_u_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I7_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3040 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)))) # label(fact_ivl__disj__un_I11_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3041 (all V_x_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)))) # label(fact_image__uminus__greaterThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3042 (all V_x_2 all T_b (class_Groups_Oordered__ab__group__add(T_b) -> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)))) # label(fact_image__uminus__lessThan) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3043 (all V_u_2 all V_l_2 all T_b (class_Orderings_Oorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_ivl__disj__int_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3044 (all V_k_2 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_greaterThan__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3045 (all V_n_2 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))) # label(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3046 (all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2))) # label(fact_ivl__disj__un_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3047 (all V_u_2 all V_l_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)))) # label(fact_ivl__disj__un_I13_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3048 (all V_f_2 all V_A_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) & class_Groups_Ocomm__monoid__mult(T_b) -> (c_Nat__Transfer_Onat__set(V_A_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))))) # label(fact_transfer__int__nat__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3049 (all V_Q_2 all V_Pa_2 all V_Q_H_2 all V_c0_2 all V_P_H_2 all V_Ga_2 all T_c all V_U_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2)) -> ((all B_p (c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) -> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_Pa_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))))) -> (c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2)) -> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_Pa_2)),V_c0_2)),V_Q_2)),V_U_2)))))) # label(fact_finite__pointwise) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3050 (all V_B_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)))))) # label(fact_the__inv__into__into) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3051 (all V_B_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (c_Nat__Transfer_Onat__set(V_B_2) -> (V_A_2 = V_B_2 <-> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))))) # label(fact_transfer__int__nat__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3052 (all V_B_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (c_Nat__Transfer_Onat__set(V_B_2) -> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3053 (all V_B_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (c_Nat__Transfer_Onat__set(V_B_2) -> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3054 (all V_S_2 (c_Nat__Transfer_Onat__set(V_S_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)))))) # label(fact_nat__set__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3055 (all V_C_2 c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3056 (all V_y_2 all V_x_2 (c_Nat__Transfer_Ois__nat(V_x_2) -> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)))) # label(fact_SetInterval_Otransfer__int__nat__set__function__closures) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3057 (all V_x_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) -> c_Nat__Transfer_Ois__nat(V_x_2)))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3058 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hAPP(V_f_2,V_x_2) = V_y_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2)))) # label(fact_the__inv__into__f__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3059 (all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2))) # label(fact_the__inv__into__f__f) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3060 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) # label(fact_inj__on__the__inv__into) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3061 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2)) # label(fact_the__inv__into__onto) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3062 (all V_x_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2)) # label(fact_the__inv__f__f) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3063 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) -> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)))) # label(fact_SetInterval_Otransfer__nat__int__set__function__closures) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3064 (all V_x_2 all V_f_2 all V_A_2 all T_c all T_b hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2)))) # label(fact_the__inv__into__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3065 (all V_B_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (c_Nat__Transfer_Onat__set(V_B_2) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3066 (all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2)) # label(fact_transfer__nat__int__set__return__embed) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3067 (all V_x_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))))) # label(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3068 (all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)))))) # label(fact_transfer__int__nat__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3069 (all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3070 (all V_y_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) -> hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2))) # label(fact_f__the__inv__into__f) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3071 (all V_A_2 all V_x_2 (c_Nat__Transfer_Ois__nat(V_x_2) -> (c_Nat__Transfer_Onat__set(V_A_2) -> (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))))))) # label(fact_transfer__int__nat__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3072 (all V_B_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (c_Nat__Transfer_Onat__set(V_B_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))))))) # label(fact_transfer__int__nat__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3073 (all V_B_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (c_Nat__Transfer_Onat__set(V_B_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))))))) # label(fact_transfer__int__nat__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3074 (all V_f_2 all V_A_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) & class_Groups_Ocomm__monoid__mult(T_b) -> (c_Nat__Transfer_Onat__set(V_A_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))))) # label(fact_transfer__int__nat__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3075 (all V_B_2 all V_A_2 (c_Nat__Transfer_Onat__set(V_A_2) -> (c_Nat__Transfer_Onat__set(V_B_2) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3076 (all V_N_2 all V_h_2 all T_b (class_Orderings_Olinorder(T_b) -> ((all B_x all B_y hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))))))) # label(fact_min__max_OSup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3077 (all V_N_2 all V_h_2 all T_b (class_Orderings_Olinorder(T_b) -> ((all B_x all B_y hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))))))) # label(fact_min__max_OInf__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3078 (all V_N_2 all V_h_2 all T_b (class_Orderings_Olinorder(T_b) -> ((all B_x all B_y hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))))))) # label(fact_Max_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3079 (all V_N_2 all V_h_2 all T_b (class_Orderings_Olinorder(T_b) -> ((all B_x all B_y hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))))))) # label(fact_Min_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3080 (all V_N_2 all V_h_2 all T_b (class_Lattices_Olattice(T_b) -> ((all B_x all B_y hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))))))) # label(fact_Inf__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3081 (all V_N_2 all V_h_2 all T_b (class_Lattices_Olattice(T_b) -> ((all B_x all B_y hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))))))) # label(fact_Sup__fin_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3082 (all V_N_2 all V_h_2 all T_b (class_Lattices_Oab__semigroup__idem__mult(T_b) -> ((all B_x all B_y hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))))))) # label(fact_hom__fold1__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3083 (all V_Q_2 all V_ca_2 all V_Ga_2 all T_b all V_Pa_2 ((all B_Z all B_s (hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))))) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))))) # label(fact_escape) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3084 (all V_g_2 all V_f_2 all V_B_2 all V_A_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) & class_Groups_Ocomm__monoid__mult(T_b) -> (V_A_2 = V_B_2 -> (c_Nat__Transfer_Onat__set(V_B_2) -> ((all B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) -> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2)))))) # label(fact_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3085 (all V_g_2 all V_f_2 all V_B_2 all V_A_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) & class_Groups_Ocomm__monoid__mult(T_b) -> (V_A_2 = V_B_2 -> (c_Nat__Transfer_Onat__set(V_B_2) -> ((all B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) -> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2)))))) # label(fact_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3086 (all V_x_2 all V_r_2 all T_b (hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))))) # label(fact_accp__acc__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3087 (all V_a2_2 all V_a1_2 all V_R_2 all T_b (c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) -> (exists B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)))))))) # label(fact_max__extp_Oequations) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3088 (all V_R2_2 all V_R1_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))))) # label(fact_acc__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.15 3089 (all V_a_2 all V_r_2 all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))))) # label(fact_acc__downward) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3090 (all V_r_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))))))) # label(fact_acc_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3091 (all V_f_2 all T_c all T_b all V_S_2 (V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) -> ((all B_A (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A))) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2))))) # label(fact_inj__on__Inter) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3092 (all V_A_2 all V_g_2 all V_f_2 all T_c all T_b all T_d hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2)))) # label(fact_image__split__eq__Sigma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3093 (all V_N_2 all V_h_2 all V_F_2 all V_f_2 all T_b (c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) -> ((all B_x all B_y hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))))))) # label(fact_folding__one__idem_Ohom__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3094 (all V_B_2 all V_b_2 all T_c all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))))) # label(fact_SigmaI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3095 (all V_B_2 all V_X_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2))) # label(fact_Sigma__Union) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3096 (all V_B_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) # label(fact_Sigma__empty1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3097 (all V_B_2 all V_A_2 all V_I_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2))) # label(fact_Sigma__Diff__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3098 (all V_C_2 all V_B_2 all V_A_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)))) # label(fact_Times__Diff__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3099 (all V_C_2 all V_J_2 all V_I_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2))) # label(fact_Sigma__Diff__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3100 (all V_B_2 all V_A_2 all T_c all V_C_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) -> (hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) <-> V_A_2 = V_B_2))) # label(fact_Times__eq__cancel2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3101 (all V_B_2 all V_A_2 all T_c all T_b hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) # label(fact_card__cartesian__product) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3102 (all V_A_2 all V_B_2 all V_f_2 all T_d all T_c all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))))) # label(fact_setsum__cartesian__product) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3103 (all V_B_2 all V_A_2 all T_c all T_b (hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) <-> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_Times__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3104 (all V_A_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) # label(fact_Sigma__empty2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3105 (all V_A_2 all T_c all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) # label(fact_Compl__Times__UNIV1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3106 (all V_A_2 all T_c all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) # label(fact_Compl__Times__UNIV2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3107 (all V_A_2 all V_B_2 all V_f_2 all T_d all T_c all T_b (class_Groups_Ocomm__monoid__mult(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))))) # label(fact_setprod__cartesian__product) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3108 (all V_C_2 all V_J_2 all V_I_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2))) # label(fact_Sigma__Un__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3109 (all V_C_2 all V_B_2 all V_A_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)))) # label(fact_Times__Un__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3110 (all V_B_2 all V_A_2 all V_I_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2))) # label(fact_Sigma__Un__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3111 (all V_B_2 all V_A_2 all T_b all T_c hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) # label(fact_swap__product) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3112 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))))) # label(fact_finite__cartesian__product) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3113 (all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))))) # label(fact_equiv__type) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3114 (all V_B_2 all V_A_2 all V_I_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2))) # label(fact_Sigma__Int__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3115 (all V_C_2 all V_B_2 all V_A_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)))) # label(fact_Times__Int__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3116 (all V_C_2 all V_J_2 all V_I_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2))) # label(fact_Sigma__Int__distrib1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3117 (all V_A_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))) # label(fact_Id__on__subset__Times) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3118 (all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) # label(fact_UNIV__Times__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3119 (all V_B_2 all V_A_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) -> -(hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> -hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))))) # label(fact_SigmaE2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3120 (all V_B_2 all V_A_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))))) # label(fact_SigmaD2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3121 (all V_B_2 all V_A_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)))) # label(fact_SigmaD1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3122 (all V_B_2 all V_A_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))))) # label(fact_mem__Sigma__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3123 (all V_A_2 all V_x_2 all T_c all T_b hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2)) # label(fact_card__cartesian__product__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3124 (all V_B_2 all V_A_2 all T_c all V_C_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Times__subset__cancel2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3125 (all V_C_2 all V_B_2 all V_A_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)))) # label(fact_Image__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3126 (all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))))) # label(fact_finite__cartesian__productD2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3127 (all V_B_2 all V_A_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))))) # label(fact_finite__cartesian__productD1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3128 (all V_A_2 all T_c all T_b all V_B_2 ((V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) & (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2))) # label(fact_fst__image__times) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3129 (all V_B_2 all T_c all T_b all V_A_2 ((V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) & (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2))) # label(fact_snd__image__times) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3130 (all V_B_2 all V_b_2 all V_A_2 all V_a_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))) # label(fact_insert__times__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3131 (all V_X_2 all V_r_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)))))) # label(fact_finite__equiv__class) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3132 (all V_F_2 all V_E_2 all V_B_2 all V_A_2 all T_c all T_b all T_e all T_d hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2)))) # label(fact_UN__Times__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3133 (all V_B_2 all V_A_2 all T_c all T_b hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))))) # label(fact_Sigma__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3134 (all V_r_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))))) # label(fact_finite__quotient) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3135 (all V_A_2 all V_I_2 all T_c all T_b exists B_f (c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))))) # label(fact_Ex__inj__on__UNION__Sigma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3136 (all V_g_2 all V_B_2 all T_c all V_A_2 all T_b all T_d (class_Groups_Ocomm__monoid__mult(T_d) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))))) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))))) # label(fact_fold__image__Sigma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3137 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_a (hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))))) # label(fact_finite__SigmaI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3138 (all V_f_2 all V_B_2 all T_c all V_A_2 all T_b all T_d (class_Groups_Ocomm__monoid__mult(T_d) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))))) # label(fact_setprod__Sigma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3139 (all V_f_2 all V_B_2 all T_c all V_A_2 all T_b all T_d (class_Groups_Ocomm__monoid__add(T_d) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))))) # label(fact_setsum__Sigma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3140 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))))) -> hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2)))) # label(fact_card__SigmaI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3141 (all V_B_2 all V_A_2 all V_ca_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) -> -(all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> (all B_y (hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) -> V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y))))))) # label(fact_SigmaE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3142 (all V_g_2 all T_d all T_e all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))))) # label(fact_map__pair__surj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3143 (all V_B_2 all V_g_2 all T_e all T_d all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2) -> c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2)))))) # label(fact_map__pair__inj__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3144 (all V_g_2 all V_f_2 all T_e all T_d all V_R_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))))) # label(fact_map__pair__imageI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3145 (all V_x_2 all V_g_2 all V_f_2 all T_e all T_d all T_c all T_b hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))) # label(fact_fst__map__pair) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3146 (all V_b_2 all V_a_2 all V_g_2 all V_f_2 all T_c all T_e all T_b all T_d hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))) # label(fact_map__pair__simp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3147 (all V_z_2 all T_c all T_b hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2) # label(fact_map__pair__ident) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3148 (all V_x_2 all V_g_2 all V_f_2 all T_e all T_d all T_b all T_c hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) # label(fact_snd__prod__fun) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3149 (all V_g_2 all V_f_2 all T_e all T_c all T_d all T_b c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2))) # label(fact_map__pair__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3150 (all V_B_H_2 all V_B_2 all V_g_2 all T_d all T_e all V_A_H_2 all V_A_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 -> (hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2 -> hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2))))) # label(fact_map__pair__surj__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3151 (all V_R_2 all V_g_2 all V_f_2 all T_e all T_d all V_ca_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) -> -(all B_x all B_y (V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)))))) # label(fact_prod__fun__imageE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3152 (all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)))))) # label(fact_refl__on__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3153 (all V_y_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) -> -(all B_x V_y_2 != hAPP(c_Int_ORep__Integ,B_x)))) # label(fact_Rep__Integ__cases) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3154 (all V_A_2 all T_b c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2))) # label(fact_refl__on__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3155 (all T_b c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) # label(fact_refl__on__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3156 (all V_s_2 all V_B_2 all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> (c_Relation_Orefl__on(T_b,V_B_2,V_s_2) -> c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))))) # label(fact_refl__on__Un) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3157 (all V_s_2 all V_B_2 all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> (c_Relation_Orefl__on(T_b,V_B_2,V_s_2) -> c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))))) # label(fact_refl__on__Int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3158 (all V_a_2 all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))))) # label(fact_refl__onD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3159 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))))) # label(fact_refl__onD1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3160 (all V_y_2 all V_x_2 all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))))) # label(fact_refl__onD2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3161 (all V_A_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)))) -> c_Relation_Orefl__on(T_b,V_A_2,V_r_2)))) # label(fact_refl__onI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3162 (all V_Pa_2 all V_y_2 (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) -> ((all B_x hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))) -> hBOOL(hAPP(V_Pa_2,V_y_2))))) # label(fact_Rep__Integ__induct) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3163 (all V_A_2 all V_f_2 all T_d all T_c all T_b all V_I_2 (V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_i (hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) -> c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)))) -> c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))))) # label(fact_inj__on__INTER) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3164 (all V_i_2 all V_M_2 (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) -> hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))))) # label(fact_card__less__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3165 (all V_i_2 all V_M_2 (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) -> hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_card__less) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3166 (all V_i_2 all V_M_2 (-hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) -> hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))))) # label(fact_card__less__Suc2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3167 (all T_b all V_a_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_a_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) # label(fact_CollectI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3168 (all V_Q_2 all V_Pa_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Q_2)))))) # label(fact_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3169 (all V_k_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2))))) # label(fact_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3170 (all V_k_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2))))) # label(fact_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3171 (all V_Q_2 all V_Pa_2 all T_c all T_b hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2)))) # label(fact_Collect__split) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3172 (all V_Q_2 all V_Pa_2 all T_c all T_b hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2))) # label(fact_SetCompr__Sigma__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3173 (all V_Pa_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))) # label(fact_Collect__neg__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3174 (all V_Q_2 all V_Pa_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2))) # label(fact_Collect__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3175 (all V_Q_2 all V_Pa_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2))) # label(fact_Collect__disj__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3176 (all V_Q_2 all V_Pa_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Q_2)))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))))) # label(fact_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3177 (all V_Pa_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2))) # label(fact_vimage__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3178 (all V_Pa_2 all T_b hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2) # label(fact_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3179 (all T_b c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) # label(fact_empty__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3180 (all V_Pa_2 all T_b (hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> (all B_x -hBOOL(hAPP(V_Pa_2,B_x))))) # label(fact_Collect__empty__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3181 (all V_Pa_2 all T_b (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) <-> (all B_x -hBOOL(hAPP(V_Pa_2,B_x))))) # label(fact_empty__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3182 (all V_Pa_2 all V_a_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2))) # label(fact_insert__Collect) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3183 (all T_b c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue))) # label(fact_UNIV__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3184 (all V_Pa_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) -> hBOOL(hAPP(V_Pa_2,V_a_2)))) # label(fact_CollectE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3185 (all V_Pa_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) -> hBOOL(hAPP(V_Pa_2,V_a_2)))) # label(fact_CollectD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3186 (all V_Pa_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) <-> hBOOL(hAPP(V_Pa_2,V_a_2)))) # label(fact_mem__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3187 (all V_A_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2) # label(fact_Collect__mem__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3188 (all V_B_2 all V_a_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) # label(fact_insert__compr) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3189 (all V_B_2 all V_a_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) # label(fact_insert__compr__raw) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3190 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) # label(fact_Un__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3191 (all V_Pa_2 all V_A_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) & hBOOL(hAPP(V_Pa_2,V_x_2)))) # label(fact_Int__Collect) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3192 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) # label(fact_Int__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3193 (all T_b all V_a_2 all V_Pa_2 ((hBOOL(hAPP(V_Pa_2,V_a_2)) -> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) & (-hBOOL(hAPP(V_Pa_2,V_a_2)) -> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_Collect__conv__if) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3194 (all T_b all V_a_2 all V_Pa_2 ((hBOOL(hAPP(V_Pa_2,V_a_2)) -> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) & (-hBOOL(hAPP(V_Pa_2,V_a_2)) -> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_Collect__conv__if2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3195 (all V_a_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3196 (all V_a_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3197 (all V_B_2 all V_A_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))) # label(fact_set__diff__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3198 (all V_Pa_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))))) # label(fact_finite__Collect__not) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3199 (all V_B_2 all V_a_2 all T_b hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2)) # label(fact_insert__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3200 (all V_A_2 all T_b hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))) # label(fact_Compl__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3201 (all V_B_2 all V_f_2 all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2))) # label(fact_vimage__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3202 (all V_Q_2 all V_Pa_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Q_2))) # label(fact_Collect__imp__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3203 (all V_i_2 all V_Pa_2 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))))) # label(fact_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3204 (all V_R_2 all V_f_2 all V_T_2 all T_c all V_S_2 all T_b all T_d (class_Groups_Ocomm__monoid__add(T_d) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2))))) # label(fact_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3205 (all V_S_2 all V_g_2 all V_f_2 all V_Pa_2 all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2)))))) # label(fact_if__image__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3206 (all V_n_2 all V_f_2 all T_b all V_A_2 (V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)))) # label(fact_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3207 (all V_B_2 all V_f_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2)))) # label(fact_setsum__restrict__set_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3208 (all V_f_2 all T_d all V_g_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2))))) # label(fact_setsum__image__gen) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3209 (all V_a_2 all V_r_2 all T_b all T_c hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2))) # label(fact_Image__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3210 (all V_g_2 all V_f_2 all V_Pa_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)))))))) # label(fact_setsum__cases) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3211 (all V_k_2 all V_R_2 all V_T_2 all T_c all V_S_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2)) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)))))) # label(fact_setsum__multicount) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3212 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))))))))) # label(fact_min__max_Oinf__Sup2__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3213 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))))))) # label(fact_min__max_Oinf__Sup1__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3214 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))))) # label(fact_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3215 (all V_A_2 all T_b hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b)))))) # label(fact_Pow__Compl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3216 (all V_A_2 all T_b hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2))) # label(fact_Pow__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3217 (all V_Q_2 all T_c all V_Pa_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))))) <-> (all B_y (hBOOL(hAPP(V_Pa_2,B_y)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))))))) # label(fact_finite__Collect__bounded__ex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3218 (all V_f_2 all T_c all V_Pa_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))))) # label(fact_finite__image__set) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3219 (all T_c all T_b c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) # label(fact_inj__graph) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3220 (all V_Pa_2 c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3221 (all T_b c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b))))) # label(fact_finite__psubset__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3222 (all V_f_2 all V_r_2 all T_b all T_c hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2)))) # label(fact_inv__image__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3223 (all V_Pa_2 hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))))) # label(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3224 (all V_Pa_2 hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat))))) # label(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3225 (all V_k_2 all V_N_2 all T_b (class_Groups_Olinordered__ab__semigroup__add(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))))))) # label(fact_add__Min__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3226 (all V_k_2 all V_N_2 all T_b (class_Groups_Olinordered__ab__semigroup__add(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2)) -> (V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))))))) # label(fact_add__Max__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3227 (all V_B_2 all V_A_2 all T_b (class_Lattices_Odistrib__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))))))))) # label(fact_sup__Inf2__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3228 (all V_x_2 all V_A_2 all T_b (class_Lattices_Odistrib__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))))))) # label(fact_sup__Inf1__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3229 (all V_B_2 all V_A_2 all T_b (class_Lattices_Odistrib__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))))))))) # label(fact_inf__Sup2__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3230 (all V_x_2 all V_A_2 all T_b (class_Lattices_Odistrib__lattice(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))))))) # label(fact_inf__Sup1__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3231 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))))))) # label(fact_min__max_Osup__Inf1__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.16 3232 (all V_B_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))))))))) # label(fact_min__max_Osup__Inf2__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3233 (all V_B_2 all V_A_2 all T_c all T_b c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))) # label(fact_Nitpick_Oprod__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3234 (all V_d_2 c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))) # label(fact_int__ge__less__than__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3235 (all V_d_2 c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint))))) # label(fact_int__ge__less__than2__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3236 (all V_r_2 all T_b (c_Predicate_Oreflp(T_b,V_r_2) <-> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))))) # label(fact_reflp__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3237 (all V_B_2 all V_A_2 all V_g_2 all V_f_2 all T_c all T_b all T_d (class_Rings_Osemiring__0(T_d) -> (c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))))))))) # label(fact_setsum__mult__setsum__if__inj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3238 (all V_k_2 all V_R_2 all V_t_2 all T_c all V_s_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2))))) # label(fact_setsum__multicount__gen) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3239 (all V_A_2 all T_b c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2)) # label(fact_inj__on__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3240 (all T_b all T_c c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c))) # label(fact_apsnd__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3241 (all V_x_2 all V_r_2 all T_b (c_Predicate_Oreflp(T_b,V_r_2) -> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)))) # label(fact_reflpE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3242 (all T_c all T_b c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c))) # label(fact_apfst__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3243 (all V_x_1 all T_a hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1) # label(fact_id__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3244 (all V_x all T_a hAPP(c_Fun_Oid(T_a),V_x) = V_x) # label(fact_id__apply) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3245 (all V_A_2 all T_b hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2) # label(fact_vimage__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3246 (all T_c all T_b c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c))) # label(fact_map__pair_Oidentity) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3247 (all T_c all T_b c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c))) # label(fact_map__pair_Oid) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3248 (all V_Y_2 all T_b hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2) # label(fact_image__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3249 (all T_b hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_surj__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3250 (all V_f_2 all T_b all T_d all T_c c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2)) # label(fact_apsnd__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3251 (all V_f_2 all T_c all T_d all T_b c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c))) # label(fact_apfst__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3252 (all T_c all T_b hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c))) # label(fact_split__Pair) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3253 (all V_B_2 all V_f_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))))) # label(fact_setsum__reindex__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3254 (all V_B_2 all V_f_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))))) # label(fact_setprod__reindex__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3255 (all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) <-> (exists B_n exists B_f V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n)))))) # label(fact_finite__conv__nat__seg__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3256 (all V_s_2 all V_r_2 all T_c all T_d all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2)))))) # label(fact_rel__comp__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3257 (all V_Pa_2 all T_b all T_c hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2)))) # label(fact_Range__Collect__split) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3258 (all V_s_2 all V_ca_2 all T_d all V_r_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_ca_2)),V_s_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))))) # label(fact_rel__compI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3259 (all V_r_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))))) # label(fact_RangeI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3260 (all V_r_2 all V_I_2 all T_e all V_s_2 all T_c all T_d all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2))) # label(fact_rel__comp__UNION__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3261 (all V_s_2 all V_r_2 all V_I_2 all T_e all T_c all T_d all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2))) # label(fact_rel__comp__UNION__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3262 (all V_T_2 all V_S_2 all V_R_2 all T_c all T_d all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2))) # label(fact_rel__comp__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3263 (all V_R_2 all V_T_2 all V_S_2 all T_c all T_d all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2))) # label(fact_rel__comp__distrib2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3264 (all V_T_2 all V_S_2 all V_R_2 all T_e all T_c all T_d all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2))) # label(fact_O__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3265 (all V_R_2 all T_c all T_d all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) # label(fact_rel__comp__empty2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3266 (all V_R_2 all T_c all T_d all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) # label(fact_rel__comp__empty1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3267 (all V_A_2 all T_b hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2) # label(fact_Range__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3268 (all V_s_2 all V_s_H_2 all T_d all V_r_2 all V_r_H_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))))) # label(fact_rel__comp__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3269 (all V_C_2 all V_B_2 all V_A_2 all T_b (hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) -> (hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) -> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))) # label(fact_union__comp__emptyR) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3270 (all V_B_2 all V_C_2 all V_A_2 all T_b (hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) -> (hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) -> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))) # label(fact_union__comp__emptyL) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3271 (all V_S_2 all T_b all T_c hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b))) # label(fact_Range__Union) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3272 (all V_r_2 all T_b all T_c (hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)))) # label(fact_Range__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3273 (all T_b all T_c hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Range__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3274 (all V_C_2 all V_s_2 all T_d all V_B_2 all V_A_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2))))))) # label(fact_rel__comp__subset__Sigma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3275 (all V_B_2 all V_A_2 all T_b all T_c hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))) # label(fact_Range__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3276 (all V_r_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))))) # label(fact_finite__Range) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3277 (all V_R_2 all T_b all T_c hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2)) # label(fact_snd__eq__Range) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3278 (all V_r_2 all T_c all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) <-> (exists B_y hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2))))) # label(fact_Range__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3279 (all V_r_2 all V_b_2 all V_a_2 all T_b all T_c hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) # label(fact_Range__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3280 (all V_B_2 all V_A_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))))) # label(fact_Range__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3281 (all V_B_2 all V_A_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Range__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3282 (all V_S_2 all V_R_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))))) # label(fact_max__ext__compat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3283 (all V_S_2 all V_R_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))))) # label(fact_min__ext__compat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3284 (all V_x_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))))) # label(fact_RangeP__Range__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3285 (all V_r_2 all T_c all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) -> -(all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))))) # label(fact_RangeE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3286 (all V_y_2 all V_x_2 all V_s_2 all V_r_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))))) # label(fact_pred__comp__rel__comp__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3287 (all T_d all T_c all T_b all V_ca_2 all V_s_2 all V_b_2 all V_a_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) -> hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_ca_2))))) # label(fact_pred__comp_Ointros) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3288 (all T_c all T_b all V_b_2 all V_a_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) -> hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)))) # label(fact_RangeP_Ointros) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3289 (all V_a2_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) <-> (exists B_a hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2))))) # label(fact_RangeP_Oequations) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3290 (all V_a3_2 all V_a1_2 all V_s_2 all V_r_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2)) <-> (exists B_b (hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)))))) # label(fact_pred__comp_Oequations) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3291 (all V_S_2 all V_R_2 all T_b (c_Wellfounded_Owf(T_b,V_R_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) -> c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))))) # label(fact_reduction__pairI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3292 (all V_Pa_2 all T_c all T_b hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2))) # label(fact_Domain__Collect__split) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3293 (all V_a_2 all T_b c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2) # label(fact_the__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3294 (all T_b c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) # label(fact_wf__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3295 (all V_f_2 all T_c all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)))) # label(fact_wf__inv__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3296 (all V_rb_2 all T_c all V_ra_2 all T_b (c_Wellfounded_Owf(T_b,V_ra_2) -> (c_Wellfounded_Owf(T_c,V_rb_2) -> c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2))))) # label(fact_wf__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3297 (all V_f_2 all T_b c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2))) # label(fact_wf__measure) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3298 (all V_r_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))))) # label(fact_DomainI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3299 (all V_R_2 all T_b (c_Wellfounded_Owf(T_b,V_R_2) <-> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)))) # label(fact_wf__comp__self) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3300 (all V_p_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2)) -> c_Wellfounded_Owf(T_b,V_p_2)))) # label(fact_wf__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3301 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)))) # label(fact_min__ext__wf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3302 (all V_r_H_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)))) # label(fact_wf__Int2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3303 (all V_r_H_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)))) # label(fact_wf__Int1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3304 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)))) # label(fact_max__ext__wf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3305 (all V_A_2 all T_b hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2) # label(fact_Domain__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3306 (all T_b c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b))) # label(fact_wf__finite__psubset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3307 (all V_f_2 all V_R_2 all T_b (c_Wellfounded_Owf(T_b,V_R_2) -> c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)))) # label(fact_wf__mlex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3308 (all V_a_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)))) # label(fact_wf__not__refl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3309 (all V_x_2 all V_a_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2))))) # label(fact_wf__not__sym) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3310 (all V_x_2 all V_a_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2))))) # label(fact_wf__asym) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3311 (all V_a_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)))) # label(fact_wf__irrefl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3312 (all V_d_2 c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2))) # label(fact_wf__int__ge__less__than2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3313 (all V_d_2 c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2))) # label(fact_wf__int__ge__less__than) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3314 (all V_s_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> (c_Wellfounded_Owf(T_b,V_s_2) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)))))) # label(fact_wf__Un) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3315 (all V_x_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))))) # label(fact_acc__wfD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3316 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) <-> (all B_x hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))))) # label(fact_wf__acc__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3317 (all V_R_2 all T_b (hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) -> c_Wellfounded_Owf(T_b,V_R_2))) # label(fact_wf__no__loop) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3318 (all V_S_2 all V_R_2 all T_b (c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) <-> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)))) # label(fact_wf__union__merge) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3319 (all V_r_2 all T_c all T_b (hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) # label(fact_Domain__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3320 (all T_c all T_b hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Domain__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3321 (all V_s_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))))) # label(fact_Domain__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3322 (all V_B_2 all V_A_2 all T_c all T_b hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))) # label(fact_Domain__Un__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3323 (all V_r_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))))) # label(fact_finite__Domain) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3324 (all V_R_2 all T_c all T_b hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2)) # label(fact_fst__eq__Domain) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3325 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) <-> -(exists B_f all B_i hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2))))) # label(fact_wf__iff__no__infinite__down__chain) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3326 (all V_A_2 all V_R_2 all T_b (c_Wellfounded_Owf(T_b,V_R_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2))) -> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_wfE__pf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3327 (all V_S_2 all V_R_2 all T_b (c_Wellfounded_Owf(T_b,V_R_2) -> (c_Wellfounded_Owf(T_b,V_S_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) -> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))))) # label(fact_wf__union__compatible) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3328 (all V_r_2 all T_c all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) <-> (exists B_y hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2))))) # label(fact_Domain__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3329 (all T_b (class_Orderings_Owellorder(T_b) -> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))))) # label(fact_wf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3330 (all V_r_2 all V_b_2 all V_a_2 all T_c all T_b hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) # label(fact_Domain__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3331 (all V_Pa_2 all T_b (c_FunDef_Oreduction__pair(T_b,V_Pa_2) <-> c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))))) # label(fact_reduction__pair__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3332 (all V_S_2 all V_R_2 all V_Pa_2 all T_b (c_FunDef_Oreduction__pair(T_b,V_Pa_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) -> (c_Wellfounded_Owf(T_b,V_S_2) -> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))))))) # label(fact_reduction__pair__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3333 (all V_B_2 all V_A_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))))) # label(fact_Domain__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3334 (all V_B_2 all V_A_2 all T_c all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_Domain__Diff__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3335 (all V_r_2 all T_b hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2))) # label(fact_Field__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3336 (all V_f_2 all T_c all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2))))) # label(fact_wf__map__pair__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3337 (all V_S_2 all T_c all T_b hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c))) # label(fact_Domain__Union) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3338 (all V_x_2 all T_b c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2) # label(fact_the__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3339 (all V_x_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))))) # label(fact_DomainP__Domain__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3340 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)))) # label(fact_wf__lenlex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3341 (all V_r_2 all T_c all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) -> -(all B_y -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2))))) # label(fact_DomainE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3342 (all T_c all T_b all V_b_2 all V_a_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) -> hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)))) # label(fact_DomainP_Ointros) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3343 (all V_a1_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) <-> (exists B_x1 hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1))))) # label(fact_DomainP_Oequations) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3344 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)))) # label(fact_wf__lex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3345 (all V_n_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))) # label(fact_wf__lexn) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3346 (all V_r_2 all T_b c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2))) # label(fact_lex__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3347 (all V_r_2 all T_b hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool))) # label(fact_lexn_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3348 (all T_b all V_R_2 all T_c all V_Pa_2 ((all B_x (hBOOL(hAPP(V_Pa_2,B_x)) -> c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)))) -> c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)))) # label(fact_wf__same__fst) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3349 (all T_b all V_g_2 all V_f_2 all V_Pa_2 ((all B_x (hBOOL(hAPP(V_Pa_2,B_x)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))))) -> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))))) # label(fact_wf__if__measure) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3350 (all V_r_2 all T_b (c_Wellfounded_OwfP(T_b,V_r_2) <-> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))))) # label(fact_wfP__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3351 (all T_b c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)))) # label(fact_wfP__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3352 (all V_x_2 all V_r_2 all T_b (c_Wellfounded_OwfP(T_b,V_r_2) -> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)))) # label(fact_accp__wfPD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3353 (all V_r_2 all T_b (c_Wellfounded_OwfP(T_b,V_r_2) <-> (all B_x1 hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1))))) # label(fact_wfP__accp__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3354 (all V_p_2 all V_r_2 all T_b (c_Wellfounded_OwfP(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2)) -> c_Wellfounded_OwfP(T_b,V_p_2)))) # label(fact_wfP__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3355 (all V_R_2 all T_b (c_Wellfounded_Owf(T_b,V_R_2) -> c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)))) # label(fact_wf__in__rel) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3356 (all V_r_2 all T_b (c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)) <-> c_Wellfounded_Owf(T_b,V_r_2))) # label(fact_wfP__wf__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3357 (all V_r_2 all T_b (c_Wellfounded_OwfP(T_b,V_r_2) -> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))))) # label(fact_wfP__acyclicP) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3358 (all V_f_2 all T_c all V_A_2 all T_b (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) -> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) & -hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))))))) # label(fact_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3359 (all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)))) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)))))) # label(fact_refl__on__def_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3360 (all V_Pa_2 all T_b all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) -> hBOOL(hAPP(V_Pa_2,B_x)))) # label(fact_ball__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3361 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Oacyclic(T_b,V_r_2))) # label(fact_wf__acyclic) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3362 (all V_r_2 all V_s_2 all T_b (c_Wellfounded_Oacyclic(T_b,V_s_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) -> c_Wellfounded_Oacyclic(T_b,V_r_2)))) # label(fact_acyclic__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3363 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) -> hBOOL(hAPP(V_A_2,B_x)))))) # label(fact_Powp__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3364 (all T_b c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b)) # label(fact_INFI__bool__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3365 (all V_Pa_2 all V_A_2 all T_c all T_b hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2)))) # label(fact_Collect__ball__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3366 (all V_f_2 all V_r_2 all T_c all T_b (c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)))))) # label(fact_congruent__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3367 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2))))) # label(fact_INTER__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3368 (all V_r_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) -> (c_Wellfounded_Owf(T_b,V_r_2) <-> c_Wellfounded_Oacyclic(T_b,V_r_2)))) # label(fact_wf__iff__acyclic__if__finite) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3369 (all V_r_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) -> (c_Wellfounded_Oacyclic(T_b,V_r_2) -> c_Wellfounded_Owf(T_b,V_r_2)))) # label(fact_finite__acyclic__wf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3370 (all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))))) # label(fact_Sup__Inf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3371 (all V_A_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))))) # label(fact_Inf__Sup) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3372 (all V_r_2 all T_b (c_Nitpick_Owf_H(T_b,V_r_2) <-> c_Wellfounded_Oacyclic(T_b,V_r_2) & (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) | c_Nitpick_Ounknown(tc_HOL_Obool)))) # label(fact_Nitpick_Owf_H__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3373 (all V_x_2 -(all B_y (V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) -> -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))))) # label(fact_Abs__Integ__cases) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3374 (all V_x_2 all V_Pa_2 ((all B_y (hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) -> hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))))) -> hBOOL(hAPP(V_Pa_2,V_x_2)))) # label(fact_Abs__Integ__induct) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3375 (all V_A_2 all T_b c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b))))) # label(fact_Inter__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3376 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_a (hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))))) # label(fact_finite__UN__I) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3377 (all V_k_2 all V_N_2 ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)))) -> c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2))) # label(fact_inj__on__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3378 (all T_b all V_r_2 all T_c ((all B_i c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))) -> ((all B_i all B_j (hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) -> c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))))) # label(fact_wfP__SUP) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3379 (all V_ca_2 all V_z_2 all T_d all T_c all T_b all V_p_2 ((all B_a all B_b (V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) -> hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))))) -> hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_ca_2),V_p_2))))) # label(fact_mem__splitI2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3380 (all V_p_2 all V_ca_2 all T_d all T_c all V_z_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),V_p_2))) -> -(all B_x all B_y (V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))))))) # label(fact_mem__splitE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3381 (all V_B_2 all V_A_2 all V_f_2 all T_d all T_c all T_b hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2))) # label(fact_vimage__Times) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3382 (all V_v_2 all V_ca_2 all V_b_2 all V_a_2 all T_b all T_c all T_d (hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_ca_2) -> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2))) # label(fact_o__eq__id__dest) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3383 (all V_g_2 all T_b all T_c hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2) # label(fact_id__o) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3384 (all V_f_2 all T_c all T_b hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2) # label(fact_o__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3385 (all V_y_2 all V_x_2 all V_g_2 all V_f_2 all T_b all T_c all T_d hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2))) # label(fact_fun__upd__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3386 (all V_x_2 all V_g_2 all T_e all V_f_2 all T_b all T_c all T_d hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2)) # label(fact_apsnd__compose) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3387 (all V_y_2 all V_x_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)))) # label(fact_fun__left__comm_Ofun__comp__comm) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3388 (all T_f all T_e all T_d all T_b all T_c all V_x_H_2 all V_g_H_2 all V_f_H_2 all V_x_2 all V_g_2 all V_f_2 (hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) -> hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2))) # label(fact_comp__cong) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3389 (all V_x_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2))) # label(fact_fun__left__comm__idem_Ofun__comp__idem) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3390 (all V_v_2 all V_ca_2 all V_b_2 all V_a_2 all T_b all T_c all T_d (hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2 -> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2))) # label(fact_o__eq__dest__lhs) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3391 (all V_x_2 all V_f_2 all V_ca_2 all T_d all T_b all T_c hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_f_2),V_x_2) = V_ca_2) # label(fact_K__record__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3392 (all V_x_2 all V_g_2 all T_e all V_f_2 all T_c all T_b all T_d hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2)) # label(fact_apfst__compose) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3393 (all V_x_2 all V_g_2 all V_f_2 all T_d all T_b all T_c hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2))) # label(fact_o__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3394 (all V_x_2 all V_f_2 all V_g_2 all T_d all T_c all T_b hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2))) # label(fact_vimage__compose) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3395 (all V_h_2 all V_g_2 all T_e all V_f_2 all T_b all T_c all T_d hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2)) # label(fact_o__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3396 (all V_x_2 all V_g_2 all V_f_2 all T_d all T_b all T_c hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2))) # label(fact_o__apply) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3397 (all V_v_2 all V_d_2 all V_ca_2 all T_e all V_b_2 all V_a_2 all T_b all T_c all T_d (hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2) -> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)))) # label(fact_o__eq__dest) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3398 (all V_d_2 all V_ca_2 all T_e all V_b_2 all V_a_2 all T_b all T_c all T_d (hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2) -> (all B_v hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v))))) # label(fact_o__eq__elim) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3399 (all V_prod_2 all V_i_2 all V_h_2 all T_g all T_f all V_g_2 all V_f_2 all T_c all T_e all T_b all T_d hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2)) # label(fact_map__pair_Ocompositionality) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3400 (all V_g2_2 all V_g1_2 all T_g all V_f2_2 all V_f1_2 all T_f all T_e all T_c all T_d all T_b c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2))) # label(fact_map__pair__compose) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3401 (all V_i_2 all V_h_2 all V_g_2 all V_f_2 all T_c all T_b all T_e all T_d all T_g all T_f hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2))) # label(fact_map__pair_Ocomp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3402 (all V_r_2 all V_g_2 all V_f_2 all T_d all T_b all T_c hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2))) # label(fact_image__compose) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3403 (all V_g_2 all T_d all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) # label(fact_comp__surj) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3404 (all V_A_2 all V_f_2 all V_f_H_2 all T_d all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2) -> c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2))) # label(fact_inj__on__imageI2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3405 (all V_g_2 all T_d all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) -> c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))))) # label(fact_inj__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3406 (all V_f_H_2 all T_d all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) <-> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2)))) # label(fact_comp__inj__on__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3407 (all V_g_2 all T_d all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) -> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2)))) # label(fact_comp__inj__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3408 (all V_A_2 all V_f_2 all V_g_2 all T_d all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2) -> c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)))) # label(fact_inj__on__imageI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3409 (all V_h_2 all V_B_2 all V_f_2 all T_c all T_b all T_d (class_Groups_Ocomm__monoid__add(T_d) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2)))) # label(fact_setsum__reindex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3410 (all V_h_2 all V_B_2 all V_f_2 all T_c all T_b all T_d (class_Groups_Ocomm__monoid__mult(T_d) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2)))) # label(fact_setprod__reindex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3411 (all V_h_2 all V_g_2 all V_B_2 all V_A_2 all V_f_2 all T_c all T_b all T_d (class_Groups_Ocomm__monoid__mult(T_d) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) -> (V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2)))))) # label(fact_setprod__reindex__cong) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3412 (all V_g_2 all V_h_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2))))) # label(fact_setsum_Oreindex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3413 (all V_g_2 all V_h_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2))))) # label(fact_setprod_Oreindex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3414 (all V_x_2 all V_A_2 all V_g_2 all T_d all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) -> (c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)))) -> hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2))))) # label(fact_the__inv__into__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.17 3415 (all V_z_2 all V_g_2 all V_h_2 all T_c all V_A_2 all T_b all T_d (class_Groups_Oab__semigroup__mult(T_d) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2))))) # label(fact_fold__image__reindex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3416 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)))))) # label(fact_folding_Oremove) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3417 (all V_g_2 all V_h_2 all V_A_2 all V_F_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> (c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2) -> hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2))))) # label(fact_folding__image_Oreindex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3418 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))))))) # label(fact_folding_Ounion) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3419 (all V_h_2 all V_g_2 all T_g all V_f_2 all T_d all T_e all T_f all V_F_2 all V_fa_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) -> hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2))) # label(fact_folding_Ocommute__comps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3420 (all V_x_2 all V_y_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))) # label(fact_folding_Ocommute__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3421 (all V_g_2 all V_x_2 all V_y_2 all T_d all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)))) # label(fact_folding_Ocommute__left__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3422 (all V_g_2 all V_f_2 all T_c all T_b all T_e all T_d hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c))) # label(fact_fst__comp__map__pair) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3423 (all V_f_2 all V_g_2 all T_d all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2)) # label(fact_UN__o) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3424 (all V_g_2 all V_f_2 all T_c all T_b all T_d all T_e hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c))) # label(fact_snd__comp__map__pair) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3425 (all V_h_2 all V_g_2 all V_A_2 all V_F_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2))))) # label(fact_folding__image_Odistrib) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3426 (all V_x_2 all V_g_2 all V_f_2 all T_e all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))) # label(fact_split__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3427 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))))) # label(fact_folding_Ocommute__comp_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3428 (all V_g_2 all V_x_2 all T_d all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2))))) # label(fact_folding_Ocommute__left__comp_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3429 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)))))) # label(fact_folding_Ocommute__comp_H_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3430 (all V_g_2 all T_d all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)))))) # label(fact_folding_Ocommute__left__comp_H_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3431 (all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c))) # label(fact_folding_Oempty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3432 (all V_s_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2)))) # label(fact_folding_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3433 (all V_g_2 all V_A_2 all V_F_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)))) # label(fact_folding__image_Oeq__fold) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3434 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)))))) # label(fact_folding_Oinsert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3435 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)))))) # label(fact_folding_Ounion__inter) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3436 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))))) # label(fact_folding_Oinsert__remove) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3437 (all V_ca_2 all V_b_2 all V_Pa_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_ca_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))))) # label(fact_Loop__sound__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3438 (all V_d_2 all V_Q_2 all V_ca_2 all V_b_2 all V_Pa_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))))) # label(fact_hoare__derivs_OIf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3439 (all V_ca_2 all V_b_2 all V_Pa_2 all V_Ga_2 all T_b (c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_b_2)),V_ca_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) -> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))))) # label(fact_Loop) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3440 (all V_s_2 all V_Z_2 all V_p_2 all V_Pa_2 all T_b (hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) <-> hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) & hBOOL(hAPP(V_p_2,V_s_2)))) # label(fact_peek__and__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3441 (all T_c all V_h_2 all V_f_2 all V_S_2 all T_b all T_d (class_Groups_Ocomm__monoid__add(T_d) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) -> (all B_y (hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) -> (B_x != B_y -> (hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) -> hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d))))))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2))))) # label(fact_setsum__reindex__nonzero) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3442 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)))))) # label(fact_folding__idem_Ounion__idem) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3443 (all V_B_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2))))) # label(fact_folding__idem_Osubset__comp__idem) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3444 (all V_g_2 all V_x_2 all T_d all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2))) # label(fact_folding__idem_Oidem__left__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3445 (all V_x_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2))) # label(fact_folding__idem_Oidem__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3446 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2))))) # label(fact_folding__idem_Oin__comp__idem) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3447 (all V_x_2 all V_A_2 all V_F_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))))) # label(fact_folding__idem_Oinsert__idem) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3448 (all V_h_2 all V_g_2 all V_B_2 all V_A_2 all V_f_2 all T_c all T_b all T_d (class_Groups_Ocomm__monoid__mult(T_d) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2)))))) # label(fact_strong__setprod__reindex__cong) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3449 (all V_Pa_2 all T_c all T_b c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c)))) # label(fact_Eps__split) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3450 (all V_R_2 all T_b ((all B_A (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A))) -> B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) -> c_Wellfounded_Owf(T_b,V_R_2))) # label(fact_wfI__pf) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3451 (all T_b all V_ca_2 all V_Pa_2 ((exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) -> (V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2) -> hBOOL(hAPP(V_Pa_2,V_ca_2))))) # label(fact_exE__some) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3452 (all T_b all B_P ((exists B_x hBOOL(hAPP(B_P,B_x))) -> hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))))) # label(fact_tfl__some) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3453 (all T_b all V_x_2 all V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_x_2)) -> hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))))) # label(fact_someI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3454 (all V_x_2 all T_b c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2) # label(fact_some__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3455 (all V_x_2 all T_b c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2) # label(fact_some__eq__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3456 (all T_b all V_Pa_2 (hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) <-> (exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1))))) # label(fact_some__eq__ex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3457 (all T_b all V_Pa_2 ((exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) -> hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))))) # label(fact_someI__ex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3458 (all V_Pa_2 all T_c all T_b c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) # label(fact_split__paired__Eps) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3459 (all V_y_2 all V_x_2 all T_c all T_b c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)) # label(fact_Eps__split__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3460 (all V_D_2 all V_B_2 all T_c all V_C_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2)))))) # label(fact_Sigma__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3461 (all V_r_2 all V_x_2 all T_b ((all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))))) # label(fact_acc_OaccI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3462 (all V_R_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) -> -(all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))))))) # label(fact_not__acc__down) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3463 (all V_R_2 all V_a2_2 all V_a1_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) -> (exists B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)))))))) # label(fact_max__ext_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3464 (all V_ca_2 all V_b_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_2))))))) # label(fact_min__max_Ofold__sup__le__sup) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3465 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> ((all B_y (hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2))))) # label(fact_Max__eqI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3466 (all V_f_2 all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> -(all B_k hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2))))) # label(fact_wf__no__infinite__down__chainE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3467 (all V_x_2 all V_f_2 all T_b all T_c all V_k_2 ((V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2)) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2))))) # label(fact_iterate_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3468 (all V_h_2 all V_g_2 all V_B_2 all V_A_2 all V_f_2 all T_c all T_b all T_d (class_Groups_Ocomm__monoid__add(T_d) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) -> ((all B_a (hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) -> hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2)))))) # label(fact_setsum__reindex__cong) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3469 (all V_f_2 all V_x_2 all T_c all T_d all T_b hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2)) # label(fact_Pair__scomp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3470 (all V_h_2 all V_g_2 all V_f_2 all T_g all T_f all T_c all T_e all T_d all T_b hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2))) # label(fact_scomp__scomp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3471 (all V_x_2 all T_d all T_c all T_b hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2) # label(fact_scomp__Pair) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3472 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_e all T_d all T_c hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2))) # label(fact_scomp__apply) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3473 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_e all T_d all T_c hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2))) # label(fact_scomp__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3474 (all V_x_2 all V_g_2 all V_f_2 all T_b all T_e all T_d all T_c hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2)))) # label(fact_scomp__unfold) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3475 (all V_g_2 all V_f_2 all V_d_2 all V_b_2 all V_ca_2 all V_a_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) & class_Orderings_Oord(T_b) -> (V_a_2 = V_ca_2 -> (V_b_2 = V_d_2 -> ((all B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2)) -> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2))))))) # label(fact_setsum__ivl__cong) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3476 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_less__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3477 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) -> c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)))) # label(fact_wf__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3478 (all V_r_2 all T_b (c_Wellfounded_Oacyclic(T_b,V_r_2) <-> (all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_acyclic__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3479 (all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))))) # label(fact_trancl_Or__into__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3480 (all V_r_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2)))))) # label(fact_trancl__subset__Field2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3481 (all V_r_2 all V_p_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))))) # label(fact_r__into__trancl_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3482 (all T_b c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) # label(fact_trancl__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3483 (all V_r_2 all T_b hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)) # label(fact_trancl__domain) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3484 (all V_r_2 all T_b hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) # label(fact_trancl__range) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3485 (all V_r_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)))) # label(fact_finite__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3486 (all V_ca_2 all V_R_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))))) # label(fact_r__r__into__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3487 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_trancl__into__trancl2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3488 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_Transitive__Closure_Otrancl__into__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3489 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_trancl__trans) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3490 (all V_s_2 all V_r_2 all V_p_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2)))))) # label(fact_trancl__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3491 (all V_r_2 all T_b c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2))) # label(fact_trancl__unfold) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3492 (all V_A_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))))) # label(fact_trancl__subset__Sigma) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3493 (all V_s_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2))))) # label(fact_trancl__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3494 (all V_r_2 all V_x_2 all V_y_2 all T_b c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))))) # label(fact_trancl__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3495 (all V_y_2 all V_x_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))))) # label(fact_reflcl__set__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3496 (all V_r_2 all V_p_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))) # label(fact_r__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3497 (all V_r_2 all V_a_2 all T_b hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) # label(fact_rtrancl_Ortrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3498 (all V_a_2 all T_b hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b)))) # label(fact_IdI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3499 (all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))) # label(fact_trancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3500 (all V_r_2 all T_b c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) # label(fact_trancl__unfold__left) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3501 (all V_r_2 all T_b c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) # label(fact_trancl__unfold__right) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3502 (all V_r_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2)) # label(fact_reflcl__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3503 (all V_r_2 all T_b c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2)) # label(fact_trancl__reflcl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3504 (all V_R_2 all T_b c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)) # label(fact_rtrancl__trancl__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3505 (all V_R_2 all T_b c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)) # label(fact_trancl__rtrancl__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3506 (all V_R_2 all T_b hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Domain__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3507 (all V_R_2 all T_b hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Range__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3508 (all V_r_2 all T_b c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) # label(fact_refl__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3509 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) # label(fact_converse__rtrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3510 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) # label(fact_rtrancl_Ortrancl__into__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3511 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) # label(fact_rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3512 (all V_r_2 all T_b c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2)) # label(fact_rtrancl__idemp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3513 (all V_r_2 all T_b c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2)) # label(fact_rtrancl__r__diff__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3514 (all V_S_2 all V_R_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))))) # label(fact_in__rtrancl__UnI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3515 (all V_S_2 all V_R_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))))) # label(fact_rtrancl__Un__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3516 (all V_R_2 all T_b c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)) # label(fact_rtrancl__reflcl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3517 (all V_S_2 all V_R_2 all T_b c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) # label(fact_rtrancl__Un__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3518 (all V_R_2 all T_b hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)) # label(fact_rtrancl__reflcl__absorb) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3519 (all V_X_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2)) -> hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2)) # label(fact_Image__closed__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3520 (all V_s_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))))) # label(fact_rtrancl__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3521 (all V_S_2 all V_R_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) -> c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)))) # label(fact_rtrancl__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3522 (all V_s_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))))) # label(fact_rtrancl__subset__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3523 (all V_R_2 all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)) # label(fact_rtrancl__idemp__self__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3524 (all V_r_2 all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) # label(fact_r__comp__rtrancl__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3525 (all V_r_2 all T_b c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2))) # label(fact_rtrancl__unfold) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3526 (all V_r_2 all V_s_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2))))) # label(fact_rtrancl__Int__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3527 (all T_b c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b)) # label(fact_rtrancl__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3528 (all V_R_2 all T_c all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2) # label(fact_R__O__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3529 (all V_R_2 all T_c all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2) # label(fact_Id__O__R) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3530 (all V_A_2 all T_b hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2) # label(fact_Image__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3531 (all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b))) <-> V_a_2 = V_b_2)) # label(fact_pair__in__Id__conv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3532 (all V_R_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) <-> V_x_2 = V_y_2 | V_x_2 != V_y_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))))) # label(fact_rtrancl__eq__or__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3533 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_rtrancl__into__trancl2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3534 (all V_R_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) -> V_a_2 = V_b_2 | V_a_2 != V_b_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))))) # label(fact_rtranclD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3535 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_rtrancl__into__trancl1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3536 (all V_ca_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_trancl__rtrancl__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3537 (all V_z_2 all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_rtrancl__trancl__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3538 (all T_b hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Domain__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3539 (all T_b hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) # label(fact_Range__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3540 (all T_b c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b))) # label(fact_refl__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3541 (all V_y_2 all V_R_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) <-> V_x_2 = V_y_2))) # label(fact_Not__Domain__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3542 (all V_r_2 all V_a_2 all V_b_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))))) # label(fact_acc__downwards__aux) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3543 (all V_b_2 all V_r_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))))) # label(fact_acc__downwards) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3544 (all V_r_2 all V_x_2 all V_y_2 all T_b (c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) <-> c_Wellfounded_Owf(T_b,V_r_2) & -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))) # label(fact_wf__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3545 (all V_r_2 all V_x_2 all V_y_2 all T_b (c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) <-> c_Wellfounded_Oacyclic(T_b,V_r_2) & -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))) # label(fact_acyclic__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3546 (all V_r_2 all T_b c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) # label(fact_refl__reflcl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3547 (all T_b c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))))) # label(fact_Id__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3548 (all V_r_2 all T_b c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) # label(fact_irrefl__diff__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3549 (all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_pred__nat__trancl__eq__le) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3550 (all V_A_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) -> V_a_2 = V_b_2 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))))) # label(fact_trancl__subset__Sigma__aux) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3551 (all V_x_2 all V_r_2 all T_b (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))))) # label(fact_irrefl__tranclI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3552 (all V_k_2 all V_i_2 all V_r_2 all V_f_2 all T_b ((all B_i hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))) # label(fact_sequence__trans) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3553 (all V_r_2 all T_b c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) # label(fact_rtrancl__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3554 (all T_b hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b)) # label(fact_converse__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3555 (all V_r_2 all T_b (c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) <-> c_Wellfounded_Oacyclic(T_b,V_r_2))) # label(fact_acyclic__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3556 (all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) <-> c_Relation_Orefl__on(T_b,V_A_2,V_r_2))) # label(fact_refl__on__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3557 (all V_A_2 all T_b hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2)) # label(fact_converse__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3558 (all V_r_2 all T_b hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2)) # label(fact_Field__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3559 (all V_r_2 all T_b all T_c hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2) # label(fact_converse__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3560 (all V_f_2 all V_R_2 all T_c all T_b hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2)) # label(fact_converse__inv__image) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3561 (all V_r_2 all T_c all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)))) # label(fact_finite__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3562 (all V_s_2 all V_r_2 all T_b all T_c hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2))) # label(fact_converse__Int) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3563 (all V_s_2 all V_r_2 all T_b all T_c hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2))) # label(fact_converse__Un) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3564 (all V_s_2 all V_r_2 all T_d all T_b all T_c hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2))) # label(fact_converse__rel__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3565 (all V_r_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)))) # label(fact_converseD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3566 (all V_r_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))))) # label(fact_converseI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3567 (all V_r_2 all V_b_2 all V_a_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)))) # label(fact_converse__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3568 (all V_r_2 all V_S_2 all T_d all T_b all T_c hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2))) # label(fact_converse__UNION) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3569 (all V_r_2 all V_S_2 all T_d all T_b all T_c hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2))) # label(fact_converse__INTER) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3570 (all V_r_2 all T_b c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) # label(fact_trancl__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3571 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) -> c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))) # label(fact_wf__converse__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3572 (all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2)) # label(fact_equiv__comp__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3573 (all V_r_2 all T_b all T_c hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) # label(fact_Range__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3574 (all V_r_2 all T_c all T_b hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) # label(fact_Domain__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3575 (all V_r_2 all T_b all T_c hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) # label(fact_Range__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3576 (all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))) # label(fact_rtrancl__converseD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3577 (all V_r_2 all V_x_2 all V_y_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))))) # label(fact_rtrancl__converseI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3578 (all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))))) # label(fact_trancl__converseD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3579 (all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))))) # label(fact_trancl__converseI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3580 (all V_B_2 all V_A_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))))) # label(fact_Image__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3581 (all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))))) # label(fact_refl__on__comp__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3582 (all V_A_2 all V_r_2 all T_b (hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 -> (hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2 -> c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)))) # label(fact_comp__equivI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3583 (all V_r_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) -> (c_Wellfounded_Oacyclic(T_b,V_r_2) -> c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))) # label(fact_finite__acyclic__wf__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3584 (all V_r_2 all T_b all T_c hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2)))) # label(fact_converse__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3585 (all V_B_2 all T_d all V_A_2 all V_r_2 all T_c all T_b (c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) -> (V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) -> hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2))))) # label(fact_Image__INT__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3586 (all V_r_2 all V_A_2 all T_b (c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) <-> c_Relation_Ototal__on(T_b,V_A_2,V_r_2))) # label(fact_total__on__diff__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3587 (all T_b c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b))) # label(fact_single__valued__Id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3588 (all V_s_2 all T_d all V_r_2 all T_c all T_b (c_Relation_Osingle__valued(T_b,T_c,V_r_2) -> (c_Relation_Osingle__valued(T_c,T_d,V_s_2) -> c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))))) # label(fact_single__valued__rel__comp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3589 (all V_s_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) -> (c_Relation_Osingle__valued(T_b,T_c,V_s_2) -> c_Relation_Osingle__valued(T_b,T_c,V_r_2)))) # label(fact_single__valued__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3590 (all V_A_2 all T_b c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2))) # label(fact_single__valued__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3591 (all V_r_2 all T_b c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2)) # label(fact_total__on__empty) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3592 (all V_r_2 all V_A_2 all T_b (c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) <-> c_Relation_Ototal__on(T_b,V_A_2,V_r_2))) # label(fact_total__on__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3593 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_c all T_b (c_Relation_Osingle__valued(T_b,T_c,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2)) -> V_y_2 = V_z_2)))) # label(fact_single__valuedD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3594 (all V_r_2 all T_c all T_b (c_Relation_Osingle__valued(T_b,T_c,V_r_2) <-> (all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) -> (all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) -> B_y = B_z)))))) # label(fact_single__valued__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3595 (all V_r_2 all V_A_2 all T_b (c_Relation_Ototal__on(T_b,V_A_2,V_r_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) -> (B_x != B_xa -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2)) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))))))))) # label(fact_total__on__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3596 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_b (c_Relation_Osingle__valued(T_b,T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))))) # label(fact_single__valued__confluent) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3597 (all V_B_2 all V_A_2 all V_R_2 all T_c all T_b (c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) -> hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) # label(fact_Image__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3598 (all V_R_2 all V_p_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))))) # label(fact_rtrancl__imp__UN__rel__pow) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3599 (all V_r_2 all T_b ((all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) -> c_Wellfounded_Oacyclic(T_b,V_r_2))) # label(fact_acyclicI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3600 (all V_n_2 all V_R_2 all T_b (c_Relation_Osingle__valued(T_b,T_b,V_R_2) -> c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))) # label(fact_single__valued__rel__pow) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3601 (all V_x_2 all V_n_2 all T_b all V_f_2 hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2))) # label(fact_funpow__swap1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3602 (all V_f_2 all V_m_2 all V_n_2 all T_b hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2)) # label(fact_funpow__mult) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3603 (all V_R_2 all V_n_2 all T_b (c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) -> c_Wellfounded_Owf(T_b,V_R_2))) # label(fact_wf__exp) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3604 (all V_f_2 all V_n_2 all T_c all T_b hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2))) # label(fact_comp__funpow) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3605 (all V_n_2 all V_R_2 all T_b hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2)) # label(fact_rel__pow__commute) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3606 (all V_R_2 all T_b hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2) # label(fact_rel__pow__1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3607 (all V_R_2 all V_p_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) <-> (exists B_n hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))))) # label(fact_rtrancl__power) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3608 (all V_R_2 all V_n_2 all V_p_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))))) # label(fact_rel__pow__imp__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.18 3609 (all V_R_2 all V_n_2 all T_b hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2)) # label(fact_relpow_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3610 (all V_R_2 all V_n_2 all V_m_2 all T_b hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) # label(fact_rel__pow__add) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3611 (all V_R_2 all T_b hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b)) # label(fact_relpow_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3612 (all V_R_2 all V_x_2 all T_b hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))) # label(fact_rel__pow__0__I) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3613 (all V_R_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) -> V_x_2 = V_y_2)) # label(fact_rel__pow__0__E) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3614 (all V_z_2 all V_R_2 all V_n_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))))) # label(fact_rel__pow__Suc__I) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3615 (all V_n_2 all V_z_2 all V_R_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))))) # label(fact_rel__pow__Suc__I2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3616 (all V_f_2 all V_n_2 all T_b hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2))) # label(fact_funpow_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3617 (all V_f_2 all V_n_2 all V_m_2 all T_b hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2))) # label(fact_funpow__add) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3618 (all V_f_2 all T_b hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b)) # label(fact_funpow_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3619 (all V_R_2 all V_p_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) <-> (exists B_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))))))) # label(fact_trancl__power) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3620 (all V_R_2 all T_b c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2))) # label(fact_rtrancl__is__UN__rel__pow) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3621 (all T_b c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b)) # label(fact_funpow__code__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3622 (all V_R_2 all V_n_2 all V_z_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) -> ((V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_x_2 != V_z_2) -> -(all B_y all B_m (V_n_2 = hAPP(c_Nat_OSuc,B_m) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)))))))) # label(fact_rel__pow__E) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3623 (all V_R_2 all V_n_2 all V_z_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) -> ((V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_x_2 != V_z_2) -> -(all B_y all B_m (V_n_2 = hAPP(c_Nat_OSuc,B_m) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))))))))) # label(fact_rel__pow__E2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3624 (all V_Q_2 all V_Pa_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2)))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) -> (all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2)) -> B_x = B_y)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))))) # label(fact_rtrancl__Un__separatorE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3625 (all V_Q_2 all V_Pa_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2)))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) -> (all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2)) -> B_y = B_x)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))))) # label(fact_rtrancl__Un__separator__converseE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3626 (all V_R_2 all V_n_2 all V_z_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) -> (exists B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))))))) # label(fact_rel__pow__Suc__D2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3627 (all V_R_2 all V_n_2 all V_z_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) -> -(all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)))))) # label(fact_rel__pow__Suc__E) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3628 (all V_R_2 all V_n_2 all V_z_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) -> -(all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))))))) # label(fact_rel__pow__Suc__E2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3629 (all V_R_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) -> (exists B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))))))) # label(fact_tranclD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3630 (all V_R_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) -> (exists B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)))))) # label(fact_tranclD2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3631 (all V_p_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) -> -(all B_x V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)))) # label(fact_IdE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3632 (all V_r_2 all T_b (c_Wellfounded_Owf(T_b,V_r_2) <-> (all B_Q ((exists B_x hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))) -> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) & (all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)))))))))) # label(fact_wf__eq__minimal) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3633 (all V_P_H_2 all V_Pa_2 ((all B_x (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) -> (hBOOL(hAPP(V_Pa_2,B_x)) <-> hBOOL(hAPP(V_P_H_2,B_x))))) -> hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)))) # label(fact_transfer__nat__int__set__cong) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3634 (all V_Q_2 all V_Pa_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> (hBOOL(hAPP(V_Pa_2,B_x)) -> hBOOL(hAPP(V_Q_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2))))))) # label(fact_Int__Collect__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3635 (all V_s_2 all V_r_2 all T_d all V_xz_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2))) -> -(all B_x all B_y all B_z (V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2))))))) # label(fact_rel__compE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3636 (all V_r_2 all V_yx_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) -> -(all B_x all B_y (V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)))))) # label(fact_converseE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3637 (all V_r_2 all V_q_2 all T_b c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint)))) # label(fact_Nitpick_Oplus__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3638 (all T_d all T_c all T_b c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d)) # label(fact_internal__split__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3639 (all V_b_2 all V_a_2 all V_ca_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2)) # label(fact_internal__split__conv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3640 (all V_r all V_q all T_a c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r)))) # label(fact_Nitpick_Otimes__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3641 (all V_q all T_a all T_b (class_Rings_Oinverse(T_b) & class_Rings_Oring__1(T_b) -> c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))))) # label(fact_Nitpick_Oof__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3642 (all V_q all T_a c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q))) # label(fact_Nitpick_Oinverse__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3643 (all V_q all T_a c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q)))) # label(fact_Nitpick_Ouminus__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3644 (all V_r_2 all V_q_2 all T_b (c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_Nitpick_Oless__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3645 (all V_r_2 all V_q_2 all T_b (c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))) # label(fact_Nitpick_Oless__eq__frac__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3646 (all T_b c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b))) # label(fact_Nitpick_Odenom__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3647 (all T_b c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b))) # label(fact_Nitpick_Onum__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3648 (all V_u_2 all V_f_2 ((all B_n hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))))) # label(fact_finite__less__ub) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3649 (all V_r_2 all T_b c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b))))) # label(fact_lenlex__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3650 (all V_ys all V_xs all T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) -> V_xs != V_ys)) # label(fact_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3651 (all V_n_2 all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2)) # label(fact_lexn__length) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3652 (all V_r_2 all T_b c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2))))))) # label(fact_lenlex__conv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3653 (all V_I_2 all V_xs_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) # label(fact_length__sublist) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3654 (all V_n_2 all V_r_2 all T_b hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))))) # label(fact_lexn_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3655 (all V_x all V_ys all V_xs all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) -> V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))) # label(fact_impossible__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3656 (all V_x all T_a all V_xs V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) # label(fact_not__Cons__self) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3657 (all V_xs all V_x all T_a hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs) # label(fact_not__Cons__self2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3658 (all V_list_H_2 all V_a_H_2 all V_list_2 all V_a_2 all T_b (hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2) <-> V_a_2 = V_a_H_2 & V_list_2 = V_list_H_2)) # label(fact_list_Oinject) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3659 (all V_list all V_a all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_list_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3660 (all V_r_2 all V_ys_2 all V_y_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) | V_x_2 = V_y_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))))) # label(fact_Cons__in__lex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3661 (all V_XS_2 all V_A_2 all T_b c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2))))))) # label(fact_set__Cons__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3662 (all V_xs all V_x all T_a all V_i ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) -> hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) -> hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))))) # label(fact_pick_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3663 (all V_xs_2 all V_x_2 all T_b c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2)) # label(fact_select__weight__cons__zero) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3664 (all V_r_2 all V_y_2 all V_b_2 all V_x_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) | V_a_2 = V_b_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))))) # label(fact_lexord__cons__cons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3665 (all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) # label(fact_lexord__lex) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3666 (all V_ys_2 all V_xs_2 all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))))) # label(fact_rtrancl__listrel1__ConsI2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3667 (all V_list_2 all V_a_2 all V_fa_2 all T_b c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_list_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3668 (all V_xs_2 all V_r_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))))) # label(fact_Cons__acc__listrel1I) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3669 (all V_r_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))) # label(fact_listrel1__rtrancl__subset__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3670 (all V_r_2 all T_b c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2))) # label(fact_listrel1__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3671 (all V_s_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))))) # label(fact_listrel1__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3672 (all V_x_2 all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))))) # label(fact_listrel1I2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3673 (all V_x_2 all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))))) # label(fact_rtrancl__listrel1__ConsI1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3674 (all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) # label(fact_listrel1__eq__len) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3675 (all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) # label(fact_rtrancl__listrel1__eq__len) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3676 (all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))))) # label(fact_in__listrel1__converse) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3677 (all V_xs_2 all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))))) # label(fact_listrel1I1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3678 (all V_r_2 all V_ys_2 all V_y_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) & V_xs_2 = V_ys_2 | V_x_2 = V_y_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))))) # label(fact_Cons__listrel1__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3679 (all V_xs_2 all V_x_2 all V_r_2 all T_b hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))))) # label(fact_listrel__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3680 (all V_y_2 all V_r_2 all T_b ((all B_x -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))))) # label(fact_lexord__irreflexive) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3681 (all V_r_2 all V_xs_2 all T_b hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))) # label(fact_listrel__rtrancl__refl) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3682 (all V_s_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))))) # label(fact_listrel__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3683 (all V_r_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))) # label(fact_listrel__subset__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3684 (all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) # label(fact_listrel__eq__len) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3685 (all V_zs_2 all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))))) # label(fact_listrel__rtrancl__trans) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3686 (all V_r_2 all T_b c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))) # label(fact_listrel__rtrancl__eq__rtrancl__listrel1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3687 (all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) # label(fact_listrel__reflcl__if__listrel1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3688 (all V_r_H_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) -> (c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2)))))) # label(fact_listrel1__subset__listrel) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3689 (all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))))) # label(fact_rtrancl__listrel1__if__listrel) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3690 (all V_ys_2 all V_xs_2 all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))))) # label(fact_listrel_OCons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3691 (all V_xa_2 all V_x_2 all V_r_2 all T_b (c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))))) # label(fact_listrelp__listrel__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3692 (all V_r_2 all V_ys_2 all V_y_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) -> -(all B_x all B_xs (V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))))))) # label(fact_listrel__Cons2) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3693 (all V_ys_2 all V_xs_2 all T_b all V_y_2 all V_x_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) -> (c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2) -> c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))))) # label(fact_listrelp_OCons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3694 (all V_a4_2 all V_a2_2 all V_a3_2 all V_a1_2 all V_r_2 all T_b (c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2)) <-> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2))) # label(fact_listrelp_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3695 (all V_r_2 all V_xs_2 all V_ys_2 all V_y_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) -> -(all B_y all B_ys (V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2)))))))) # label(fact_listrel__Cons1) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3696 (all V_A_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))))) # label(fact_listrel__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3697 (all T_b c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) # label(fact_lists__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3698 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))))) # label(fact_lists__mono) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3699 (all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)))) # label(fact_equiv__listrel) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3700 (all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)))) # label(fact_listrel__refl__on) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3701 (all V_A_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))))) # label(fact_Cons__in__lists__iff) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3702 (all V_r_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))))) # label(fact_lists__accI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3703 (all V_r_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))))) # label(fact_lists__accD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3704 (all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) <-> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) & (all B_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)))))) # label(fact_listrel__iff__nth) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3705 (all V_y_2 all V_x_2 all V_r_2 all T_b ((all B_a all B_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) | B_a = B_b | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) | V_x_2 = V_y_2 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))))) # label(fact_lexord__linear) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3706 (all T_b -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) # label(fact_infinite__UNIV__listI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3707 (all T_b all V_ys_2 all V_xs_2 (V_xs_2 = V_ys_2 <-> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) & (all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i))))) # label(fact_list__eq__iff__nth__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3708 (all V_xs all V_x all T_a hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x) # label(fact_nth__Cons__0) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3709 (all V_n all V_xs all V_x all T_a hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n)) # label(fact_nth__Cons__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3710 (all V_n_2 all V_xs_2 all V_x_2 all T_b hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) # label(fact_nth_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3711 (all V_xs all V_x all T_a all V_n ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) # label(fact_nth__Cons_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3712 (all V_xs all V_x all T_a all V_v ((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x) & (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) # label(fact_nth__Cons__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3713 (all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 | (exists B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)))))) # label(fact_lexord__take__index__conv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3714 (all V_I_2 all V_xs_2 all T_b hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))))) # label(fact_set__sublist) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3715 (all V_xs_2 all T_b hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2)))) # label(fact_finite__set) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3716 (all V_x_2 all V_xs_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))) # label(fact_set__subset__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3717 (all V_n all V_xs all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) -> hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs)) # label(fact_take__all) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3718 (all V_xs_2 all V_n_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2)))) # label(fact_set__take__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3719 (all V_xs_2 all T_b all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))))) # label(fact_set__take__subset__set__take) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3720 (all V_I_2 all V_xs_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2)))) # label(fact_set__sublist__subset) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3721 (all V_xs all T_a all V_n all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) # label(fact_nth__take) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3722 (all V_I_2 all V_xs_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))))) # label(fact_notin__set__sublistI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3723 (all V_xs_2 all V_n_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_in__set__takeD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3724 (all V_I_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_in__set__sublistD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3725 (all V_xs_2 all V_x_2 all V_y_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) -> V_y_2 = V_x_2 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_set__ConsD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3726 (all V_xs all V_x all V_n all T_a hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs))) # label(fact_take__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3727 (all V_xs all V_n all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) # label(fact_length__take) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3728 (all V_xs all V_m all V_n all T_a hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs)) # label(fact_take__take) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3729 (all V_xs_2 all V_x_2 all T_b hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) # label(fact_List_Oset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3730 (all V_n_2 all V_l_2 all T_b c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2)) # label(fact_sublist__upt__eq__take) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3731 (all V_xs_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) # label(fact_card__length) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3732 (all V_Pa_2 all V_xs_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> (all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))))))) # label(fact_all__set__conv__all__nth) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3733 (all V_f_2 all V_y_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)))))) # label(fact_list__size__estimation) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3734 (all V_f_2 all V_y_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)))))) # label(fact_list__size__estimation_H) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3735 (all V_A_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)))))) # label(fact_in__lists__conv__set) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3736 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) # label(fact_length__pos__if__in__set) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3737 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) <-> (exists B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2)))) # label(fact_in__set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3738 (all V_xs_2 all T_b all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_nth__mem) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3739 (all V_A_2 all T_b c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))) # label(fact_lists__eq__set) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3740 (all V_xs_2 all T_b hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) # label(fact_set__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3741 (all V_n_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))))) # label(fact_finite__lists__length__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3742 (all V_n_2 all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))))) # label(fact_finite__lists__length__le) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3743 (all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) <-> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) & (all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)))))) # label(fact_listrel__iff__zip) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3744 (all V_ys_2 all V_xs_2 all T_c all T_b hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))))))) # label(fact_set__zip) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3745 (all V_ys all V_xs all V_n all T_b all T_a hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys))) # label(fact_take__zip) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3746 (all V_ys all V_xs all T_b all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys))) # label(fact_length__zip) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3747 (all V_ys all V_y all V_xs all V_x all T_b all T_a hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) # label(fact_zip__Cons__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3748 (all T_b all V_ys_2 all V_xs_2 (V_xs_2 = V_ys_2 <-> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) & (all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)))))) # label(fact_list__eq__iff__zip__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3749 (all V_xs_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2)))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) & V_a_2 = V_b_2)) # label(fact_zip__same) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3750 (all V_ys_2 all V_xs_2 all V_y_2 all V_x_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_set__zip__leftD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3751 (all V_ys_2 all V_xs_2 all V_y_2 all V_x_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) -> hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))))) # label(fact_set__zip__rightD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3752 (all V_ys_2 all V_xs_2 all V_y_2 all V_x_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) -> -(hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> -hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2)))))) # label(fact_in__set__zipE) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3753 (all V_ys all T_b all V_xs all T_a all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys))) -> hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i))))) # label(fact_nth__zip) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3754 (all V_j_2 all V_i_2 c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))) # label(fact_greaterThanLessThan__upto) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3755 (all V_xs_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) # label(fact_listsum__setsum__nth) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3756 (all V_j_2 all V_i_2 hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)) # label(fact_set__upto) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3757 (all V_j_2 all V_i_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) # label(fact_atLeastAtMost__upto) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3758 (all V_ns_2 (hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) -> B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) # label(fact_listsum__eq__0__nat__iff__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3759 (all V_ns all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))))) # label(fact_elem__le__listsum__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3760 (all V_xs all V_x all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)))) # label(fact_listsum__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3761 (all V_j_2 all V_i_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))) # label(fact_atLeastLessThan__upto) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3762 (all V_j_2 all V_i_2 c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2))) # label(fact_greaterThanAtMost__upto) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3763 (all V_l_2 (c_List_Onat__list(V_l_2) <-> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)))) # label(fact_nat__list__def) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3764 (all V_g_2 all V_f_2 all V_xs_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))))) # label(fact_list__size__pointwise) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3765 (all V_n all V_ns all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) -> hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)))) # label(fact_listsum__update__nat) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3766 (all V_xs all T_a all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs))) # label(fact_butlast__take) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3767 (all V_x all V_i all V_xs all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)) -> hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs)) # label(fact_list__update__beyond) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3768 (all V_x all V_xs all T_a all V_j all V_i (V_i != V_j -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) # label(fact_nth__list__update__neq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3769 (all V_i all V_xs all T_a hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs) # label(fact_list__update__id) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3770 (all V_x all V_xs all T_a all V_k ((V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs)) & (V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x)))) # label(fact_butlast__list__update) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3771 (all V_x all V_i all V_xs all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) # label(fact_length__list__update) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3772 (all V_y all V_ys all V_x all V_i all V_xs all T_b all T_a hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y))) # label(fact_zip__update) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.19 3773 (all V_xy all V_i all V_ys all V_xs all T_b all T_a hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy)))) # label(fact_update__zip) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3774 (all V_y all V_x all V_i all V_xs all T_a hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) # label(fact_list__update__overwrite) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3775 (all V_x_H all V_x all V_xs all T_a all V_i_H all V_i (V_i != V_i_H -> hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x))) # label(fact_list__update__swap) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3776 (all V_y all V_xs all V_x all T_a hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) # label(fact_list__update__code_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3777 (all V_y all V_i all V_xs all V_x all T_a hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y))) # label(fact_list__update__code_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3778 (all V_v_2 all V_i_2 all V_xs_2 all V_x_2 all T_b hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2)) # label(fact_list__update_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3779 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_in__set__butlastD) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3780 (all V_i_2 all V_x_2 all V_A_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2))))) # label(fact_set__update__subsetI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3781 (all V_x_2 all V_i_2 all V_xs_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_set__update__subset__insert) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3782 (all V_x all V_j all V_xs all T_a all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> (V_i = V_j -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x) & (V_i != V_j -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)))) # label(fact_nth__list__update) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3783 (all V_x_2 all V_xs_2 all T_b all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> (hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2 <-> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2))) # label(fact_list__update__same__conv) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3784 (all V_x all V_xs all T_a all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x)) # label(fact_nth__list__update__eq) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3785 (all V_xs all T_a all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs))) # label(fact_take__butlast) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3786 (all V_xs all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_length__butlast) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3787 (all V_x_2 all V_xs_2 all T_b all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))))) # label(fact_set__update__memI) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3788 (all V_xs all T_a c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) # label(fact_butlast__conv__take) # label(axiom) # label(non_clause). [assumption].
% 6.16/6.20 3789 (all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) <-> (exists B_y exists B_n (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y))))) # label(fact_listrel1__iff__update) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3790 (all V_i_2 all V_a_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) -> hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2)))))) # label(fact_distinct__list__update) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3791 (all V_j all V_i hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j)))) # label(fact_distinct__upto) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3792 (all V_i all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))))) # label(fact_distinct__take) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3793 (all V_I_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))) # label(fact_distinct__sublistI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3794 (all V_ys all T_b all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))))) # label(fact_distinct__zipI1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3795 (all V_xs all T_b all V_ys all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) -> hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))))) # label(fact_distinct__zipI2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3796 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) <-> -hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)))) # label(fact_distinct_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3797 (all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) # label(fact_distinct__card) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3798 (all V_xs_2 all T_b (hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) -> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)))) # label(fact_card__distinct) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3799 (all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) <-> (all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> (all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> (B_i != B_j -> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)))))))) # label(fact_distinct__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3800 (all V_j_2 all V_i_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> (hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) <-> V_i_2 = V_j_2))))) # label(fact_nth__eq__iff__index__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3801 (all V_xs_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_distinct__listsum__conv__Setsum) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3802 (all V_A_2 all T_b ((hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) & (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_Nitpick_Ocard_H__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3803 (all V_ys all V_xs all T_a all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) -> ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) -> hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i))) -> hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys))))) # label(fact_nth__take__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3804 (all V_x_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_set__remove1__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3805 (all V_xs all V_x all T_a all V_v ((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)) & (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs))))) # label(fact_take__Cons__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3806 (all V_A_2 all T_b hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2)))) # label(fact_lists_ONil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3807 (all V_r_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) -> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_listrel__Nil1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3808 (all V_r_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) -> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_listrel__Nil2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3809 (all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs)))))) # label(fact_distinct__butlast) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3810 (all V_x all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))))) # label(fact_distinct__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3811 (all T_a hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a)))) # label(fact_distinct_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3812 (all T_a c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_butlast_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3813 (all V_x all T_a all V_xs ((V_xs = c_List_Olist_ONil(T_a) -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)) & (V_xs != c_List_Olist_ONil(T_a) -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs))))) # label(fact_butlast_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3814 (all V_list_H all V_a_H all T_a c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H)) # label(fact_list_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3815 (all V_list_H all V_a_H all T_a hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a)) # label(fact_list_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3816 (all V_xs all T_a all V_y all V_x ((V_x = V_y -> c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs) & (V_x != V_y -> c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs))))) # label(fact_remove1_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3817 (all V_i all V_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) -> c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint))) # label(fact_upto__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3818 (all V_xs_2 all V_n_2 all T_b (hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_take__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3819 (all V_xs all T_a hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a)) # label(fact_take__0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3820 (all V_n all T_a hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_take__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3821 (all V_A_2 all T_b c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b)) # label(fact_sublist__nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3822 (all V_zs all V_y all V_x all T_a c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs))) # label(fact_remove1__commute) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3823 (all V_x all T_a c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_remove1_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3824 (all V_r_2 all T_b c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b))) # label(fact_listrelp_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3825 (all V_r_2 all T_b c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b))) # label(fact_listrelp_ONil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3826 (all V_ys all T_b all T_a hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b))) # label(fact_zip__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3827 (all V_xs all T_b all T_a hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b))) # label(fact_zip_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3828 (all V_fa_2 all T_b c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_list_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3829 (all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a))) # label(fact_listsum__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3830 (all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_list_Osize_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3831 (all V_xs_2 all T_b (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_length__0__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3832 (all V_xs_2 all T_b (hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_set__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3833 (all V_xs_2 all T_b (c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_set__empty2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3834 (all T_b hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) # label(fact_List_Oset_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3835 (all V_y all V_i all T_a hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a)) # label(fact_list__update__code_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3836 (all V_v all V_i all T_a hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a)) # label(fact_list__update_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3837 (all V_x_2 all V_k_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_list__update__nonempty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3838 (all V_xs_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2)) # label(fact_remove1__idem) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3839 (all V_y_2 all V_xs_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> -hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))))) # label(fact_notin__set__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3840 (all V_xs_2 all T_b all V_b_2 all V_a_2 (V_a_2 != V_b_2 -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2)))) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))))) # label(fact_in__set__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3841 (all V_xs_2 all T_b c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b)) # label(fact_sublist__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3842 (all V_xs_2 all V_x_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2)))) # label(fact_set__remove1__subset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3843 (all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) <-> V_xs_2 != c_List_Olist_ONil(T_b))) # label(fact_length__greater__0__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3844 (all V_xs all V_x all T_a hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) # label(fact_take__1__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3845 (all V_r_2 all V_xs_2 all T_b -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2)))) # label(fact_not__Nil__listrel1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3846 (all V_r_2 all V_xs_2 all T_b -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2)))) # label(fact_not__listrel1__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3847 (all V_r_2 all T_b hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))) # label(fact_listrel_ONil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3848 (all V_r_2 all V_x_2 all T_b -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2)))) # label(fact_lexord__Nil__right) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3849 (all V_r_2 all V_ys_2 all T_b -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2)))) # label(fact_Nil__notin__lex) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3850 (all V_r_2 all V_xs_2 all T_b -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2)))) # label(fact_Nil2__notin__lex) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3851 (all V_xs_2 all V_x_2 all V_n_2 all T_b hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2)) # label(fact_take__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3852 (all V_j all V_i ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) -> c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) -> c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint)))) # label(fact_upto_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3853 (all V_x_2 all T_b all V_A_2 ((hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) -> c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) & (-hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) -> c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b)))) # label(fact_sublist__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3854 (all T_b c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) # label(fact_lists__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3855 (all V_xs all V_x all T_a all V_n ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs))))) # label(fact_take__Cons_H) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3856 (all V_n all V_m ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) -> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) -> c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint)))) # label(fact_upto__rec__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3857 (all V_r_2 all T_b hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) # label(fact_listrel__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3858 (all V_A_2 all T_b c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2)) # label(fact_set__Cons__sing__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3859 (all V_xs_2 all V_x_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) # label(fact_length__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3860 (all V_j_2 all V_i_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) -> c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) -> c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint)))) # label(fact_upto_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3861 (all V_s_2 all T_b all V_xs_2 (V_xs_2 != c_List_Olist_ONil(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_select) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3862 (all T_b c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) # label(fact_listset_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3863 (all V_ys_2 all V_xs_2 all V_x_2 all T_c all T_b hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2)) # label(fact_zip__Cons1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3864 (all V_list_2 all V_a_2 all V_f2_2 all V_f1_2 all T_c all T_b hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2)) # label(fact_list_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3865 (all V_f2_2 all V_f1_2 all T_c all T_b hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2) # label(fact_list_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3866 (all V_As_2 all V_A_2 all T_b c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2))) # label(fact_listset_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3867 (all V_ys_2 all V_y_2 all V_xs_2 all T_c all T_b hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2)) # label(fact_zip__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3868 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))))) # label(fact_sorted__list__of__set__remove) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3869 (all V_Pa_2 all V_a1_2 all V_a0_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) -> ((all B_i all B_j (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j))) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) -> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j))) -> hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))))) # label(fact_upto_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3870 (all T_b (class_Orderings_Olinorder(T_b) -> c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b))) # label(fact_sorted__list__of__set__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3871 (all V_x_2 all V_f_2 all T_b all T_c all V_k_2 ((V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2)) & (V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(V_f_2,V_x_2))))) # label(fact_anamorph_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3872 (all V_A_2 all V_l_2 all V_x_2 all T_b c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2))))) # label(fact_sublist__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3873 (all V_xs_2 all V_x_2 all V_zs_2 all V_ys_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) <-> V_ys_2 = c_List_Olist_ONil(T_b) & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) | (exists B_ys_H (V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2)))) # label(fact_append__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3874 (all V_zs_2 all V_ys_2 all V_xs_2 all V_x_2 all T_b (hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) <-> V_ys_2 = c_List_Olist_ONil(T_b) & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 | (exists B_ys_H (hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2))))) # label(fact_Cons__eq__append__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3875 (all V_y_2 all V_ys_2 all V_x_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) <-> V_xs_2 = V_ys_2 & V_x_2 = V_y_2)) # label(fact_append1__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3876 (all V_ys all V_xs all V_x all T_a hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))) # label(fact_append__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3877 (all V_zs all V_xs all V_ys all V_xs1 all V_x all T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys -> (V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) -> hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)))) # label(fact_Cons__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3878 (all V_A_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))))) # label(fact_append__in__lists__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3879 (all V_us all V_ys all V_zs all V_xs1 all V_xs all T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs -> (V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) -> hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us)))) # label(fact_append__eq__appendI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3880 (all V_zs_2 all V_xs_2 all V_ys_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2) <-> V_ys_2 = V_zs_2)) # label(fact_append__same__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3881 (all V_zs_2 all V_ys_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2) <-> V_ys_2 = V_zs_2)) # label(fact_same__append__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3882 (all V_ts_2 all V_zs_2 all V_ys_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2) <-> (exists B_us (V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2))))) # label(fact_append__eq__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3883 (all V_zs all V_ys all V_xs all T_a hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs))) # label(fact_append__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3884 (all V_ys all V_xs all T_a (class_Groups_Omonoid__add(T_a) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)))) # label(fact_listsum__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3885 (all V_ys all V_xs all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) # label(fact_length__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3886 (all V_vs all V_ys all V_us all T_b all V_xs all T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us) -> (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs) -> hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs))))) # label(fact_zip__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3887 (all V_ys_2 all V_xs_2 all T_b hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) # label(fact_set__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3888 (all V_ys all T_a hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys) # label(fact_append__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3889 (all V_ys_2 all V_xs_2 all T_b (c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) <-> V_xs_2 = c_List_Olist_ONil(T_b) & V_ys_2 = c_List_Olist_ONil(T_b))) # label(fact_Nil__is__append__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3890 (all V_xs all T_a hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs) # label(fact_append__Nil2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3891 (all V_ys_2 all T_b all V_xs_2 (V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) <-> V_ys_2 = c_List_Olist_ONil(T_b))) # label(fact_self__append__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3892 (all V_xs_2 all T_b all V_ys_2 (V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_self__append__conv2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3893 (all V_ys_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b) <-> V_xs_2 = c_List_Olist_ONil(T_b) & V_ys_2 = c_List_Olist_ONil(T_b))) # label(fact_append__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3894 (all V_ys_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2 <-> V_ys_2 = c_List_Olist_ONil(T_b))) # label(fact_append__self__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3895 (all V_ys_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2 <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_append__self__conv2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3896 (all T_a all V_ys all V_xs (V_xs = V_ys -> V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys))) # label(fact_eq__Nil__appendI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3897 (all V_xs all T_a all V_ys ((V_ys = c_List_Olist_ONil(T_a) -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs)) & (V_ys != c_List_Olist_ONil(T_a) -> c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys))))) # label(fact_butlast__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3898 (all V_ys all V_x all V_xs all T_a hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x) # label(fact_nth__append__length) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3899 (all V_n all V_ys all V_xs all T_a hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n)) # label(fact_nth__append__length__plus) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3900 (all V_ys all V_xs all V_n all T_a hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys))) # label(fact_take__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3901 (all V_x all V_ys all V_xs all T_a all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys))) # label(fact_list__update__append1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3902 (all V_y all V_ys all V_x all V_xs all T_a hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys))) # label(fact_list__update__length) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3903 (all V_ys_2 all V_xs_2 all V_x_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2))))) # label(fact_remove1__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3904 (all V_ys_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))))) # label(fact_in__set__butlast__appendI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3905 (all V_x all V_xs all T_a c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs) # label(fact_butlast__snoc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3906 (all V_vs_2 all V_us_2 all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) & V_us_2 = V_vs_2 | V_xs_2 = V_ys_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))))) # label(fact_append__listrel1I) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3907 (all V_x_2 all V_r_2 all V_v_2 all V_u_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))))) # label(fact_lexord__append__leftI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3908 (all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) <-> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_distinct__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3909 (all V_ys all V_xs all T_a all V_n ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))))) # label(fact_nth__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3910 (all V_x all V_ys all V_xs all T_a all V_n ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x))))) # label(fact_list__update__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3911 (all V_A_2 all V_l_H_2 all V_l_2 all T_b c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2))))) # label(fact_sublist__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3912 (all V_ys_2 all V_vs_2 all V_us_2 all V_xs_2 all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) -> (V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2)) -> (V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))))))) # label(fact_listrel1I) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3913 (all V_y_2 all V_x_2 all V_u_2 all V_r_2 all V_b_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))))) # label(fact_lexord__append__left__rightI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3914 (all V_xs all T_a all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))))) # label(fact_take__Suc__conv__app__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3915 (all V_r_2 all V_y_2 all V_ys_2 all V_x_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2))) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) & V_x_2 = V_y_2 | V_xs_2 = V_ys_2 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)))) # label(fact_snoc__listrel1__snoc__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3916 (all V_r_2 all V_ys_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) -> -(all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) -> (all B_us all B_vs (V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) -> V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)))))))) # label(fact_listrel1E) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3917 (all V_r_2 all V_v_2 all V_u_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) -> ((all B_a -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))))) # label(fact_lexord__append__leftD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3918 (all V_xs_2 all T_b hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2)) # label(fact_rotate1__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3919 (all V_a all V_xs all T_a all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))))) # label(fact_upd__conv__take__nth__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3920 (all V_xs all V_n all T_a hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs) # label(fact_append__take__drop__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3921 (all V_xs all V_x all T_a hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs) # label(fact_drop__1__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3922 (all V_xs all V_x all V_n all T_a hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) # label(fact_drop__Suc__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3923 (all V_ys all V_y all V_xs all V_n all T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) -> hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y)) # label(fact_nth__via__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3924 (all V_i all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))))) # label(fact_distinct__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3925 (all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) <-> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)))) # label(fact_distinct1__rotate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3926 (all V_xs all V_n all T_a c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs))) # label(fact_butlast__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3927 (all V_xs all V_n all T_a hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))) # label(fact_drop__butlast) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3928 (all V_xs all V_m all V_n all T_a hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))) # label(fact_drop__take) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3929 (all V_xs all V_m all V_n all T_a hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs))) # label(fact_take__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3930 (all V_xs all V_m all V_n all T_a hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)) # label(fact_drop__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3931 (all V_xs all T_a hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs) # label(fact_drop__0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3932 (all V_ys all V_xs all V_n all T_b all T_a hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys))) # label(fact_drop__zip) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3933 (all V_xs all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) # label(fact_length__rotate1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3934 (all V_xs all V_n all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) # label(fact_length__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3935 (all V_xs_2 all T_b hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2)) # label(fact_set__rotate1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3936 (all V_xs_2 all V_n_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_in__set__dropD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3937 (all V_xs_2 all V_n_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2)))) # label(fact_set__drop__subset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3938 (all V_n all T_a hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_drop__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3939 (all V_xs_2 all T_b (hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_rotate1__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3940 (all V_xs_2 all T_b all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))))) # label(fact_set__drop__subset__set__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3941 (all V_n all V_xs all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) -> hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a))) # label(fact_drop__all) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3942 (all V_xs_2 all V_n_2 all T_b (hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)))) # label(fact_drop__eq__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3943 (all V_ys all V_xs all V_n all T_a hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys))) # label(fact_drop__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3944 (all V_zs_2 all V_ys_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2 <-> V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2))) # label(fact_append__eq__conv__conj) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3945 (all V_xs_2 all V_x_2 all V_n_2 all T_b hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2)) # label(fact_drop__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3946 (all V_xs all V_x all T_a all V_n ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)))) # label(fact_drop__Cons_H) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3947 (all V_xs all T_a all V_i all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)))) # label(fact_nth__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3948 (all V_ys_092_060_094isub_0622_2 all V_ys_092_060_094isub_0621_2 all V_xs_092_060_094isub_0622_2 all V_xs_092_060_094isub_0621_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) <-> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) -> V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) -> hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2))) # label(fact_append__eq__append__conv__if) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3949 (all V_xs all T_a all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) # label(fact_nth__drop_H) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3950 (all V_xs all V_x all T_b all T_a (hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) & hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))))) # label(fact_rotate__simps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3951 (all V_xs all V_x all T_a all V_v ((hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) & (hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)))) # label(fact_drop__Cons__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3952 (all V_xs all T_a all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))))) # label(fact_take__add) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3953 (all V_xs all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) -> hAPP(c_List_Orotate1(T_a),V_xs) = V_xs)) # label(fact_rotate1__length01) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3954 (all V_zs all V_ys all V_xs all T_b all T_a hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs))) # label(fact_zip__append2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3955 (all V_zs all V_ys all V_xs all T_b all T_a hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs)))) # label(fact_zip__append1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3956 (all V_xs all T_a all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))))) # label(fact_id__take__nth__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3957 (all V_xs all T_a all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs))) # label(fact_take__hd__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3958 (all V_n all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n)))) # label(fact_hd__drop__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3959 (all V_xs all V_x all T_a hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x) # label(fact_hd_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3960 (all V_ys all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs))) # label(fact_hd__append2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3961 (all V_ys all T_a all V_xs ((V_xs = c_List_Olist_ONil(T_a) -> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys)) & (V_xs != c_List_Olist_ONil(T_a) -> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs)))) # label(fact_hd__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3962 (all T_b all V_xs_2 (V_xs_2 != c_List_Olist_ONil(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_hd__in__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3963 (all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_hd__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3964 (all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))))) # label(fact_rotate1__hd__tl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3965 (all V_n all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))))) # label(fact_hd__rotate__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3966 (all V_xs all V_n all T_a hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))) # label(fact_drop__tl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3967 (all V_xs all V_n all T_a hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) # label(fact_tl__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3968 (all V_xs all V_x all T_a hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs) # label(fact_tl_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3969 (all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))))) # label(fact_distinct__tl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3970 (all V_xs_2 all V_n_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) <-> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)))) # label(fact_distinct__rotate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3971 (all V_xs all V_n all V_m all T_a hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs)) # label(fact_rotate__rotate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3972 (all T_b c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b))) # label(fact_rotate0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3973 (all V_n_2 all V_m_2 all T_b c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2))) # label(fact_rotate__add) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3974 (all V_xs all V_n all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) # label(fact_length__rotate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3975 (all V_xs_2 all V_n_2 all T_b hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2)) # label(fact_set__rotate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3976 (all T_a hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_tl_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3977 (all V_xs_2 all V_n_2 all T_b (hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_rotate__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3978 (all V_n_2 all T_b c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b))) # label(fact_rotate__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3979 (all V_xs all V_n all T_a hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs))) # label(fact_rotate1__rotate__swap) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3980 (all V_ys all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys))) # label(fact_tl__append2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3981 (all V_xs all V_n all T_a hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs))) # label(fact_take__tl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3982 (all V_xs all V_n all T_a hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)) # label(fact_rotate__conv__mod) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3983 (all V_xs all V_n all T_a hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) # label(fact_drop__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3984 (all V_xs all V_n all T_a hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs))) # label(fact_rotate__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3985 (all V_ys_2 all V_xs_2 all T_b hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2)) # label(fact_tl__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3986 (all V_xs all T_a all V_n (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs)) # label(fact_rotate__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3987 (all V_n all V_xs all T_a (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) -> hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs)) # label(fact_rotate__length01) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3988 (all V_xs all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) # label(fact_length__tl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3989 (all V_xs all V_n all T_a hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs))) # label(fact_tl__take) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.20 3990 (all V_n all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))))) # label(fact_take__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3991 (all V_xs all V_n all T_a hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs))) # label(fact_rotate__drop__take) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3992 (all V_xs_2 all T_b (class_Lattices_Oab__semigroup__idem__mult(T_b) -> (V_xs_2 != c_List_Olist_ONil(T_b) -> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2))))) # label(fact_fold1__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3993 (all V_r_2 all V_x_2 all T_b all V_y_2 ((exists B_b exists B_z V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))))) # label(fact_lexord__append__rightI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3994 (all V_a_2 all V_f_2 all T_c all T_b hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2) # label(fact_foldl__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3995 (all V_ns_2 all V_n_2 all V_m_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))))) # label(fact_start__le__sum) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3996 (all V_zs_2 all V_y_2 all V_x_2 all T_b (class_Groups_Osemigroup__add(T_b) -> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)))) # label(fact_foldl__assoc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3997 (all V_zs_2 all V_x_2 all T_b (class_Groups_Omonoid__add(T_b) -> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2))) # label(fact_foldl__absorb0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3998 (all V_xs_2 all V_x_2 all V_a_2 all V_f_2 all T_c all T_b hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2)) # label(fact_foldl__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 3999 (all V_ys_2 all V_xs_2 all V_a_2 all V_f_2 all T_c all T_b hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2)) # label(fact_foldl__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4000 (all T_b (class_Groups_Omonoid__add(T_b) -> c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_listsum__foldl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4001 (all V_ns_2 all V_m_2 (hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <-> V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) & (all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) -> B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) # label(fact_sum__eq__0__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4002 (all V_xs_2 all V_y_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2))) # label(fact_fun__left__comm__idem_Ofold__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4003 (all V_xs_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2))) # label(fact_Sup__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4004 (all V_xs_2 all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2))) # label(fact_Inf__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4005 (all V_xs_2 all V_x_2 all T_b (class_Lattices_Olattice(T_b) -> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2))) # label(fact_Sup__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4006 (all V_xs_2 all V_x_2 all T_b (class_Lattices_Olattice(T_b) -> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2))) # label(fact_Inf__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4007 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2))) # label(fact_Min__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4008 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2))) # label(fact_Max__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4009 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2))) # label(fact_min__max_OInf__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4010 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2))) # label(fact_min__max_OSup__fin__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4011 (all V_f_2 all V_xs_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2))) # label(fact_SUPR__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4012 (all V_f_2 all V_xs_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2))) # label(fact_INFI__set__fold) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4013 (all V_ns_2 all V_n_2 (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))))) # label(fact_elem__le__sum) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4014 (all V_x_2 all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))))) # label(fact_sorted__list__of__set__insert) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4015 (all V_r_2 all V_y_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2))) <-> (exists B_a exists B_x V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x)))) # label(fact_lexord__Nil__left) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4016 (all V_x_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))) # label(fact_insort__key_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4017 (all V_ys_2 all T_c all V_y_2 all V_x_2 all V_f_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2))))) # label(fact_insort__key_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4018 (all V_xs_2 all V_x_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) # label(fact_length__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4019 (all V_xs_2 all T_c all V_y_2 all V_x_2 all V_f_2 all T_b (class_Orderings_Olinorder(T_b) -> (hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2))))) # label(fact_insort__key__left__comm) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4020 (all V_xs_2 all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)))) # label(fact_insort__left__comm) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4021 (all T_b (class_Orderings_Olinorder(T_b) -> c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))))) # label(fact_fun__left__comm__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4022 (all V_xs_2 all V_x_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) # label(fact_set__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4023 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2)) # label(fact_remove1__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4024 (all V_xs_2 all V_a_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b))) # label(fact_insort__not__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4025 (all V_xs_2 all V_x_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> (hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2))) <-> -hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))))) # label(fact_distinct__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4026 (all V_xs_2 all T_c all V_x_2 all V_f_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)))) -> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))) # label(fact_insort__insert__insort__key) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4027 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)))) # label(fact_insort__insert__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4028 (all V_x_2 all V_f_2 all V_xs_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2)))))) # label(fact_distinct__insort__insert) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4029 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2))) # label(fact_insort__insert__triv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4030 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) # label(fact_set__insort__insert) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4031 (all V_xs_2 all T_c all V_x_2 all V_f_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)))) -> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2))) # label(fact_insort__insert__key__triv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4032 (all V_x all V_k all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> (V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x) & (V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs)))) # label(fact_last__list__update) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4033 (all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) # label(fact_last__conv__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4034 (all V_x all T_a all V_xs ((V_xs = c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x) & (V_xs != c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs)))) # label(fact_last_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4035 (all V_x all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs))) # label(fact_last__ConsR) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4036 (all V_x all T_a all V_xs (V_xs = c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x)) # label(fact_last__ConsL) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4037 (all V_xs all T_a all V_ys ((V_ys = c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs)) & (V_ys != c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys)))) # label(fact_last__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4038 (all V_xs all T_a all V_ys (V_ys != c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys))) # label(fact_last__appendR) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4039 (all V_xs all T_a all V_ys (V_ys = c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs))) # label(fact_last__appendL) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4040 (all T_b all V_as_2 (V_as_2 != c_List_Olist_ONil(T_b) -> hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))))) # label(fact_last__in__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4041 (all V_x all V_xs all T_a c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x) # label(fact_last__snoc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4042 (all V_xs all T_a all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs))) # label(fact_last__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4043 (all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs)) # label(fact_append__butlast__last__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4044 (all V_ys_2 all V_x_2 all V_xs_2 all T_b (hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2 <-> V_ys_2 != c_List_Olist_ONil(T_b) & c_List_Obutlast(T_b,V_ys_2) = V_xs_2 & c_List_Olast(T_b,V_ys_2) = V_x_2)) # label(fact_snoc__eq__iff__butlast) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4045 (all V_A_2 all V_a_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) <-> V_a_2 = c_List_Olist_ONil(T_b) | (exists B_a exists B_l (V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))))))) # label(fact_lists_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4046 (all T_b all V_xs_2 (V_xs_2 != c_List_Olist_ONil(T_b) -> c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2))) # label(fact_select__weigth__select) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4047 (all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) # label(fact_inj__mapI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4048 (all V_f_2 all T_c all T_b all V_xs_2 (V_xs_2 != c_List_Olist_ONil(T_b) -> c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)))) # label(fact_last__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4049 (all V_xs_2 all V_f_2 all T_d all V_a_2 all V_g_2 all T_c all T_b hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2)) # label(fact_foldl__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4050 (all V_xs_2 all V_f_2 all T_c all V_n_2 all T_b hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2))) # label(fact_rotate__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4051 (all V_xs_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) # label(fact_map__tl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4052 (all V_ys_2 all V_f_2 all T_d all V_xs_2 all T_c all T_b hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2))) # label(fact_zip__map2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4053 (all V_ys_2 all V_g_2 all T_e all V_xs_2 all V_f_2 all T_b all T_d all T_c hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2))) # label(fact_map__zip__map2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4054 (all V_ys_2 all V_xs_2 all V_g_2 all T_e all V_f_2 all T_b all T_d all T_c hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2))) # label(fact_map__zip__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4055 (all V_ys_2 all V_xs_2 all V_f_2 all T_d all T_c all T_b hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2))) # label(fact_zip__map1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4056 (all V_ys_2 all V_g_2 all T_e all V_xs_2 all V_f_2 all T_d all T_c all T_b hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2))) # label(fact_zip__map__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4057 (all V_xs_2 all T_b hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2)) # label(fact_zip__same__conv__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4058 (all V_xs_2 all V_f_2 all T_b all T_c (hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b) <-> V_xs_2 = c_List_Olist_ONil(T_c))) # label(fact_map__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4059 (all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b)) # label(fact_map_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4060 (all V_xs_2 all V_f_2 all T_c all T_b (c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) <-> V_xs_2 = c_List_Olist_ONil(T_c))) # label(fact_Nil__is__map__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4061 (all V_y_2 all V_k_2 all V_xs_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2))) # label(fact_map__update) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4062 (all V_g_2 all V_xs_2 all V_f_2 all T_b all T_c (hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) -> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x))))) # label(fact_map__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4063 (all V_ys_2 all V_g_2 all T_d all V_xs_2 all V_f_2 all T_b all T_c (hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2))) # label(fact_map__eq__imp__length__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4064 (all V_xs_2 all V_f_2 all T_c all T_b hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)) # label(fact_length__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4065 (all V_xs_2 all V_ca_2 all V_f_2 all T_c all T_b (class_Rings_Osemiring__0(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_ca_2))) # label(fact_listsum__mult__const) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4066 (all V_xs_2 all V_f_2 all V_ca_2 all T_c all T_b (class_Rings_Osemiring__0(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))))) # label(fact_listsum__const__mult) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4067 (all V_xs_2 all T_c all T_b (class_Groups_Omonoid__add(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b))) # label(fact_listsum__0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4068 (all V_xs_2 all V_g_2 all V_f_2 all T_c all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))))) # label(fact_listsum__addf) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4069 (all V_xs_2 all V_g_2 all V_f_2 all T_c all T_b (class_Groups_Oab__group__add(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))))) # label(fact_listsum__subtractf) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4070 (all V_ys_2 all V_xs_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) <-> V_xs_2 = V_ys_2))) # label(fact_inj__map__eq__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4071 (all V_ys_2 all V_xs_2 all V_f_2 all T_b all T_c (hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) -> (c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> V_xs_2 = V_ys_2))) # label(fact_map__injective) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4072 (all V_xs_2 all T_b hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2) # label(fact_map__ident) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4073 (all V_xs_2 all V_f_2 all T_c all V_n_2 all T_b hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2))) # label(fact_take__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4074 (all V_xs_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) # label(fact_map__butlast) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4075 (all V_xs_2 all V_f_2 all T_c all T_b hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))) # label(fact_set__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4076 (all V_xs_2 all V_x_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) # label(fact_map_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4077 (all V_ys_2 all V_xs_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2))) # label(fact_map__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4078 (all V_f_2 all T_c all T_b all V_xs_2 (V_xs_2 != c_List_Olist_ONil(T_b) -> hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)))) # label(fact_hd__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4079 (all V_xs_2 all V_f_2 all T_c all V_n_2 all T_b hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2))) # label(fact_drop__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4080 (all T_b hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b))) # label(fact_List_Omap_Oid) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4081 (all T_b hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b))) # label(fact_List_Omap_Oidentity) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4082 (all V_g_2 all V_f_2 all T_b all T_c all T_d hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2))) # label(fact_List_Omap_Ocomp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4083 (all V_g_2 all V_f_2 all T_b all T_c all T_d hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2))) # label(fact_map__comp__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4084 (all V_list_2 all V_g_2 all T_d all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2)) # label(fact_List_Omap_Ocompositionality) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4085 (all V_xs_2 all V_g_2 all T_d all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2)) # label(fact_map__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4086 (all V_xs_2 all V_g_2 all T_c all V_f_2 all T_b c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2)) # label(fact_list__size__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4087 (all V_ys_2 all V_xs_2 all V_f_2 all T_b all T_c (hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) -> (c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2))) -> V_xs_2 = V_ys_2))) # label(fact_map__inj__on) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4088 (all V_ys_2 all V_xs_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) -> (hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) <-> V_xs_2 = V_ys_2))) # label(fact_inj__on__map__eq__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4089 (all V_f_2 all T_c all V_xs_2 all T_b all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)))) # label(fact_nth__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4090 (all V_v_2 all V_f_2 all T_c all V_xs_2 all V_y_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) # label(fact_map__fun__upd) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4091 (all V_xs_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) <-> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)))) # label(fact_distinct__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4092 (all V_xs_2 all T_b (class_Groups_Oordered__ab__group__add__abs(T_b) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))))) # label(fact_listsum__abs) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4093 (all V_xs_2 all V_f_2 all T_c all T_b (class_Groups_Oab__group__add(T_b) -> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)))) # label(fact_uminus__listsum__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4094 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2))) -> c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2))) # label(fact_inj__on__mapI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4095 (all V_f_2 all T_c all T_b (c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_inj__mapD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4096 (all V_f_2 all T_c all T_b (c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) <-> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_inj__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4097 (all V_f_2 all V_xs_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_listsum__distinct__conv__setsum__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4098 (all V_xs_2 all V_r_2 all T_c all T_b (class_Rings_Osemiring__1(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2))) # label(fact_listsum__triv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4099 (all V_f_2 all V_xs_2 all V_x_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))))))) # label(fact_listsum__map__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4100 (all V_f_2 all V_A_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))))) & (-hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c)))) # label(fact_Nitpick_Osetsum_H__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4101 (all V_xs_2 all T_b all V_l_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2))) # label(fact_pick__same) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4102 (all V_m all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) # label(fact_times__code__numeral__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4103 (all V_m_2 all V_n_2 (hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) <-> V_n_2 = V_m_2)) # label(fact_Code__Numeral_Oof__nat__inject) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4104 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)))) # label(fact_less__code__numeral__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4105 (all V_y_2 all V_x_2 (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) -> (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) -> (hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) <-> V_x_2 = V_y_2)))) # label(fact_code__numeral_Oof__nat__inject) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4106 (all V_ys_2 all T_c all V_xs_2 all T_b (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) -> hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2)) # label(fact_map__fst__zip) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4107 (all V_ys_2 all T_c all V_xs_2 all T_b (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) -> hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2)) # label(fact_map__snd__zip) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4108 (all V_zs_2 all T_c all T_b hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2) # label(fact_zip__map__fst__snd) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4109 (all V_m all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) # label(fact_plus__code__numeral__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4110 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)))) # label(fact_less__eq__code__numeral__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4111 (all V_m all V_n hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m))) # label(fact_subtract__code__numeral__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4112 (all V_xs_2 all T_b all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))))) # label(fact_pick__member) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4113 (all V_zs_2 all V_ys_2 all T_c all V_xs_2 all T_b (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) -> (hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2 <-> hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2))) # label(fact_zip__eq__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4114 (all V_xs_2 all V_f_2 all T_b c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) # label(fact_list__size__conv__listsum) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4115 (all V_i_2 (V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)))) # label(fact_code__numeral__not__eq__zero) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4116 (all V_l_2 all V_k_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))))) # label(fact_interv__listsum__conv__setsum__set__int) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4117 (all V_j_2 all V_i_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))))) # label(fact_setsum__set__upto__conv__listsum__int) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4118 (all V_s_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))))) # label(fact_select__weight__member) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4119 (all V_xs_2 all T_b c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2)))) # label(fact_select__weight__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4120 (all V_xs_2 all T_b c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of)))) # label(fact_select__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4121 (all V_g_2 all V_f_2 all V_xs_2 all T_b all T_c (class_Groups_Omonoid__add(T_c) & class_Groups_Oordered__ab__semigroup__add(T_c) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2))))))) # label(fact_listsum__mono) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4122 (all V_x hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x) # label(fact_nat__of__inverse) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4123 (all V_k hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k) # label(fact_of__nat__nat__of) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4124 (all V_n hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n) # label(fact_nat__of__of__nat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4125 (all V_m all V_n hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m)))) # label(fact_times__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4126 (all V_l_2 all V_k_2 (hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) <-> V_k_2 = V_l_2)) # label(fact_Code__Numeral_Onat__of__inject) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4127 (all V_y_2 all V_x_2 (hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) <-> V_x_2 = V_y_2)) # label(fact_code__numeral_Onat__of__inject) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4128 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))))) # label(fact_less__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4129 (all V_x_2 hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_nat__of) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4130 (all V_k hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k)) # label(fact_nat__of__number) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4131 (all V_m_2 all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))))) # label(fact_less__eq__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4132 (all V_i hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_nat__of__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4133 (all V_n all V_i c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n)) # label(fact_nat__of__aux__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4134 (all V_k c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k)))) # label(fact_Suc__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4135 (all V_m all V_n hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m)))) # label(fact_minus__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4136 (all V_y_2 (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) -> hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2)) # label(fact_of__nat__inverse) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4137 (all V_m all V_n hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m)))) # label(fact_plus__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4138 (all V_m all V_n hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m)))) # label(fact_div__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4139 (all V_m all V_n c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m)))) # label(fact_mod__code__numeral__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4140 (all V_k (V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))))) # label(fact_code__numeral__decr) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4141 (all V_i_2 all V_xq_2 hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2)))) # label(fact_New__DSequence_Opos__not__seq__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4142 (all V_no_2 all V_yes_2 all V_xs_2 all V_Pa_2 all T_b (c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) -> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2))) # label(fact_partition__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4143 (all V_no_2 all V_yes_2 all V_xs_2 all V_Pa_2 all T_b (c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) -> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) -> -hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_partition__P) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4144 (all V_Pa_2 all T_b c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))) # label(fact_partition_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4145 (all V_xs_2 all V_x_2 all V_Pa_2 all T_b c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2))) # label(fact_partition_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4146 (all V_B_2 all V_A_2 all V_l_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2))) -> hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2))))) # label(fact_lists__IntI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4147 (all V_B_2 all V_A_2 all T_b c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2)))) # label(fact_lists__Int__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4148 (all V_A_2 all T_b hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b)))) # label(fact_listsp_ONil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4149 (all V_A_2 all T_b hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b)))) # label(fact_listsp_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4150 (all V_xs_2 all V_A_2 all T_b (hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_A_2,B_x)))))) # label(fact_in__listsp__conv__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4151 (all V_x_2 all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2)) <-> hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)))) # label(fact_listsp__conj__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4152 (all V_B_2 all V_A_2 all T_b c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) # label(fact_listsp__inf__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4153 (all V_B_2 all V_l_2 all V_A_2 all T_b (hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2)) -> (hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2)) -> hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2))))) # label(fact_listsp__infI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4154 (all V_a2_2 all V_a1_2 all V_A_2 all T_b (hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2))) <-> hBOOL(hAPP(V_A_2,V_a1_2)) & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)))) # label(fact_listsp_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4155 (all V_ys_2 all V_xs_2 all V_A_2 all T_b (hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) <-> hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)))) # label(fact_append__in__listsp__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4156 (all V_B_2 all V_A_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))))) # label(fact_listsp__mono) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4157 (all V_x_2 all V_A_2 all T_b (hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))))) # label(fact_listsp__lists__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4158 (all V_ys_2 all V_xs_2 all V_x_2 all T_c all T_b c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2))) # label(fact_product_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4159 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) <-> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) & (all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)))))) # label(fact_list__all2__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4160 (all V_bs_2 all V_f_2 all T_d all V_as_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2)) <-> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2))) # label(fact_list__all2__map2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4161 (all V_bs_2 all V_as_2 all V_f_2 all T_d all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2) <-> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2))) # label(fact_list__all2__map1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4162 (all V_n_2 all V_bs_2 all V_as_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2) -> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)))) # label(fact_list__all2__dropI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4163 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) -> (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2) -> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2))))) # label(fact_list__all2__appendI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4164 (all V_vs_2 all V_us_2 all V_Pa_2 all V_ys_2 all T_c all V_xs_2 all T_b (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) -> (c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2)) <-> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2)))) # label(fact_list__all2__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4165 (all V_ys_2 all V_y_2 all V_xs_2 all V_x_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) <-> hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2))) # label(fact_list__all2__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4166 (all V_n_2 all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) -> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)))) # label(fact_list__all2__takeI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4167 (all T_b all V_ys_2 all V_xs_2 (V_xs_2 = V_ys_2 <-> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2))) # label(fact_list__all2__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4168 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) # label(fact_list__all2__lengthD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4169 (all V_ys_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2) <-> V_ys_2 = c_List_Olist_ONil(T_c))) # label(fact_list__all2__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4170 (all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c)) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_list__all2__Nil2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4171 (all V_uu all T_b all T_a c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b))) # label(fact_product_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4172 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) <-> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) & (all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))))))) # label(fact_list__all2__conv__all__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4173 (all V_p_2 all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2)))))) # label(fact_list__all2__nthD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4174 (all V_p_2 all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) -> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2)))))) # label(fact_list__all2__nthD2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4175 (all V_y_2 all V_x_2 all V_ys_2 all V_Pa_2 all T_c all V_xs_2 all T_b all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)))))) # label(fact_list__all2__update__cong) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4176 (all V_i_2 all V_y_2 all V_x_2 all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))) -> c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)))))) # label(fact_list__all2__update__cong2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4177 (all V_ys all T_b all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> (hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) -> hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys)))))) # label(fact_distinct__product) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4178 (all V_ys_2 all V_xs_2 all T_c all T_b hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2)))) # label(fact_product__list__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4179 (all V_xs_2 all T_b hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) # label(fact_sublists__powset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4180 (all V_xs all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) # label(fact_length__sublists) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4181 (all T_a c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) # label(fact_sublists_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4182 (all V_xs_2 all V_x_2 all T_b c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b)))))) # label(fact_sublists_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4183 (all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))))) # label(fact_distinct__set__sublists) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4184 (all V_xs_2 all V_n_2 all T_b hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_set__n__lists) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4185 (all V_Pa_2 all T_b c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2)) # label(fact_enum__the__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4186 (all V_n all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))))) # label(fact_distinct__n__lists) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4187 (all T_a all V_n ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) & (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a))))) # label(fact_n__lists__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4188 (all V_xs all T_a c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) # label(fact_n__lists_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4189 (all V_xs all V_n all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) # label(fact_length__n__lists) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4190 (all V_xs_2 all V_n_2 all V_ys_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2)) # label(fact_length__n__lists__elem) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4191 (all V_Pa_2 all V_b_2 all V_a_2 all T_c all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2)))) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)))) -> (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2) -> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)))) # label(fact_list__all2I) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4192 (all V_x_2 all V_Pa_2 all V_xs_2 all T_b ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))))) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,V_x_2))))) # label(fact_all__nth__imp__all__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4193 (all V_xs_2 all V_y_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) -> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)))) # label(fact_fun__left__comm_Ofold__set__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4194 (all V_xs_2 all V_x_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))) # label(fact_map__removeAll__inj__on) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4195 (all V_xs all T_a hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs)))) # label(fact_distinct__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4196 (all V_xs all T_a hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))) # label(fact_length__remdups__leq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4197 (all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> c_List_Oremdups(T_a,V_xs) = V_xs)) # label(fact_distinct__remdups__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4198 (all V_x all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))))) # label(fact_distinct__removeAll) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.21 4199 (all V_xs_2 all T_b (c_List_Oremdups(T_b,V_xs_2) = V_xs_2 <-> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)))) # label(fact_remdups__id__iff__distinct) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4200 (all V_xs_2 all T_b hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2)) # label(fact_set__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4201 (all V_xs_2 all T_b (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) <-> c_List_Oremdups(T_b,V_xs_2) = V_xs_2)) # label(fact_length__remdups__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4202 (all V_xs all T_a c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs)) # label(fact_remdups__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4203 (all V_x_2 all T_b (c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b) <-> V_x_2 = c_List_Olist_ONil(T_b))) # label(fact_remdups__eq__nil__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4204 (all V_x all T_a hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_removeAll_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4205 (all V_x_2 all T_b (c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2) <-> V_x_2 = c_List_Olist_ONil(T_b))) # label(fact_remdups__eq__nil__right__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4206 (all T_a c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_remdups_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4207 (all V_xs all T_a all V_y all V_x ((V_x = V_y -> hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) & (V_x != V_y -> hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))))) # label(fact_removeAll_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4208 (all V_ys all V_xs all V_x all T_a hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys))) # label(fact_removeAll__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4209 (all V_xs_2 all V_f_2 all T_c all T_b c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) # label(fact_remdups__map__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4210 (all V_x all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)))) # label(fact_remove1__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4211 (all V_xs_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2)) # label(fact_removeAll__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4212 (all V_x all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) # label(fact_distinct__remove1__removeAll) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4213 (all V_xs_2 all V_x_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2)) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2))))) # label(fact_remdups_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4214 (all V_xs_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) # label(fact_length__remdups__card__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4215 (all V_xs_2 all V_x_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))) # label(fact_map__removeAll__inj) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4216 (all V_xs_2 all V_x_2 all T_b hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_set__removeAll) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4217 (all V_xss_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b)))) # label(fact_length__remdups__concat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4218 (all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)))) # label(fact_sorted__list__of__set__sort__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4219 (all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b))) # label(fact_sort__key__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4220 (all V_xss_2 all V_xs_2 all T_b hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2))) # label(fact_foldl__conv__concat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4221 (all V_xss_2 all T_b c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2)) # label(fact_concat__conv__foldl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4222 (all V_xs_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) # label(fact_length__sort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4223 (all V_xs_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2))) # label(fact_set__sort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4224 (all V_xs_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> (hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2))) <-> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))))) # label(fact_distinct__sort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4225 (all T_a c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a)) # label(fact_concat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4226 (all V_xs all V_x all T_a c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs))) # label(fact_concat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4227 (all V_xss_2 all T_b (c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) -> B_x = c_List_Olist_ONil(T_b))))) # label(fact_concat__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4228 (all V_xss_2 all T_b (c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) -> B_x = c_List_Olist_ONil(T_b))))) # label(fact_Nil__eq__concat__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4229 (all V_xs_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2))) # label(fact_map__concat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4230 (all V_xss_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2))) # label(fact_length__concat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4231 (all V_xs_2 all T_b hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b))) # label(fact_set__concat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4232 (all V_xs_2 all V_x_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))) # label(fact_sort__key__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4233 (all V_ys all V_xs all T_a c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys))) # label(fact_concat__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4234 (all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2))) # label(fact_sort__foldl__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4235 (all V_ys_2 all V_xs_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)))) -> (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2) -> (c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) <-> V_xs_2 = V_ys_2)))) # label(fact_concat__eq__concat__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4236 (all V_ys_2 all V_xs_2 all T_b (c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2) -> (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) -> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)))) -> V_xs_2 = V_ys_2)))) # label(fact_concat__injective) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4237 (all V_xs_2 all V_f_2 all T_c all T_b c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) # label(fact_concat__map__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4238 (all V_xs_2 all V_n_2 all T_b c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)))) # label(fact_n__lists_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4239 (all V_xss_2 all V_xs_2 all V_x_2 all T_b c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)))))) # label(fact_transpose_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4240 (all V_xss_2 all T_b c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2))) # label(fact_transpose__aux__filter__head) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4241 (all V_xs_2 all V_p_2 all T_b hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2))) # label(fact_filter__concat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4242 (all V_xs_2 all V_f_2 all V_Pa_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)))) # label(fact_filter__sort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4243 (all V_Pa_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))))) # label(fact_distinct__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4244 (all V_xs_2 all V_Pa_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2)))) # label(fact_filter__is__subset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4245 (all V_xs_2 all V_Pa_2 all T_b (hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2 <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_filter__id__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4246 (all V_xs_2 all V_Pa_2 all T_b hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) # label(fact_sum__length__filter__compl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4247 (all V_xs_2 all V_Pa_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) # label(fact_length__filter__le) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4248 (all V_xs_2 all V_Q_2 all V_Pa_2 all T_b hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_Pa_2)),V_xs_2)) # label(fact_filter__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4249 (all V_xs_2 all V_x_2 all V_Q_2 all T_b hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2))) # label(fact_filter__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4250 (all V_xs_2 all T_b all V_x_2 all V_Pa_2 (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) # label(fact_remove1__filter__not) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4251 (all V_xs_2 all V_f_2 all T_b all V_x_2 all V_Pa_2 all T_c (class_Orderings_Olinorder(T_c) -> (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)))) # label(fact_filter__insort__triv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4252 (all V_xs_2 all V_Pa_2 all T_b hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) # label(fact_partition__filter1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4253 (all V_xs_2 all V_f_2 all T_c all V_Pa_2 all T_b hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2))) # label(fact_filter__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4254 (all V_Pa_2 all T_b hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b)) # label(fact_filter_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4255 (all T_a c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a))) # label(fact_transpose_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4256 (all V_xs_2 all T_b all V_x_2 all V_Pa_2 ((hBOOL(hAPP(V_Pa_2,V_x_2)) -> hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) & (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)))) # label(fact_filter_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4257 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_b hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2))) # label(fact_filter__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4258 (all V_xs_2 all V_Pa_2 all T_b (hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> -hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_filter__empty__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4259 (all V_x_2 all T_b c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2)))) # label(fact_removeAll__filter__not__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4260 (all V_xs_2 all V_Pa_2 all T_b c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2))) # label(fact_remdups__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4261 (all V_xs_2 all T_b all V_x_2 all V_Pa_2 (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) # label(fact_removeAll__filter__not) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4262 (all V_xs_2 all V_Pa_2 all T_b hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2)) # label(fact_partition__filter2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4263 (all V_xss all T_a c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss)) # label(fact_transpose_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4264 (all V_xs_2 all T_b all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) -> hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)))) # label(fact_nth__transpose) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4265 (all V_xs_2 all V_f_2 all T_c all T_b c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2))) # label(fact_transpose__map__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4266 (all V_xs_2 all V_Pa_2 all T_b hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2))) # label(fact_set__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4267 (all V_xs_2 all V_f_2 all T_c all V_Pa_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2))) # label(fact_length__filter__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4268 (all V_Pa_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) # label(fact_length__filter__less) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4269 (all V_xs_2 all V_f_2 all T_b c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2))) # label(fact_partition__filter__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4270 (all V_y_2 all V_xs_2 all T_b hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2))) # label(fact_set__minus__filter__out) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4271 (all V_s_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2))) # label(fact_filter__in__sublist) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4272 (all V_xs_2 all T_b (c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) -> B_x = c_List_Olist_ONil(T_b))))) # label(fact_transpose__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4273 (all V_xs_2 all V_p_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2)))))) # label(fact_length__filter__conv__card) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4274 (all V_xss_2 all T_b c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2))) # label(fact_transpose__aux__filter__tail) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4275 (all V_xss_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2))) -> c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))))) # label(fact_transpose_Opsimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4276 (all V_xss_2 all T_b (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2))) -> c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2))) # label(fact_transpose_Opsimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4277 (all V_is_2 all V_xs_2 all V_Pa_2 all T_b hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2))))) # label(fact_sublist__shift__lemma__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4278 (all V_xs_2 all T_b c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2)) # label(fact_select__weigth__drop__zero) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4279 (all V_xs_2 all T_b c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2)) # label(fact_pick__drop__zero) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4280 (all T_b (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b)))) -> c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)))) # label(fact_transpose_Opsimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4281 (all V_xs_2 all T_b c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2))) # label(fact_transpose__max__length) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4282 (all V_xss_2 all T_c all V_xs_2 all T_b hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) # label(fact_transpose__aux__max) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4283 (all V_a_2 all V_f_2 all T_b all T_c c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2) # label(fact_foldr_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4284 (all V_a_2 all V_xs_2 all V_x_2 all V_f_2 all T_b all T_c c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2))) # label(fact_foldr_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4285 (all V_a_2 all V_ys_2 all V_xs_2 all V_f_2 all T_b all T_c c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2))) # label(fact_foldr__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4286 (all V_a_2 all V_xs_2 all T_b (class_Groups_Oab__semigroup__add(T_b) -> c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2))) # label(fact_foldr__conv__foldl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4287 (all V_a_2 all V_xs_2 all V_f_2 all T_d all V_g_2 all T_b all T_c c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2)) # label(fact_foldr__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4288 (all V_xs_2 all T_b (class_Groups_Omonoid__add(T_b) -> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_foldl__foldr1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4289 (all V_xs_2 all V_a_2 all T_b (class_Groups_Omonoid__add(T_b) -> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))))) # label(fact_foldl__foldr1__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4290 (all V_xs_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_length__transpose) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4291 (all V_A_2 all V_xs_2 all T_b c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) # label(fact_sublist__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4292 (all V_i_2 all V_xs_2 all V_A_2 all T_b hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) # label(fact_sublist__shift__lemma) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4293 (all V_j_2 all V_i_2 hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2))) # label(fact_atLeastLessThan__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4294 (all V_j_2 all V_i_2 hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) # label(fact_set__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4295 (all V_j all V_i ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat)))) # label(fact_upt__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4296 (all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))))) # label(fact_upt__Suc__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4297 (all V_k all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))))) # label(fact_upt__add__eq__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4298 (all V_j all V_i ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat)))) # label(fact_upt__rec) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4299 (all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)))) # label(fact_upt__conv__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4300 (all V_i all V_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) -> c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat))) # label(fact_upt__conv__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4301 (all V_j_2 all V_i_2 (c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) <-> V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)))) # label(fact_upt__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4302 (all V_i c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat)) # label(fact_upt__0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4303 (all V_n all V_m all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) -> hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) # label(fact_take__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4304 (all V_n_2 all V_m_2 c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2)) # label(fact_sorted__list__of__set__range) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4305 (all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i)) # label(fact_hd__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4306 (all V_j all V_i all V_m hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j)) # label(fact_drop__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4307 (all V_j all V_i hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j)))) # label(fact_distinct__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4308 (all V_j all V_i hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)) # label(fact_length__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4309 (all V_n all V_m ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) -> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) -> c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat)))) # label(fact_upt__rec__number__of) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4310 (all V_xs_2 all V_x_2 all V_j_2 all V_i_2 (c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) & V_i_2 = V_x_2 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2)) # label(fact_upt__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4311 (all V_j all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) -> c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_last__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4312 (all V_n_2 all V_m_2 hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) # label(fact_map__Suc__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4313 (all V_m_2 all V_n_2 c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2)))) # label(fact_atLeastAtMost__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4314 (all V_n_2 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) # label(fact_atLeast__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4315 (all V_j all V_k all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)) -> hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k))) # label(fact_nth__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4316 (all V_m_2 all V_n_2 c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))) # label(fact_greaterThanAtMost__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4317 (all V_m_2 all V_n_2 c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2))) # label(fact_greaterThanLessThan__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4318 (all V_n_2 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)))) # label(fact_atMost__upto) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4319 (all V_xs_2 all T_b hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2) # label(fact_map__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4320 (all V_n_2 all V_m_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))))) # label(fact_interv__listsum__conv__setsum__set__nat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4321 (all V_n_2 all V_m_2 all V_f_2 all T_b (class_Groups_Ocomm__monoid__add(T_b) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))))) # label(fact_setsum__set__upt__conv__listsum__nat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4322 (all V_f_2 all T_b all V_m_2 all V_n_2 all V_i_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) -> hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)))) # label(fact_nth__map__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4323 (all V_n_2 all T_b all V_xs_2 ((V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) -> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) -> ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2)) -> c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))))) # label(fact_transpose__rectangle) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4324 (all V_f_2 all V_xs_2 all V_a_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> (c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) -> (hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2))))) # label(fact_insort__key__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4325 (all T_a (class_Orderings_Olinorder(T_a) -> c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)))) # label(fact_sorted_ONil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4326 (all V_x all T_a (class_Orderings_Olinorder(T_a) -> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))))) # label(fact_sorted__single) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4327 (all V_j all V_i c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j))) # label(fact_sorted__upt) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4328 (all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)))) # label(fact_sorted__sort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4329 (all V_x_2 all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,V_xs_2) -> c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2))))) # label(fact_sorted__insort__insert) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4330 (all V_n all V_xs all T_a (class_Orderings_Olinorder(T_a) -> (c_List_Olinorder__class_Osorted(T_a,V_xs) -> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))))) # label(fact_sorted__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4331 (all V_j all V_i c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j))) # label(fact_sorted__upto) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4332 (all V_n all V_xs all T_a (class_Orderings_Olinorder(T_a) -> (c_List_Olinorder__class_Osorted(T_a,V_xs) -> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs))))) # label(fact_sorted__take) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4333 (all V_a all V_xs all T_a (class_Orderings_Olinorder(T_a) -> (c_List_Olinorder__class_Osorted(T_a,V_xs) -> c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs))))) # label(fact_sorted__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4334 (all V_xs all T_a (class_Orderings_Olinorder(T_a) -> (c_List_Olinorder__class_Osorted(T_a,V_xs) -> c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs))))) # label(fact_sorted__tl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4335 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) <-> c_List_Olinorder__class_Osorted(T_b,V_xs_2)))) # label(fact_sorted__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4336 (all V_xs all T_a (class_Orderings_Olinorder(T_a) -> (V_xs != c_List_Olist_ONil(T_a) -> (c_List_Olinorder__class_Osorted(T_a,V_xs) -> c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)))))) # label(fact_sorted__butlast) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4337 (all T_a (class_Orderings_Olinorder(T_a) -> c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)))) # label(fact_sorted_Oequations_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4338 (all V_zs_2 all V_y_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))))) # label(fact_sorted__many__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4339 (all V_zs all V_y all V_x all T_a (class_Orderings_Olinorder(T_a) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) -> (c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) -> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))))))) # label(fact_sorted__many) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4340 (all V_l all T_a (class_Orderings_Olinorder(T_a) -> (c_List_Olinorder__class_Osorted(T_a,V_l) -> c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l))))) # label(fact_sorted__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4341 (all V_ys_2 all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,V_xs_2) -> (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> (c_List_Olinorder__class_Osorted(T_b,V_ys_2) -> (hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2)) -> (hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) -> V_xs_2 = V_ys_2))))))) # label(fact_sorted__distinct__set__unique) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4342 (all V_xs_2 all V_f_2 all T_c all T_b (class_Orderings_Olinorder(T_b) -> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))))) # label(fact_sorted__sort__key) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4343 (all V_x_2 all V_xs_2 all V_f_2 all T_c all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) -> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2)))))) # label(fact_sorted__insort__insert__key) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4344 (all V_x_2 all V_xs_2 all V_f_2 all T_c all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) -> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2)))))) # label(fact_sorted__map__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4345 (all V_xs_2 all V_x_2 all V_f_2 all T_c all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2))) <-> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))))) # label(fact_sorted__insort__key) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4346 (all V_xs_2 all V_g_2 all V_f_2 all T_c all T_b (class_Orderings_Olinorder(T_b) -> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))))) # label(fact_sorted__map__same) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4347 (all V_Pa_2 all V_xs_2 all V_f_2 all T_c all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) -> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)))))) # label(fact_sorted__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4348 (all V_xs_2 all V_g_2 all T_b (class_Orderings_Olinorder(T_b) -> c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)))) # label(fact_sorted__same) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4349 (all V_xs_2 all V_x_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) <-> c_List_Olinorder__class_Osorted(T_b,V_xs_2) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))))))) # label(fact_sorted__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4350 (all V_ys_2 all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) <-> c_List_Olinorder__class_Osorted(T_b,V_xs_2) & c_List_Olinorder__class_Osorted(T_b,V_ys_2) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))))))))) # label(fact_sorted__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4351 (all V_x_2 all V_Pa_2 all V_xs_2 all V_f_2 all T_c all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) -> (hBOOL(hAPP(V_Pa_2,V_x_2)) -> hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)))))) # label(fact_filter__insort) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4352 (all V_a1_2 all V_a2_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)))) & c_List_Olinorder__class_Osorted(T_b,V_a1_2)))) # label(fact_sorted_Oequations_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4353 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))))) # label(fact_sorted__list__of__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4354 (all V_xs_2 all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> (c_List_Olinorder__class_Osorted(T_b,V_xs_2) -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2)))) # label(fact_insort__remove1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4355 (all V_j all V_i all V_xs all T_a (class_Orderings_Olinorder(T_a) -> (c_List_Olinorder__class_Osorted(T_a,V_xs) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)))))))) # label(fact_sorted__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4356 (all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,V_xs_2) <-> (all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> (all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)))))))))) # label(fact_sorted__equals__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4357 (all V_ys_2 all V_xs_2 all V_f_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> (c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) -> (c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) -> (hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))) -> (c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)) -> (hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))) -> (hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2) -> V_xs_2 = V_ys_2)))))))) # label(fact_map__sorted__distinct__set__unique) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4358 (all V_i_2 all V_xs_2 all T_b (c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2))) -> hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)))) # label(fact_transpose__column) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4359 (all V_j_2 all V_i_2 all V_xs_2 all T_b (c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)))) -> hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2))))) # label(fact_nth__nth__transpose__sorted) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4360 (all V_A_2 all T_b c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2)) # label(fact_inj__on__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4361 (all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) <-> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)))) # label(fact_distinct__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4362 (all V_xs_2 all T_b (hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_rev__is__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4363 (all V_xs_2 all T_b (c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2) <-> V_xs_2 = c_List_Olist_ONil(T_b))) # label(fact_Nil__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4364 (all T_a hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)) # label(fact_rev_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4365 (all V_xs_2 all V_x_2 all T_b (hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2) <-> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))) # label(fact_singleton__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4366 (all V_x_2 all V_xs_2 all T_b (hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) <-> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))) # label(fact_rev__singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4367 (all V_ys all V_xs all T_a hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs))) # label(fact_rev__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4368 (all V_xs_2 all T_b hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2)))) # label(fact_rev__concat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4369 (all V_xs_2 all V_f_2 all T_c all T_b hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2))) # label(fact_rev__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4370 (all V_xs_2 all V_Pa_2 all T_b hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2))) # label(fact_rev__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4371 (all V_ys all T_b all V_xs all T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) -> hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)))) # label(fact_zip__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4372 (all V_xs_2 all T_b hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2)) # label(fact_set__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4373 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2)) <-> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2))) # label(fact_list__all2__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4374 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b (c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2) <-> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)))) # label(fact_list__all2__rev1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4375 (all V_xs all T_a hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs) # label(fact_rev__rev__ident) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4376 (all V_ys_2 all V_xs_2 all T_b (hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2 <-> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2))) # label(fact_rev__swap) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4377 (all V_ys_2 all V_xs_2 all T_b (hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2) <-> V_xs_2 = V_ys_2)) # label(fact_rev__is__rev__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4378 (all V_xs all T_a (class_Groups_Ocomm__monoid__add(T_a) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs))) # label(fact_listsum__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4379 (all V_xs all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) # label(fact_length__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4380 (all V_xs_2 all V_a_2 all V_f_2 all T_c all T_b hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2)) # label(fact_foldl__foldr) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4381 (all V_a_2 all V_xs_2 all V_f_2 all T_b all T_c c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2))) # label(fact_foldr__foldl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4382 (all V_ys_2 all V_y_2 all V_xs_2 all T_b (hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) <-> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))) # label(fact_rev__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4383 (all V_xs all V_x all T_a hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) # label(fact_rev_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4384 (all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs))) # label(fact_hd__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4385 (all T_a all V_xs (V_xs != c_List_Olist_ONil(T_a) -> c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs))) # label(fact_last__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4386 (all V_xs_2 all T_b c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))) # label(fact_sorted__transpose) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4387 (all V_xs_2 all T_b hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)) # label(fact_rev__foldl__cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4388 (all V_xs all V_i all T_a hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs))) # label(fact_rev__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4389 (all V_xs all V_i all T_a hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs))) # label(fact_rev__take) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4390 (all V_xs all V_n all T_a hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs))) # label(fact_rotate__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4391 (all V_xs all T_a all V_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))))) # label(fact_rev__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4392 (all V_y all V_xs all T_a all V_k (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y))) # label(fact_rev__update) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4393 (all V_j all V_i all V_xs all T_a (class_Orderings_Olinorder(T_a) -> (c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)))))))) # label(fact_sorted__rev__nth__mono) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4394 (all V_y_2 all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2)) -> (V_xs_2 = c_List_Olist_ONil(T_b) -> c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2) & (V_xs_2 != c_List_Olist_ONil(T_b) -> c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2))))) # label(fact_foldr__max__sorted) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4395 (all V_xs_2 all T_b (c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) -> (V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) & (V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) # label(fact_length__transpose__sorted) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4396 (all V_i_2 all V_xs_2 all T_b (c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2))) -> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2))))) # label(fact_transpose__column__length) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4397 (all V_xs_2 all T_b (c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) -> c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2))) # label(fact_transpose__transpose) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4398 (all V_Pa_2 all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,V_xs_2) -> c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) # label(fact_sorted__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4399 (all V_xs_2 all V_Pa_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) # label(fact_length__takeWhile__le) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4400 (all V_xs_2 all V_Pa_2 all T_b (c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2 <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_takeWhile__eq__all__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4401 (all V_xs_2 all V_Pa_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) -> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(V_Pa_2,V_x_2)))) # label(fact_set__takeWhileD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4402 (all V_ys_2 all V_Pa_2 all V_xs_2 all T_c all T_b hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) # label(fact_zip__takeWhile__snd) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4403 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_c all T_b hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) # label(fact_zip__takeWhile__fst) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4404 (all V_xs_2 all V_f_2 all T_c all V_Pa_2 all T_b c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2))) # label(fact_takeWhile__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4405 (all V_l_2 all V_xs_2 all T_b all V_x_2 all V_Pa_2 (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) # label(fact_takeWhile__tail) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4406 (all V_xs_2 all T_b all V_x_2 all V_Pa_2 ((hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) & (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b)))) # label(fact_takeWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4407 (all V_Pa_2 all T_b c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b)) # label(fact_takeWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4408 (all V_xs_2 all V_Pa_2 all T_b c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2)) # label(fact_takeWhile__eq__take) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4409 (all V_Pa_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) # label(fact_distinct__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4410 (all V_l_2 c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2)) # label(fact_return__list__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4411 (all V_ys_2 all V_Pa_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) # label(fact_takeWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4412 (all V_xs_2 all V_Pa_2 all T_b all V_j_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) -> hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2))) # label(fact_takeWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4413 (all V_xs_2 all V_Pa_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> -hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))))) # label(fact_nth__length__takeWhile) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4414 (all T_b all V_xs_2 (V_xs_2 != c_List_Olist_ONil(T_b) -> (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2)))) # label(fact_takeWhile__not__last) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4415 (all V_t_2 all V_xs_2 all V_f_2 all T_c all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) -> hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2)))) # label(fact_filter__equals__takeWhile__sorted__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4416 (all V_l (c_List_Onat__list(V_l) -> c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l)) # label(fact_transfer__nat__int__list__return__embed) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4417 (all V_m all V_l hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m)))) # label(fact_transfer__nat__int__list__functions_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4418 (all V_l_2 c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2)) # label(fact_embed__list__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.22 4419 (all V_x_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))))) # label(fact_takeWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4420 (all V_x_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))))) # label(fact_dropWhile__neq__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4421 (all V_xs_2 all V_Pa_2 all T_b hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2) # label(fact_takeWhile__dropWhile__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4422 (all V_Pa_2 all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,V_xs_2) -> c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))) # label(fact_sorted__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4423 (all V_xs_2 all V_Pa_2 all T_b hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) # label(fact_length__dropWhile__le) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4424 (all V_xs_2 all V_Pa_2 all T_b (c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_dropWhile__eq__Nil__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4425 (all V_xs_2 all T_b all V_x_2 all V_Pa_2 ((hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) & (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) # label(fact_dropWhile_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4426 (all V_Pa_2 all T_b c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b)) # label(fact_dropWhile_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4427 (all V_Pa_2 all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) -> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))) # label(fact_distinct__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4428 (all V_xs_2 all V_Pa_2 all T_b (c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b) -> -hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))))) # label(fact_hd__dropWhile) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4429 (all V_xs_2 all V_f_2 all T_c all V_Pa_2 all T_b c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2))) # label(fact_dropWhile__map) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4430 (all V_ys_2 all V_Pa_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2)))) # label(fact_dropWhile__append1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4431 (all V_ys_2 all V_y_2 all V_xs_2 all V_Pa_2 all T_b (c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) <-> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) & -hBOOL(hAPP(V_Pa_2,V_y_2)))) # label(fact_dropWhile__eq__Cons__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4432 (all V_xs_2 all V_Pa_2 all T_b c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2)) # label(fact_dropWhile__eq__drop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4433 (all V_xs_2 all V_Pa_2 all T_b all V_j_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) -> hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))))) # label(fact_dropWhile__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4434 (all V_f_2 all V_Pa_2 all V_xs_2 all T_b all T_c (class_Groups_Omonoid__add(T_c) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> (-hBOOL(hAPP(V_Pa_2,B_x)) -> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)))) -> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))))) # label(fact_listsum__map__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4435 (all V_xs all T_a (class_Orderings_Olinorder(T_a) -> ((all B_i all B_j (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j)))))) -> c_List_Olinorder__class_Osorted(T_a,V_xs)))) # label(fact_sorted__nth__monoI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4436 (all V_xs_2 all V_Pa_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) -> -hBOOL(hAPP(V_Pa_2,B_x)))) -> c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) # label(fact_takeWhile__eq__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4437 (all V_Pa_2 all V_xs_2 all T_b all V_n_2 ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))))) -> ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> -hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)))) -> c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) # label(fact_takeWhile__eq__take__P__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4438 (all V_xs_2 all T_b all V_Pa_2 all V_j_2 ((all B_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))))) # label(fact_length__takeWhile__less__P__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4439 (all V_a_2 all T_b (class_Orderings_Olinorder(T_b) -> (c_List_Olinorder__class_Osorted(T_b,V_a_2) <-> V_a_2 = c_List_Olist_ONil(T_b) | (exists B_xs exists B_x (V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) & (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)))) & c_List_Olinorder__class_Osorted(T_b,B_xs)))))) # label(fact_sorted_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4440 (all V_xs_2 all V_x_2 all T_b ((hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2) & (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) # label(fact_List_Oinsert__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4441 (all V_xs_2 all V_x_2 all T_b (-hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) # label(fact_not__in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4442 (all V_xs all V_x all T_a c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs))) # label(fact_insert__remdups) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4443 (all V_x all V_xs all T_a (hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) -> hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))))) # label(fact_distinct__insert) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4444 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) -> c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2)) # label(fact_in__set__insert) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4445 (all V_xs_2 all V_x_2 all T_b hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) # label(fact_List_Oset__insert) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4446 (all V_x all T_a c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) # label(fact_insert__Nil) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4447 (all V_xs_2 all V_f_2 all T_b all T_c c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2))) # label(fact_maps__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4448 (all V_xs_2 all V_f_2 all T_c all T_b c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)) # label(fact_concat__map__maps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4449 (all V_f_2 all T_b all T_c c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b)) # label(fact_maps__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4450 (all V_xs_2 all V_x_2 all V_f_2 all T_b all T_c c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2))) # label(fact_maps__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4451 (all V_xs_2 all T_b (hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2)) -> ((all B_ys (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)))) -> ((all B_ys (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) -> (all B_zs (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) -> (B_ys != B_zs -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) -> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))))))) # label(fact_distinct__concat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4452 (all V_fs_2 all T_b all V_y_2 all V_x_2 all V_f_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))))) # label(fact_measures__lesseq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4453 (all V_fs_2 all T_b c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2))) # label(fact_wf__measures) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4454 (all V_y_2 all V_x_2 all T_b -hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat)))))) # label(fact_in__measures_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4455 (all V_fs_2 all T_b c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2))) # label(fact_measures__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4456 (all V_fs_2 all T_b all V_y_2 all V_x_2 all V_f_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))))) # label(fact_measures__less) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4457 (all V_fs_2 all V_f_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) | hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))))) # label(fact_in__measures_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4458 (all V_s_2 all V_g_2 all V_h_2 all V_f_2 all T_c all T_d all V_xs_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)))) -> hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)))) # label(fact_foldl__apply) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4459 (all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oorder(T_c) & class_Enum_Oenum(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2))))))) # label(fact_order__fun_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4460 (all V_Pa_2 all T_b all T_c (class_Enum_Oenum(T_c) & class_Enum_Oenum(T_b) -> (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2)) <-> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))))))) # label(fact_enum__ex__prod__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4461 (all V_Pa_2 all T_b (class_Enum_Oenum(T_b) -> (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) <-> (exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1)))))) # label(fact_enum__ex) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4462 (all V_Pa_2 all T_b (class_Enum_Oenum(T_b) -> ((exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) <-> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))))) # label(fact_exists__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4463 (all V_Pa_2 all V_ys_2 all T_c all V_xs_2 all T_b ((hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2))))) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))) # label(fact_zip__obtain__same__length) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4464 (all V_seed_2 all V_size_2 all V_nrandom_2 all V_R_2 c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2))) # label(fact_pos__not__random__dseq__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4465 (all V_ys_2 all V_Pa_2 all V_xs_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) -> c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2))) # label(fact_dropWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4466 (all V_Pa_2 all V_b_2 all T_c all V_a_2 all T_b (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2) -> ((all B_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2))) -> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))))) -> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)))) # label(fact_list__all2__all__nthI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4467 (all V_A_2 all T_b (class_Orderings_Olinorder(T_b) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (exists B_x (hAPP(c_List_Oset(T_b),B_x) = V_A_2 & c_List_Olinorder__class_Osorted(T_b,B_x) & hBOOL(hAPP(c_List_Odistinct(T_b),B_x)) & (all B_y (hAPP(c_List_Oset(T_b),B_y) = V_A_2 & c_List_Olinorder__class_Osorted(T_b,B_y) & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) -> B_y = B_x))))))) # label(fact_finite__sorted__distinct__unique) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4468 (all V_ys_2 all V_Pa_2 all V_xs_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) -> c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)))) # label(fact_takeWhile__append2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4469 (all V_a_2 all V_f_2 all V_xs_2 all T_b all T_c (class_Orderings_Olinorder(T_c) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))))) -> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2)))) # label(fact_insort__is__Cons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4470 (all V_ys_2 all V_Pa_2 all V_xs_2 all V_x_2 all T_b (hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) <-> (exists B_us exists B_vs (V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) -> -hBOOL(hAPP(V_Pa_2,B_x)))) & hBOOL(hAPP(V_Pa_2,V_x_2)) & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs))))) # label(fact_Cons__eq__filter__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4471 (all V_xs_2 all V_x_2 all V_ys_2 all V_Pa_2 all T_b (hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) <-> (exists B_us exists B_vs (V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) -> -hBOOL(hAPP(V_Pa_2,B_x)))) & hBOOL(hAPP(V_Pa_2,V_x_2)) & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs))))) # label(fact_filter__eq__Cons__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4472 (all V_g_2 all V_f_2 all T_b all T_c (class_Orderings_Oorder(T_c) & class_Enum_Oenum(T_b) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) <-> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2)))))) # label(fact_order__fun_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4473 (all V_Pa_2 all T_b (class_Enum_Oenum(T_b) -> ((all B_x1 hBOOL(hAPP(V_Pa_2,B_x1))) <-> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))))) # label(fact_all__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4474 (all V_Pa_2 all T_b (class_Enum_Oenum(T_b) -> (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) <-> (all B_x1 hBOOL(hAPP(V_Pa_2,B_x1)))))) # label(fact_enum__all) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4475 (all V_Pa_2 all T_b all T_c (class_Enum_Oenum(T_c) & class_Enum_Oenum(T_b) -> (hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2)) <-> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))))))) # label(fact_enum__all__prod__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4476 (all V_Pa_2 all V_xs_2 all T_b all V_n_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)))))) # label(fact_list__ball__nth) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4477 (all V_x_2 all V_xs_2 all T_b (class_Orderings_Olinorder(T_b) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)))) -> (c_List_Olinorder__class_Osorted(T_b,V_xs_2) -> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))))) # label(fact_sorted_OCons) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4478 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) <-> (exists B_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))))))) # label(fact_list__ex__length) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4479 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) <-> (exists B_ys exists B_zs V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))))) # label(fact_in__set__conv__decomp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4480 (all V_Pa_2 all T_b -c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b))) # label(fact_list__ex__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4481 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) <-> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2))) # label(fact_list__ex__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4482 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_list__ex__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4483 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) <-> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2))) # label(fact_list__ex__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4484 (all V_xs_2 all V_x_2 all V_Pa_2 all T_b (c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) <-> hBOOL(hAPP(V_Pa_2,V_x_2)) | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2))) # label(fact_list__ex__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4485 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) <-> (exists B_ys ((exists B_zs V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))) & -hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))))))) # label(fact_in__set__conv__decomp__first) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4486 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) <-> (exists B_ys exists B_zs (V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) & -hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))))))) # label(fact_in__set__conv__decomp__last) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4487 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__all(T_b,V_Pa_2,V_xs_2) <-> (all B_n (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))))))) # label(fact_list__all__length) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4488 (all V_Pa_2 all T_b c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b))) # label(fact_list__all__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4489 (all V_ys_2 all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) <-> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) & c_List_Olist__all(T_b,V_Pa_2,V_ys_2))) # label(fact_list__all__append) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4490 (all T_b (class_Nat_Osize(T_b) -> c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)))) # label(fact_measure__size) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4491 (all V_a_2 all T_b c_FunDef_Ois__measure(T_b,V_a_2)) # label(fact_is__measure_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4492 (all V_a_2 all T_b c_FunDef_Ois__measure(T_b,V_a_2)) # label(fact_is__measure_Oequations) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4493 (all V_f_2 all T_b c_FunDef_Ois__measure(T_b,V_f_2)) # label(fact_is__measure_Ointros) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4494 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__all(T_b,V_Pa_2,V_xs_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_list__all__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4495 (all T_c all V_f_2 all T_b (c_FunDef_Ois__measure(T_b,V_f_2) -> c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))))) # label(fact_measure__fst) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4496 (all T_c all V_f_2 all T_b (c_FunDef_Ois__measure(T_b,V_f_2) -> c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))))) # label(fact_measure__snd) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4497 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2)) <-> c_List_Olist__all(T_b,V_Pa_2,V_xs_2))) # label(fact_list__all__rev) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4498 (all V_xs_2 all V_x_2 all V_Pa_2 all T_b (c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) <-> hBOOL(hAPP(V_Pa_2,V_x_2)) & c_List_Olist__all(T_b,V_Pa_2,V_xs_2))) # label(fact_list__all__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4499 (all V_Pa_2 all V_xs_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> c_List_Olist__all(T_b,V_Pa_2,V_xs_2))) # label(fact_Ball__set__list__all) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4500 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__all(T_b,V_Pa_2,V_xs_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_list__all__iff__raw) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4501 (all V_xs_2 all V_x_2 all V_Pa_2 all T_b (c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) <-> (hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2)) & (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)))) # label(fact_list__ex1__simps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4502 (all V_Pa_2 all T_b -c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b))) # label(fact_list__ex1__simps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4503 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(V_Pa_2,B_x)) & (all B_y (hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(V_Pa_2,B_y)) -> B_y = B_x)))))) # label(fact_list__ex1__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4504 (all V_f_2 all V_x_2 all T_b all T_c all V_i_2 ((V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b)) & (V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2))))) # label(fact_New__DSequence_Oneg__decr__bind__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4505 (all V_f_2 all V_x_2 all T_b all T_c all V_i_2 ((V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b)) & (V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) -> hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2))))) # label(fact_New__DSequence_Opos__decr__bind__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4506 (all V_seed_2 all V_size_2 all V_nrandom_2 all V_f_2 all V_R_2 all T_b all T_c c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2))) # label(fact_New__Random__Sequence_Opos__decr__bind__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4507 (all V_seed_2 all V_size_2 all V_nrandom_2 all V_f_2 all V_R_2 all T_b all T_c c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2))) # label(fact_New__Random__Sequence_Oneg__decr__bind__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4508 (all V_i_2 all V_f_2 all V_x_2 all T_b all T_c hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2))) # label(fact_New__DSequence_Oneg__bind__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4509 (all V_i_1 all T_a hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a)) # label(fact_New__DSequence_Opos__empty__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4510 (all V_seed_2 all V_size_2 all V_nrandom_2 all T_b c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b)) # label(fact_pos__empty__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4511 (all V_seed_2 all V_size_2 all V_nrandom_2 all V_f_2 all V_R_2 all T_b all T_c hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2))) # label(fact_neg__bind__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4512 (all V_i_2 all V_f_2 all V_x_2 all T_b all T_c hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2))) # label(fact_New__DSequence_Opos__bind__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4513 (all V_Pa_2 all V_f_2 all T_b all T_c c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2))) # label(fact_neg__map__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4514 (all V_seed_2 all V_size_2 all V_nrandom_2 all V_x_2 all T_b hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2)) # label(fact_neg__single__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4515 (all V_seed_2 all V_size_2 all V_nrandom_2 all V_f_2 all V_R_2 all T_b all T_c hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2))) # label(fact_pos__bind__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4516 (all V_i_1 all V_x all T_a hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x)) # label(fact_New__DSequence_Oneg__single__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4517 (all V_Pa_2 all V_f_2 all T_b all T_c c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2))) # label(fact_pos__map__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4518 (all V_seed_2 all V_size_2 all V_nrandom_2 all V_x_2 all T_b hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2)) # label(fact_pos__single__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4519 (all V_ys all V_xs all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) # label(fact_length__splice) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4520 (all V_ys all V_y all V_xs all V_x all T_a c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys)))) # label(fact_splice_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4521 (all V_ys all T_a c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys) # label(fact_splice_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4522 (all V_xs all T_a c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs) # label(fact_splice__Nil2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4523 (all V_va all V_v all T_a c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va)) # label(fact_splice_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4524 (all V_i_1 all V_x all T_a hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x)) # label(fact_New__DSequence_Opos__single__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4525 (all V_r_2 all T_b (c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2)))) <-> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))))) # label(fact_acyclicP__converse) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4526 (all V_s_2 all V_r_2 all T_b all T_c c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2))) # label(fact_converse__meet) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4527 (all V_s_2 all V_r_2 all T_b all T_c c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2))) # label(fact_converse__join) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4528 (all V_s_2 all V_r_2 all T_d all T_b all T_c c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2))) # label(fact_converse__pred__comp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4529 (all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2)) <-> V_x_2 != V_y_2)) # label(fact_conversep__noteq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4530 (all V_b_2 all V_a_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) -> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)))) # label(fact_conversepD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4531 (all T_c all T_b all V_b_2 all V_a_2 all V_r_2 (hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) -> hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)))) # label(fact_conversep_Ointros) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4532 (all V_a1_2 all V_a2_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2)) <-> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)))) # label(fact_conversep_Oequations) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4533 (all V_b_2 all V_a_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) <-> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)))) # label(fact_conversep__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4534 (all V_r_2 all T_b all T_c c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2) # label(fact_conversep__conversep) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4535 (all T_b c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal) # label(fact_conversep__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4536 (all V_y_2 all V_x_2 all V_r_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2)) <-> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))))) # label(fact_conversep__converse__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4537 (all V_s2_2 all V_s1_2 all T_c all T_b c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))) # label(fact_) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4538 (all V_x all T_a all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x))) # label(fact_tl__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4539 (all V_xs_2 all V_x_2 all T_b c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)) # label(fact_replicate__length__filter) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4540 (all V_x all V_n all T_a hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n) # label(fact_length__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4541 (all V_lst_2 all V_k_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2)) # label(fact_map__replicate__const) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4542 (all V_xs all V_x all V_n all T_a hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs))) # label(fact_replicate__app__Cons__same) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4543 (all V_x all V_n all T_a c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x))) # label(fact_replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4544 (all V_x all V_n all T_a hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x)) # label(fact_rev__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4545 (all V_x all V_k all V_i all T_a hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x)) # label(fact_take__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4546 (all V_x all V_k all V_i all T_a hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x)) # label(fact_drop__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4547 (all V_x all T_a all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x)) # label(fact_hd__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4548 (all V_x all T_a all V_n (V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x)) # label(fact_last__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4549 (all V_y all V_j all V_x all V_i all T_b all T_a hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y))) # label(fact_zip__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4550 (all V_Pa_2 all V_a_2 all V_n_2 all T_b ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> hBOOL(hAPP(V_Pa_2,V_a_2)) & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_Bex__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4551 (all V_Pa_2 all V_a_2 all V_n_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) -> hBOOL(hAPP(V_Pa_2,B_x)))) <-> hBOOL(hAPP(V_Pa_2,V_a_2)) | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_Ball__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4552 (all V_y_2 all V_n_2 all V_x_2 all V_m_2 all T_b (c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2) <-> V_m_2 = V_n_2 & (V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> V_x_2 = V_y_2))) # label(fact_replicate__eq__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4553 (all V_x all T_a all V_n all V_i (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) -> hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x)) # label(fact_nth__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4554 (all V_x all V_m all V_n all T_a c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x))) # label(fact_replicate__add) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4555 (all V_k all V_x all V_n all T_a hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x))) # label(fact_append__replicate__commute) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4556 (all V_n_2 all T_b all V_x_2 all V_Pa_2 ((hBOOL(hAPP(V_Pa_2,V_x_2)) -> hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2)) & (-hBOOL(hAPP(V_Pa_2,V_x_2)) -> hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b)))) # label(fact_filter__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4557 (all V_i all T_a c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a)) # label(fact_concat__replicate__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4558 (all V_x all T_a c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a)) # label(fact_replicate__0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4559 (all V_x_2 all V_n_2 all T_b (c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_empty__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4560 (all V_x_2 all V_n_2 all T_b (c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b) <-> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_replicate__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4561 (all V_x_2 all V_n_2 all V_f_2 all T_b all T_c hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2))) # label(fact_map__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4562 (all V_y_2 all V_n_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2)))) <-> V_x_2 = V_y_2 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) # label(fact_in__set__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4563 (all V_x all V_i all T_a hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x))) # label(fact_replicate__append__same) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4564 (all V_i_2 all V_x_2 all T_b hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2)) # label(fact_map__replicate__trivial) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4565 (all V_x_2 all T_b all V_n_2 (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_set__replicate) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4566 (all V_x_2 all T_b all V_n_2 ((V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) & (V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) -> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) # label(fact_set__replicate__conv__if) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4567 (all V_x_2 all V_n_2 all T_b hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_set__replicate__Suc) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4568 (all V_d_2 all T_b (class_Lazy__Sequence_Osmall__lazy(T_b) -> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))))) # label(fact_small__lazy__list_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4569 (all V_R_2 all T_b c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2) # label(fact_eq__comp__r) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4570 (all V_d all T_b all T_a (class_Lazy__Sequence_Osmall__lazy(T_a) & class_Lazy__Sequence_Osmall__lazy(T_b) -> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)))) # label(fact_small__lazy__prod__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4571 (all V_i_2 all V_yq_2 all V_xq_2 all T_b hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2))) # label(fact_New__DSequence_Opos__union__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4572 (all V_lazy__sequence all V_a all T_a hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_lazy__sequence_Osize_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4573 (all V_yq all V_xq all V_x all T_a c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq))) # label(fact__01) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4574 (all V_lazy__sequence_H_2 all V_a_H_2 all V_lazy__sequence_2 all V_a_2 all T_b (c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2) <-> V_a_2 = V_a_H_2 & V_lazy__sequence_2 = V_lazy__sequence_H_2)) # label(fact_lazy__sequence_Oinject) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4575 (all V_seed_2 all V_size_2 all V_nrandom_2 all V_R2_2 all V_R1_2 all T_b c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2))) # label(fact_pos__union__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4576 (all V_lazy__sequence_2 all V_a_2 all V_fa_2 all T_b hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) # label(fact_lazy__sequence_Osize_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4577 (all V_i all V_d ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) -> c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) -> c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) # label(fact_small__lazy_H_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4578 (all V_i_2 all V_d_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) -> c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint)) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) -> c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) # label(fact_small__lazy_H_Opsimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4579 (all V_d c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d))) # label(fact_small__lazy__int__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4580 (all V_Pa_2 all V_a1_2 all V_a0_2 (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) -> ((all B_d all B_i (hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))) -> ((-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) -> hBOOL(hAPP(hAPP(V_Pa_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))))) -> hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i))))) -> hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))))) # label(fact_small__lazy_H_Opinduct) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4581 (all V_xq_2 all T_b hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2))) # label(fact_size__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4582 (all V_xq_2 all V_s_2 all T_b hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2))) # label(fact_lazy__sequence__size__code) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4583 (all V_xq_2 all V_g_2 all V_f_2 all T_c all T_b c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2))) # label(fact_seq__case) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4584 (all T_b c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b))) # label(fact_yieldn__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4585 (all V_lazy__sequence_2 all V_a_2 all V_f2_2 all V_f1_2 all T_c all T_b c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2)) # label(fact_lazy__sequence_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4586 (all V_r_2 all V_A_2 all T_c all V_S_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) -> c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)))) -> c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)))) # label(fact_refl__on__INTER) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4587 (all V_x_2 all V_xs_2 all T_b (hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) <-> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))))) # label(fact_List_Omember__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4588 (all V_y all T_a -hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y))) # label(fact_member__rec_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4589 (all T_b c_List_Omember(T_b) = c_List_Oset(T_b)) # label(fact_member__set) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4590 (all V_y_2 all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2)) <-> V_x_2 = V_y_2 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)))) # label(fact_member__rec_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4591 (all V_xs_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) <-> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)))) # label(fact_in__set__member) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4592 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(V_Pa_2,B_x)) & (all B_y (hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(V_Pa_2,B_y)) -> B_y = B_x)))))) # label(fact_list__ex1__iff__raw) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4593 (all V_f_2 all V_S_2 all T_b all T_c (class_Groups_Ocomm__monoid__add(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)))) -> ((all B_T1 (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2)) -> (all B_T2 (hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2)) -> (B_T1 != B_T2 -> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1)) -> (hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2)) -> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c))))))))) -> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2)))))) # label(fact_setsum__UNION__zero) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4594 (all V_d_2 all T_b all V_Pa_2 (((exists B_x (hBOOL(hAPP(V_Pa_2,B_x)) & (all B_y (hBOOL(hAPP(V_Pa_2,B_y)) -> B_y = B_x)))) -> c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2)) & (-(exists B_x (hBOOL(hAPP(V_Pa_2,B_x)) & (all B_y (hBOOL(hAPP(V_Pa_2,B_y)) -> B_y = B_x)))) -> c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2))) # label(fact_THE__default__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4595 (all V_ca_2 all V_b_2 all V_B_2 all V_A_2 all T_d all T_c all T_b (hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) -> -(all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> -hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)))))) # label(fact_SUP2__E) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4596 (all T_d all T_c all V_ca_2 all V_b_2 all V_B_2 all V_A_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)))) # label(fact_INF2__I) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4597 (all V_M_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2)) -> (exists B_n all B_x (hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)))))) # label(fact_finite__maxlen) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4598 (all T_a hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_lazy__sequence_Osize_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4599 (all V_fa_2 all T_b hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_lazy__sequence_Osize_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4600 (all V_yq all T_a c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq) # label(fact__02) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4601 (all V_lazy__sequence_H all V_a_H all T_a c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H)) # label(fact_lazy__sequence_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4602 (all V_lazy__sequence_H all V_a_H all T_a c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) # label(fact_lazy__sequence_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4603 (all V_f2_2 all V_f1_2 all T_c all T_b c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2) # label(fact_lazy__sequence_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4604 (all V_j_2 all V_i_2 all V_Pa_2 (c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) <-> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2))) # label(fact_list__all__iff__all__interval__int) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4605 (all V_j_2 all V_i_2 all V_Pa_2 (c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2)) <-> -c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_Pa_2),V_i_2,V_j_2))) # label(fact_list__ex__iff__not__all__inverval__int) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4606 (all V_j_2 all V_i_2 all V_Pa_2 (c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_all__interval__int__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4607 (all V_code__numeral_2 all V_f2_2 all V_f1_2 all T_b c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2))) # label(fact_code__numeral_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4608 (all V_size_2 all V_g_2 all T_b all V_nrandom_2 ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) -> c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b))) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) -> c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))))) # label(fact_Random_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4609 (all V_f2_2 all V_f1_2 all T_b c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2) # label(fact_code__numeral_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4610 (all V_size_2 all V_nrandom_2 all T_b c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b))) # label(fact_Random__Sequence_Oempty__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4611 (all V_size_2 all V_nrandom_2 all V_x_2 all T_b hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2))) # label(fact_Random__Sequence_Osingle__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4612 (all V_Pa_2 all V_f_2 all T_b all T_c c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2))) # label(fact_Random__Sequence_Omap__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4613 (all T_d all V_f_2 all V_Q_2 all V_p_2 all T_b all T_c all V_Pa_2 (hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2))) -> ((all B_x all B_y (hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) -> hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))))) -> hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2)))))) # label(fact_exE__realizer) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4614 (all V_A_2 all V_Pa_2 all T_b all T_c hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))))) # label(fact_Image__Collect__split) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.23 4615 (all V_z_2 all V_r_2 all V_y_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) -> (c_Relation_Otrans(T_b,V_r_2) -> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))))))) # label(fact_lexord__trans) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4616 (all V_R2_2 all T_c all V_R1_2 all T_b (c_Relation_Otrans(T_b,V_R1_2) -> (c_Relation_Otrans(T_c,V_R2_2) -> c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2))))) # label(fact_trans__lex__prod) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4617 (all V_ca_2 all V_b_2 all V_a_2 all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),V_r_2)))))) # label(fact_transD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4618 (all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) <-> (all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) -> (all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)))))))) # label(fact_trans__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4619 (all V_r_2 all T_b c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))) # label(fact_trans__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4620 (all T_b c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b))) # label(fact_trans__finite__psubset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4621 (all V_A_2 all T_b c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2))) # label(fact_trans__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4622 (all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2)) # label(fact_trancl__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4623 (all V_r_2 all T_b c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))) # label(fact_trans__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4624 (all T_b c_Relation_Otrans(T_b,c_Relation_OId(T_b))) # label(fact_trans__Id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4625 (all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)))) # label(fact_lexord__transI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4626 (all V_r_2 all T_b (c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) <-> c_Relation_Otrans(T_b,V_r_2))) # label(fact_trans__converse) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4627 (all V_Pa_2 all T_b -(exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) & hBOOL(hAPP(V_Pa_2,B_x))))) # label(fact_bex__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4628 (all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)))) # label(fact_listrel__trans) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4629 (all V_Q_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2))))) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x))))))))) # label(fact_finite__Collect__bex) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4630 (all V_Pa_2 all T_b ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> (exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1))))) # label(fact_bex__UNIV) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4631 (all V_s_2 all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> (c_Relation_Otrans(T_b,V_s_2) -> c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))))) # label(fact_trans__Int) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4632 (all T_b c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b)) # label(fact_SUPR__bool__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4633 (all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)))) # label(fact_trans__O__subset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4634 (all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))))) # label(fact_trans__reflclI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4635 (all V_f_2 all T_c all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)))) # label(fact_trans__inv__image) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4636 (all V_A_2 all T_b c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b))))) # label(fact_Union__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4637 (all V_xs_2 all V_Pa_2 all T_b (c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) <-> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_list__ex__iff__raw) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4638 (all V_Pa_2 all V_xs_2 all T_b ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2))) # label(fact_Bex__set__list__ex) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4639 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2)))))) # label(fact_UN__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4640 (all V_B_2 all V_A_2 all T_b all T_c hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2)))))) # label(fact_INT__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4641 (all V_x_2 all V_A_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))))) # label(fact_Sup__fun__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4642 (all V_x_2 all V_A_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))))) # label(fact_Sup__apply) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4643 (all V_x_2 all V_A_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))))) # label(fact_Inf__fun__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4644 (all V_x_2 all V_A_2 all T_c all T_b (class_Complete__Lattice_Ocomplete__lattice(T_b) -> hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))))) # label(fact_Inf__apply) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4645 (all V_R_2 all V_Y_2 all V_X_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2)) -> (V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) -> (exists B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)))))) -> c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2)))))) # label(fact_max__extp_Ointros) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4646 (all V_r_2 all T_b (c_Predicate_Otransp(T_b,V_r_2) <-> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))))) # label(fact_transp__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4647 (all V_z_2 all V_y_2 all V_x_2 all V_r_2 all T_b (c_Predicate_Otransp(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2)) -> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)))))) # label(fact_transpE) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4648 (all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) -> -(c_Predicate_Oreflp(T_b,V_R_2) -> (c_Predicate_Osymp(T_b,V_R_2) -> -c_Predicate_Otransp(T_b,V_R_2))))) # label(fact_equivpE) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4649 (all V_R_2 all T_b (c_Predicate_Oreflp(T_b,V_R_2) -> (c_Predicate_Osymp(T_b,V_R_2) -> (c_Predicate_Otransp(T_b,V_R_2) -> c_Equiv__Relations_Oequivp(T_b,V_R_2))))) # label(fact_equivpI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4650 (all V_y_2 all V_x_2 all V_r_2 all T_b (c_Predicate_Osymp(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2))))) # label(fact_sympE) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4651 (all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) <-> c_Predicate_Oreflp(T_b,V_R_2) & c_Predicate_Osymp(T_b,V_R_2) & c_Predicate_Otransp(T_b,V_R_2))) # label(fact_equivp__reflp__symp__transp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4652 (all V_a2_2 all V_a1_2 all V_R_2 all T_b (c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2)) & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) & (all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) -> (exists B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)))))))) # label(fact_max__extp_Osimps) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4653 (all V_r_2 all T_b (c_Relation_Otrans(T_b,V_r_2) -> (c_Relation_Oantisym(T_b,V_r_2) -> c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))))) # label(fact_trans__diff__Id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4654 (all V_A_2 all T_b c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2))) # label(fact_antisym__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4655 (all T_b c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) # label(fact_antisym__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4656 (all V_r_2 all T_b (c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) <-> c_Relation_Oantisym(T_b,V_r_2))) # label(fact_antisym__converse) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4657 (all T_b c_Relation_Oantisym(T_b,c_Relation_OId(T_b))) # label(fact_antisym__Id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4658 (all V_s_2 all V_r_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) -> (c_Relation_Oantisym(T_b,V_s_2) -> c_Relation_Oantisym(T_b,V_r_2)))) # label(fact_antisym__subset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4659 (all V_b_2 all V_a_2 all V_r_2 all T_b (c_Relation_Oantisym(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) -> V_a_2 = V_b_2)))) # label(fact_antisymD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4660 (all V_r_2 all T_b (c_Relation_Oantisym(T_b,V_r_2) <-> (all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) -> B_x = B_y))))) # label(fact_antisym__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4661 (all V_r_2 all T_b (c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) <-> c_Relation_Oantisym(T_b,V_r_2))) # label(fact_antisym__reflcl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4662 (all V_r_2 all T_b (c_Wellfounded_Oacyclic(T_b,V_r_2) -> c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) # label(fact_acyclic__impl__antisym__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4663 (all V_x_2 all V_A_2 all V_L_2 all T_d all T_b all T_c c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2))))))) # label(fact_fun__lub__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4664 (all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) -> (c_Relation_Otrans(T_b,V_r_2) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2))))) # label(fact_sym__trans__comp__subset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4665 (all V_b_2 all V_a_2 all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))))) # label(fact_symD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4666 (all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) <-> (all B_x all B_y (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) -> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)))))) # label(fact_sym__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4667 (all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) -> c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) # label(fact_sym__rtrancl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4668 (all V_A_2 all T_b c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2))) # label(fact_sym__Id__on) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4669 (all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) -> c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)))) # label(fact_sym__trancl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4670 (all V_s_2 all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) -> (c_Relation_Osym(T_b,V_s_2) -> c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))))) # label(fact_sym__Un) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4671 (all T_b c_Relation_Osym(T_b,c_Relation_OId(T_b))) # label(fact_sym__Id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4672 (all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) <-> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2)) # label(fact_sym__conv__converse__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4673 (all V_r_2 all T_b (c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) <-> c_Relation_Osym(T_b,V_r_2))) # label(fact_sym__converse) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4674 (all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) -> c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)))) # label(fact_listrel__sym) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4675 (all V_s_2 all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) -> (c_Relation_Osym(T_b,V_s_2) -> c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))))) # label(fact_sym__Int) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4676 (all V_r_2 all T_b c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) # label(fact_sym__Un__converse) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4677 (all V_f_2 all T_c all V_r_2 all T_b (c_Relation_Osym(T_b,V_r_2) -> c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)))) # label(fact_sym__inv__image) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4678 (all V_r_2 all T_b c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) # label(fact_sym__Int__converse) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4679 (all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) <-> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) & c_Relation_Osym(T_b,V_r_2) & c_Relation_Otrans(T_b,V_r_2))) # label(fact_equiv__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4680 (all V_r_2 all V_A_2 all T_b (c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> (c_Relation_Osym(T_b,V_r_2) -> (c_Relation_Otrans(T_b,V_r_2) -> c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2))))) # label(fact_equivI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4681 (all V_r_2 all V_A_2 all T_b (c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) -> -(c_Relation_Orefl__on(T_b,V_A_2,V_r_2) -> (c_Relation_Osym(T_b,V_r_2) -> -c_Relation_Otrans(T_b,V_r_2))))) # label(fact_equivE) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4682 (all V_r_2 all T_b (c_Predicate_Osymp(T_b,V_r_2) <-> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))))) # label(fact_symp__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4683 (all T_b all V_R_2 ((exists B_x hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))) -> (c_Predicate_Osymp(T_b,V_R_2) -> (c_Predicate_Otransp(T_b,V_R_2) -> c_Equiv__Relations_Opart__equivp(T_b,V_R_2))))) # label(fact_part__equivpI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4684 (all V_R_2 all T_b (c_Equiv__Relations_Opart__equivp(T_b,V_R_2) <-> (exists B_x hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))) & c_Predicate_Osymp(T_b,V_R_2) & c_Predicate_Otransp(T_b,V_R_2))) # label(fact_part__equivp__refl__symp__transp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4685 (all V_z_2 all V_y_2 all V_x_2 all V_R_2 all T_b (c_Equiv__Relations_Opart__equivp(T_b,V_R_2) -> (hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) -> (hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) -> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)))))) # label(fact_part__equivp__transp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4686 (all V_y_2 all V_x_2 all V_R_2 all T_b (c_Equiv__Relations_Opart__equivp(T_b,V_R_2) -> (hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) -> hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2))))) # label(fact_part__equivp__symp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4687 (all V_R_2 all T_b (c_Equiv__Relations_Opart__equivp(T_b,V_R_2) <-> (exists B_x hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))) & (all B_x all B_y (hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) <-> hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y)) & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y))))) # label(fact_part__equivp__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4688 (all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) -> c_Equiv__Relations_Opart__equivp(T_b,V_R_2))) # label(fact_equivp__implies__part__equivp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4689 (all V_R_2 all T_b (c_Equiv__Relations_Opart__equivp(T_b,V_R_2) -> -((exists B_x hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))) -> (c_Predicate_Osymp(T_b,V_R_2) -> -c_Predicate_Otransp(T_b,V_R_2))))) # label(fact_part__equivpE) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4690 (all V_R_2 all T_b (c_Equiv__Relations_Opart__equivp(T_b,V_R_2) -> (exists B_d hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2)))))))) # label(fact_part__equivp__typedef) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4691 (all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b))) # label(fact_inv__o__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4692 (all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) <-> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b))) # label(fact_inj__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4693 (all T_b c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b)) # label(fact_inv__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4694 (all V_x_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2)) # label(fact_inv__f__f) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4695 (all V_y_2 all V_x_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hAPP(V_f_2,V_x_2) = V_y_2 -> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2))) # label(fact_inv__f__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4696 (all V_y_2 all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> (hAPP(V_f_2,V_x_2) = V_y_2 -> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2)))) # label(fact_inv__into__f__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4697 (all V_x_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) -> hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2))) # label(fact_inv__into__f__f) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4698 (all V_y_2 all V_x_2 all V_f_2 all V_A_2 all T_c all T_b (hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) -> V_x_2 = V_y_2)))) # label(fact_inv__into__injective) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4699 (all V_A_2 all V_f_2 all T_c all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) -> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)))) # label(fact_inv__into__into) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4700 (all V_A_2 all V_f_2 all T_c all V_y_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) -> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2)) # label(fact_f__inv__into__f) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4701 (all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) <-> (all B_x hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x))) # label(fact_surj__iff__all) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4702 (all V_y_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2)) # label(fact_surj__f__inv__f) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4703 (all V_A_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2)) # label(fact_image__surj__f__inv__f) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4704 (all V_B_H_2 all V_A_H_2 all V_A_2 all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2 -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2)) -> hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2))) # label(fact_image__inv__into__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4705 (all V_x_2 all V_f_2 all V_A_2 all T_c all T_b hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2)))) # label(fact_inv__into__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4706 (all V_y_2 all V_f_2 all T_c all T_b hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2))) # label(fact_inv__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4707 (all V_g_2 all T_d all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2)) # label(fact_o__inv__o__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4708 (all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) -> c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_surj__imp__inj__inv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4709 (all V_X_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2)) # label(fact_inv__image__comp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4710 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2)) # label(fact_image__inv__f__f) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4711 (all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_inj__imp__surj__inv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4712 (all V_S_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2)) -> hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2))) # label(fact_inv__into__image__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4713 (all V_A_2 all V_f_2 all T_c all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) -> c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2))) # label(fact_inj__on__inv__into) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4714 (all V_x_2 all V_A_2 all V_g_2 all T_d all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) -> (c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)))) -> hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2))))) # label(fact_inv__into__comp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4715 (all V_f_2 all T_b all T_c (hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) <-> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b))) # label(fact_surj__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4716 (all V_x_2 all V_Pa_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> ((all B_y (hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) -> hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))))) -> hBOOL(hAPP(V_Pa_2,V_x_2))))) # label(fact_inj__transfer) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4717 (all V_g_2 all V_A_2 all T_c all V_I_2 all T_b all T_d (class_Groups_Ocomm__monoid__mult(T_d) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) -> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))))) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) -> (all B_xa (hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2)) -> (B_x != B_xa -> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))) -> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2)))))) # label(fact_fold__image__UN__disjoint) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4718 (all V_Pa_2 all V_y_2 (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) -> ((all B_x hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x)))) -> hBOOL(hAPP(V_Pa_2,V_y_2))))) # label(fact_nat__of__induct) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4719 (all V_y_2 (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) -> -(all B_x V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x)))) # label(fact_nat__of__cases) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4720 (all V_x_2 all V_Pa_2 ((all B_y (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) -> hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))))) -> hBOOL(hAPP(V_Pa_2,V_x_2)))) # label(fact_of__nat__induct) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4721 (all V_x_2 -(all B_y (V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y) -> -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))))) # label(fact_of__nat__cases) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4722 (all V_f2_2 all V_f1_2 all T_c all T_b c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2) # label(fact_lazy__sequence_Orecs_I1_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4723 (all V_l all V_k ((hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) -> c_Quickcheck_Obeyond(V_k,V_l) = V_l) & (-hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) -> c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))) # label(fact_beyond__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4724 (all V_k c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) # label(fact_beyond__zero) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4725 (all V_lazy__sequence_2 all V_a_2 all V_f2_2 all V_f1_2 all T_c all T_b c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2))) # label(fact_lazy__sequence_Orecs_I2_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4726 (all V_Pa_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))))) # label(fact_bij__image__Collect__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4727 (all V_y_2 all V_x_2 all V_ca_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2))) # label(fact_curry__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4728 (all V_b_2 all V_a_2 all T_c all T_b all V_f_2 (hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) -> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)))) # label(fact_curryI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4729 (all V_A_2 all T_b c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2)) # label(fact_bij__betw__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4730 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) -> c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2))) # label(fact_bij__betw__inv__into) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4731 (all V_a_2 all V_A_H_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) -> hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2)))) # label(fact_inv__into__inv__into__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4732 (all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2)) # label(fact_inv__inv__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4733 (all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_bij__imp__bij__inv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4734 (all V_g_2 all T_d all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> (c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))))) # label(fact_o__inv__distrib) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4735 (all V_B_2 all V_A_2 all T_d all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)))) # label(fact_bij__image__INT) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4736 (all V_A_2 all V_f_2 all T_d all V_A_H_H_2 all V_A_H_2 all V_f_H_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2)) -> (c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2) <-> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2))))) # label(fact_bij__betw__comp__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4737 (all V_C_2 all V_g_2 all T_d all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) -> (c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2) -> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2)))) # label(fact_bij__betw__trans) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4738 (all V_A_H_H_2 all V_f_H_2 all T_d all V_A_H_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) -> (c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2) <-> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2)))) # label(fact_bij__betw__comp__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4739 (all V_g_2 all T_d all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> (c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) -> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))))) # label(fact_bij__comp) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4740 (all V_b_2 all V_a_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) -> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))))) # label(fact_curryE) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4741 (all V_b_2 all V_a_2 all V_f_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) -> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))))) # label(fact_curryD) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4742 (all V_b_2 all V_a_2 all V_f_2 all T_b all T_d all T_c hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) # label(fact_curry__conv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4743 (all V_F_2 all V_h_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))))) # label(fact_finite__vimage__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4744 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) # label(fact_bij__image__Compl__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4745 (all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) <-> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_bij__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4746 (all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) -> (hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) -> c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))) # label(fact_bijI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4747 (all V_D_2 all V_C_2 all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) -> (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) -> c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)))))) # label(fact_bij__betw__combine) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4748 (all V_f_2 all V_B_H_2 all V_A_H_2 all T_c all V_B_2 all V_A_2 all T_b (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) -> (hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) -> (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) -> (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) -> c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2))))))) # label(fact_bij__betw__Disj__Un) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4749 (all V_B_H_2 all V_B_2 all V_A_H_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> (hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2 -> c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2))))) # label(fact_bij__betw__subset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4750 (all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_bij__is__surj) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4751 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_bij__betw__imp__surj) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4752 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) <-> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2)) # label(fact_bij__betw__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4753 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) # label(fact_inj__on__imp__bij__betw) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4754 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2))) # label(fact_bij__betw__imp__inj__on) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4755 (all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) # label(fact_bij__is__inj) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4756 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) -> c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2))) # label(fact_bij__betw__the__inv__into) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4757 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) -> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) # label(fact_bij__betw__same__card) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4758 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) -> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_bij__betw__empty2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4759 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2) -> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) # label(fact_bij__betw__empty1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4760 (all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) <-> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))))) # label(fact_bij__betw__finite) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4761 (all V_B_2 all T_c all V_A_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) -> ((exists B_f c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)) <-> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2))))) # label(fact_BIJ) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4762 (all V_B_2 all V_A_2 all T_b (c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2) <-> V_A_2 = V_B_2)) # label(fact_bij__betw__id__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4763 (all T_b c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_bij__id) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4764 (all V_f_2 all T_d all T_c all T_b hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2) # label(fact_split__curry) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4765 (all V_f_2 all T_d all T_c all T_b c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2) # label(fact_curry__split) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4766 (all V_A_2 all V_B_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) <-> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))))) # label(fact_vimage__subset__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4767 (all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) -> hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2))) # label(fact_bij__vimage__eq__inv__image) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4768 (all V_M_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) -> (exists B_h c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2)))) # label(fact_ex__bij__betw__nat__finite__1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4769 (all V_g_2 all V_B_2 all V_A_2 all V_f_2 all T_c all T_b (c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2)) -> (c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2)) -> (exists B_h c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2))))))) # label(fact_Cantor__Bernstein) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4770 (all V_M_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) -> (exists B_h c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2)))) # label(fact_ex__bij__betw__nat__finite) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4771 (all V_M_2 all T_b (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) -> (exists B_h c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)))))) # label(fact_ex__bij__betw__finite__nat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4772 (all V_r_2 all V_A_2 all T_c all V_S_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) -> c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)))) -> c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)))) # label(fact_refl__on__UNION) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4773 (all V_Pa_2 all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) -> ((exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) & hBOOL(hAPP(V_Pa_2,B_x)))) <-> (exists B_x1 hBOOL(hAPP(V_Pa_2,B_x1)))))) # label(fact_bex__reg__eqv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4774 (all V_R_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2))) <-> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)))) # label(fact_in__respects) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4775 (all V_x_2 all V_R_2 all T_b (hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2)) <-> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)))) # label(fact_Respects__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4776 (all V_Pa_2 all V_Q_2 all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) -> ((all B_x (hBOOL(hAPP(V_Q_2,B_x)) -> hBOOL(hAPP(V_Pa_2,B_x)))) -> ((exists B_x1 hBOOL(hAPP(V_Q_2,B_x1))) -> (exists B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) & hBOOL(hAPP(V_Pa_2,B_x)))))))) # label(fact_bex__reg__right) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4777 (all V_Pa_2 all T_c all V_R_2 all T_b (c_Equiv__Relations_Oequivp(T_b,V_R_2) -> c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2)) # label(fact_babs__reg__eqv) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4778 (all V_m_2 all T_c all V_p_2 all V_x_2 all T_b (hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2)) -> hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2))) # label(fact_Babs__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4779 (all V_r_2 all V_f_2 all T_b ((all B_i hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) -> (c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) -> (exists B_i all B_k hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i))))) # label(fact_wf__weak__decr__stable) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4780 (all V_g_2 all V_f_2 all T_c all V_A_2 all V_B_2 all T_b (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2)))))) # label(fact_INT__anti__mono) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4781 (all V_B_2 all V_C_2 all T_c all V_A_2 all T_b ((all B_x (hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))))) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))))) # label(fact_INT__greatest) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4782 (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_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) -> (hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) -> ((all B_a all B_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) -> (all B_aa all B_ba (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),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].
% 6.25/6.24 4783 (all V_r_2 all V_zb_2 all V_za_2 all V_xb_2 all V_xa_2 all T_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) -> (hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2) -> -(all B_a all B_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2)) -> -hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))))))) # label(fact_converse__rtranclE2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4784 (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_c all T_b (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),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 (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) -> (hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),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].
% 6.25/6.24 4785 (all T_d all V_f_2 all V_r2_2 all T_c all V_r1_2 all T_b ((all B_y1 all B_z1 (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2)) -> (all B_y2 all B_z2 (hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2)) -> hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2))))) -> c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2))) # label(fact_congruent2I_H) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4786 (all T_c all V_f_2 all V_r_2 all T_b ((all B_y all B_z (hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) -> hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z))) -> c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2))) # label(fact_congruentI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4787 (all V_xqq all V_xq all T_a c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq))) # label(fact__03) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4788 (all V_j_2 all V_i_2 all V_Pa_2 (c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) <-> (all B_x (hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2))) -> hBOOL(hAPP(V_Pa_2,B_x)))))) # label(fact_all__interval__nat__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4789 (all T_a c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) # label(fact__04) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4790 (all V_j_2 all V_i_2 all V_Pa_2 (c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) <-> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2))) # label(fact_list__all__iff__all__interval__nat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4791 (all V_j_2 all V_i_2 all V_Pa_2 (c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2)) <-> -c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_Pa_2),V_i_2,V_j_2))) # label(fact_list__ex__iff__not__all__inverval__nat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.24 4792 (all V_f_2 all V_xq_2 all T_b all T_c hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2))) # label(fact__05) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4793 (all V_h_2 all V_g_2 all V_A_2 all V_F_2 all V_z_2 all V_f_2 all T_c all T_b (c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) -> ((all B_x (hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) -> hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x))) -> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2))))) # label(fact_folding__image_Ocong) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4794 (all V_xq_2 all V_x_2 all V_f_2 all T_b all T_c c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2))) # label(fact__06) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4795 (all V_f_2 all T_b all T_c c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) # label(fact__07) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4796 (all V_i_2 all V_xq_2 all V_f_2 all T_b all T_c c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2))) # label(fact_New__DSequence_Opos__map__def) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4797 (all V_n all V_m all V_i (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i)) -> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))))) # label(fact_power__dvd__imp__le) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4798 (all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x))) # label(fact_dvd_Oorder__refl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4799 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))))) # label(fact_dvd__0__right) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4800 (all V_k hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k))) # label(fact_dvd__1__left) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4801 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))))) # label(fact_dvd__mult__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4802 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))))) # label(fact_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4803 (all V_f_2 all V_A_2 all V_B_2 all T_b all T_c (class_Groups_Ocomm__monoid__mult(T_c) & class_Rings_Odvd(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) -> (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))))))) # label(fact_setprod__dvd__setprod__subset) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4804 (all V_t_2 all V_D_2 all V_d_2 all T_b (class_Rings_Ocomm__ring(T_b) & class_Rings_Odvd(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) -> (all B_x all B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)))))))) # label(fact_inf__period_I4_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4805 (all V_t_2 all V_D_2 all V_d_2 all T_b (class_Rings_Ocomm__ring(T_b) & class_Rings_Odvd(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2)) -> (all B_x all B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)))))))) # label(fact_inf__period_I3_J) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4806 (all V_d_2 all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Divides_Osemiring__div(T_b) -> (V_a_2 != c_Groups_Ozero__class_Ozero(T_b) -> (V_ca_2 != c_Groups_Ozero__class_Ozero(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2)) -> (hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_ca_2) <-> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)))))))) # label(fact_dvd__div__div__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4807 (all V_ca_2 all V_b_2 all V_a_2 all T_b (class_Divides_Osemiring__div(T_b) -> (V_a_2 != c_Groups_Ozero__class_Ozero(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) -> (hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_ca_2 <-> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)))))) # label(fact_dvd__div__eq__mult) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4808 (all V_l_2 all V_Pa_2 all T_b (class_Rings_Odvd(T_b) & class_Rings_Osemiring__0(T_b) -> ((exists B_x hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))) <-> (exists B_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) & hBOOL(hAPP(V_Pa_2,B_x))))))) # label(fact_unity__coeff__ex) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4809 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b))) # label(fact_dvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4810 (all V_a all V_b all V_c all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)))) # label(fact_div__mult__swap) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4811 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b))) # label(fact_dvd__div__mult__self) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4812 (all V_c all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a)))) # label(fact_dvd__div__mult) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4813 (all V_w all V_z all V_x all V_y all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w)) -> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)))))) # label(fact_div__mult__div__if__dvd) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4814 (all V_b_2 all V_a_2 all V_ca_2 all T_b (class_Rings_Oidom(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))) <-> V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))))) # label(fact_dvd__mult__cancel__left) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4815 (all V_b_2 all V_ca_2 all V_a_2 all T_b (class_Rings_Oidom(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))) <-> V_ca_2 = c_Groups_Ozero__class_Ozero(T_b) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))))) # label(fact_dvd__mult__cancel__right) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4816 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))) # label(fact_dvd__triv__left) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4817 (all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))))) # label(fact_dvd__triv__right) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4818 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_dvd__mult2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4819 (all V_b all V_c all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))) # label(fact_dvd__mult) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4820 (all V_d all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))) # label(fact_mult__dvd__mono) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4821 (all V_k all V_b all V_a all T_a (class_Rings_Odvd(T_a) -> (V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a))))) # label(fact_dvdI) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4822 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))))) # label(fact_dvd__mult__left) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4823 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))))) # label(fact_dvd__mult__right) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4824 (all V_n_2 all V_m_2 all V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) <-> V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)))) # label(fact_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4825 (all V_f_2 all V_i_2 all V_A_2 all T_b all T_c (class_Rings_Ocomm__semiring__1(T_c) -> (hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) -> (hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))))))) # label(fact_dvd__setprod) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4826 (all V_ca_2 all V_b_2 all V_a_2 (c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) <-> V_a_2 = V_b_2 & V_b_2 = V_ca_2)) # label(fact_dvd_OatLeastAtMost__singleton__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4827 (all V_a_2 c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) # label(fact_dvd_OatLeastAtMost__singleton) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4828 (all V_b_2 all V_a_2 (V_a_2 = V_b_2 -> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) # label(fact_dvd_OatLeastAtMost__singleton_H) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4829 (all V_b_2 all V_a_2 (c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) <-> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)))) # label(fact_dvd_OatLeastatMost__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4830 (all V_b_2 all V_a_2 (c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) <-> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)))) # label(fact_dvd_OatLeastatMost__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4831 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) -> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) # label(fact_dvd_OatLeastatMost__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4832 (all V_k_2 all V_l_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) -> c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) # label(fact_dvd_OgreaterThanAtMost__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4833 (all V_a_2 all V_b_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) -> c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) # label(fact_dvd_OatLeastLessThan__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4834 (all V_k_2 all V_l_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) -> c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) # label(fact_dvd_OgreaterThanLessThan__empty) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4835 (all V_l_2 all V_k_2 (c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) <-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))))) # label(fact_dvd_OgreaterThanAtMost__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4836 (all V_b_2 all V_a_2 (c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) <-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))))) # label(fact_dvd_OatLeastLessThan__empty__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4837 (all V_l_2 all V_k_2 (c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) <-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))))) # label(fact_dvd_OgreaterThanAtMost__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4838 (all V_b_2 all V_a_2 (c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) <-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))))) # label(fact_dvd_OatLeastLessThan__empty__iff2) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4839 (all V_n all V_m all V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))))) # label(fact_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4840 (all V_z all V_y all V_x all T_a (class_Rings_Ocomm__ring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))))))) # label(fact_dvd__diff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4841 (all V_y_2 all V_x_2 all T_b (class_Rings_Ocomm__ring__1(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))))) # label(fact_dvd__minus__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4842 (all V_y_2 all V_x_2 all T_b (class_Rings_Ocomm__ring__1(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))))) # label(fact_minus__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4843 (all V_x all V_y all T_a (class_Divides_Oring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y))))) # label(fact_dvd__neg__div) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4844 (all V_x all V_y all T_a (class_Divides_Oring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x)) -> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y))))) # label(fact_dvd__div__neg) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4845 (all V_b_2 all V_a_2 all T_b (class_Divides_Osemiring__div(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) <-> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)))) # label(fact_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4846 (all V_b all V_a all T_a (class_Divides_Osemiring__div(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a)))) # label(fact_dvd__imp__mod__0) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4847 (all V_d_2 all V_ca_2 all V_b_2 all V_a_2 (hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2,V_d_2))) <-> (-hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) & (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ca_2)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)))) & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_d_2)))) # label(fact_dvd_OatLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4848 (all V_k_2 all V_m_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2))) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2))))) # label(fact_dvd__abs__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4849 (all V_k_2 all V_m_2 all T_b (class_Rings_Olinordered__idom(T_b) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2)) <-> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2))))) # label(fact_abs__dvd__iff) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4850 (all V_k all V_l all T_a (class_Rings_Olinordered__idom(T_a) -> (hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k))))) # label(fact_dvd__if__abs__eq) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4851 (all V_c all V_b all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)))))) # label(fact_dvd__trans) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4852 (all V_a all T_a (class_Rings_Ocomm__semiring__1(T_a) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)))) # label(fact_dvd__refl) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4853 (all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))))) # label(fact_dvd_Oless__asym) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4854 (all V_z all V_y all V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) -> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) -> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) & -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))))) # label(fact_dvd_Oless__trans) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4855 (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].
% 6.25/6.25 4856 (all T_2 all T_1 (class_Complete__Lattice_Ocomplete__lattice(T_1) -> class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)))) # label(arity_fun__Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4857 (all T_2 all T_1 (class_Lattices_Obounded__lattice(T_1) -> class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Obounded__lattice__top) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4858 (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].
% 6.25/6.25 4859 (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].
% 6.25/6.25 4860 (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].
% 6.25/6.25 4861 (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].
% 6.25/6.25 4862 (all T_2 all T_1 (class_Lattices_Oboolean__algebra(T_1) -> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)))) # label(arity_fun__Lattices_Oboolean__algebra) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4863 (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].
% 6.25/6.25 4864 (all T_1 all T_2 (class_Finite__Set_Ofinite(T_2) & class_Finite__Set_Ofinite(T_1) -> class_Finite__Set_Ofinite(tc_fun(T_2,T_1)))) # label(arity_fun__Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4865 (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].
% 6.25/6.25 4866 (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].
% 6.25/6.25 4867 (all T_2 all T_1 (class_Orderings_Otop(T_1) -> class_Orderings_Otop(tc_fun(T_2,T_1)))) # label(arity_fun__Orderings_Otop) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4868 (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].
% 6.25/6.25 4869 (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].
% 6.25/6.25 4870 (all T_2 all T_1 (class_Groups_Ouminus(T_1) -> class_Groups_Ouminus(tc_fun(T_2,T_1)))) # label(arity_fun__Groups_Ouminus) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4871 (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].
% 6.25/6.25 4872 (all T_1 all T_2 (class_Enum_Oenum(T_2) & class_Enum_Oenum(T_1) -> class_Enum_Oenum(tc_fun(T_2,T_1)))) # label(arity_fun__Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4873 (all T_1 (class_Lazy__Sequence_Osmall__lazy(T_1) -> class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)))) # label(arity_List__Olist__Lazy__Sequence_Osmall__lazy) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4874 (all T_1 class_Nat_Osize(tc_List_Olist(T_1))) # label(arity_List__Olist__Nat_Osize) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4875 (all T_1 all T_2 (class_Finite__Set_Ofinite(T_2) & class_Finite__Set_Ofinite(T_1) -> class_Finite__Set_Ofinite(tc_sum(T_2,T_1)))) # label(arity_sum__Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4876 (all T_1 all T_2 (class_Enum_Oenum(T_2) & class_Enum_Oenum(T_1) -> class_Enum_Oenum(tc_sum(T_2,T_1)))) # label(arity_sum__Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4877 (all T_1 all T_2 class_Nat_Osize(tc_sum(T_2,T_1))) # label(arity_sum__Nat_Osize) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4878 (all T_1 (class_Finite__Set_Ofinite(T_1) -> class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)))) # label(arity_Option__Ooption__Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4879 (all T_1 (class_Enum_Oenum(T_1) -> class_Enum_Oenum(tc_Option_Ooption(T_1)))) # label(arity_Option__Ooption__Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4880 (all T_1 class_Nat_Osize(tc_Option_Ooption(T_1))) # label(arity_Option__Ooption__Nat_Osize) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4881 (all T_1 all T_2 class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1))) # label(arity_Nitpick__Opair____box__Nat_Osize) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4882 (all T_1 all T_2 (class_Lazy__Sequence_Osmall__lazy(T_2) & class_Lazy__Sequence_Osmall__lazy(T_1) -> class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)))) # label(arity_prod__Lazy__Sequence_Osmall__lazy) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4883 (all T_1 all T_2 (class_Finite__Set_Ofinite(T_2) & class_Finite__Set_Ofinite(T_1) -> class_Finite__Set_Ofinite(tc_prod(T_2,T_1)))) # label(arity_prod__Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4884 (all T_1 all T_2 (class_Enum_Oenum(T_2) & class_Enum_Oenum(T_1) -> class_Enum_Oenum(tc_prod(T_2,T_1)))) # label(arity_prod__Enum_Oenum) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4885 (all T_1 all T_2 class_Nat_Osize(tc_prod(T_2,T_1))) # label(arity_prod__Nat_Osize) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4886 (all T_1 class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1))) # label(arity_Hoare____Mirabelle__Otriple__Nat_Osize) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4887 (all T_1 class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1))) # label(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4888 (all V_P all T_a hAPP(c_COMBI(T_a),V_P) = V_P) # label(help_c__COMBI__1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4889 (all V_Q all V_P all T_b all T_a hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P) # label(help_c__COMBK__1) # label(axiom) # label(non_clause). [assumption].
% 6.25/6.25 4890 (all V_R_2 all V_Q_2 all V_Pa_2 all T_d all T_b all T_c hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2))) # label(help_c__COMBB__1) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4891 (all V_R_2 all V_Q_2 all V_Pa_2 all T_b all T_d all T_c hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2)) # label(help_c__COMBC__1) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4892 (all V_R_2 all V_Q_2 all V_Pa_2 all T_b all T_d all T_c hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2))) # label(help_c__COMBS__1) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4893 (all V_y_2 all V_x_2 (-hBOOL(hAPP(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].
% 10.97/10.95 4894 (all V_y_2 all V_x_2 (V_x_2 != V_y_2 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)))) # label(help_c__fequal__2) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4895 (all V_Pa_2 (-hBOOL(hAPP(c_fNot,V_Pa_2)) | -hBOOL(V_Pa_2))) # label(help_c__fNot__1) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4896 (all V_Pa_2 (--hBOOL(V_Pa_2) | hBOOL(hAPP(c_fNot,V_Pa_2)))) # label(help_c__fNot__2) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4897 (all V_Q_2 all V_Pa_2 (-hBOOL(V_Pa_2) | -hBOOL(V_Q_2) | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)))) # label(help_c__fconj__1) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4898 (all V_Q_2 all V_Pa_2 (-hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) | hBOOL(V_Pa_2))) # label(help_c__fconj__2) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4899 (all V_Q_2 all V_Pa_2 (-hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) | hBOOL(V_Q_2))) # label(help_c__fconj__3) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4900 (all V_Q_2 all V_Pa_2 (-hBOOL(V_Pa_2) | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)))) # label(help_c__fdisj__1) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4901 (all V_Pa_2 all V_Q_2 (-hBOOL(V_Q_2) | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)))) # label(help_c__fdisj__2) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4902 (all V_Q_2 all V_Pa_2 (-hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) | hBOOL(V_Pa_2) | hBOOL(V_Q_2))) # label(help_c__fdisj__3) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4903 (all V_Q_2 all V_Pa_2 (hBOOL(V_Pa_2) | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)))) # label(help_c__fimplies__1) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4904 (all V_Pa_2 all V_Q_2 (-hBOOL(V_Q_2) | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)))) # label(help_c__fimplies__2) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4905 (all V_Q_2 all V_Pa_2 (-hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) | -hBOOL(V_Pa_2) | hBOOL(V_Q_2))) # label(help_c__fimplies__3) # label(axiom) # label(non_clause). [assumption].
% 10.97/10.95 4906 -((exists B_Z exists B_x1 v_P(B_Z,B_x1)) -> (exists B_P_H exists B_Q_H c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 10.97/10.95
% 10.97/10.95 ============================== end of process non-clausal formulas ===
% 10.97/10.95
% 10.97/10.95 ============================== PROCESS INITIAL CLAUSES ===============
% 10.97/10.95
% 10.97/10.95 ============================== PREDICATE ELIMINATION =================
% 10.97/10.95 4907 class_Orderings_Olinorder(tc_Int_Oint) # label(arity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 10.97/10.95 4908 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_linorder__linear) # label(axiom). [clausify(52)].
% 10.97/10.95 4909 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_linorder__le__cases) # label(axiom). [clausify(90)].
% 10.97/10.95 4910 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(283)].
% 10.97/10.95 4911 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(283)].
% 10.97/10.95 4912 -class_Orderings_Olinorder(A) | B != C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_linorder__neq__iff) # label(axiom). [clausify(283)].
% 10.97/10.95 4913 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | C = B # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(284)].
% 10.97/10.95 4914 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(284)].
% 10.97/10.95 4915 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C != B # label(fact_not__less__iff__gr__or__eq) # label(axiom). [clausify(284)].
% 10.97/10.95 4916 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__less__linear) # label(axiom). [clausify(287)].
% 10.97/10.95 4917 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | B = C # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(291)].
% 10.97/10.95 4918 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | B != C # label(fact_linorder__antisym__conv3) # label(axiom). [clausify(291)].
% 10.97/10.95 4919 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_linorder__neqE) # label(axiom). [clausify(292)].
% 10.97/10.95 4920 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__cases) # label(axiom). [clausify(308)].
% 10.97/10.95 4921 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_linorder__not__less) # label(axiom). [clausify(337)].
% 10.97/10.95 4922 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_linorder__not__less) # label(axiom). [clausify(337)].
% 10.97/10.95 4923 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__not__le) # label(axiom). [clausify(338)].
% 10.97/10.95 4924 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__not__le) # label(axiom). [clausify(338)].
% 10.97/10.95 4925 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_linorder__le__less__linear) # label(axiom). [clausify(339)].
% 10.97/10.95 4926 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_leI) # label(axiom). [clausify(343)].
% 10.97/10.95 4927 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_not__leE) # label(axiom). [clausify(344)].
% 10.97/10.95 4928 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | C = B # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(345)].
% 10.97/10.95 4929 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | C != B # label(fact_linorder__antisym__conv1) # label(axiom). [clausify(345)].
% 10.97/10.95 4930 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_leD) # label(axiom). [clausify(348)].
% 10.97/10.95 4931 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C = B # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(350)].
% 10.97/10.95 4932 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | C != B # label(fact_linorder__antisym__conv2) # label(axiom). [clausify(350)].
% 10.97/10.95 4933 -class_Orderings_Olinorder(A) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),C)),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B))) # label(fact_fold1__antimono) # label(axiom). [clausify(607)].
% 10.97/10.95 4934 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),B) = B # label(fact_Min_Oidem) # label(axiom). [clausify(608)].
% 10.97/10.95 4935 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) # label(fact_min__max_Oinf__assoc) # label(axiom). [clausify(609)].
% 10.97/10.95 4936 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) # label(fact_min__max_Oinf_Oassoc) # label(axiom). [clausify(610)].
% 10.97/10.95 4937 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)) # label(fact_min__max_Oinf__left__commute) # label(axiom). [clausify(611)].
% 10.97/10.95 4938 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)) # label(fact_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(612)].
% 10.97/10.95 4939 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) # label(fact_min__max_Oinf__left__idem) # label(axiom). [clausify(613)].
% 10.97/10.95 4940 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) # label(fact_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(614)].
% 10.97/10.95 4941 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),B) # label(fact_min__max_Oinf__commute) # label(axiom). [clausify(615)].
% 10.97/10.95 4942 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),B) # label(fact_min__max_Oinf_Ocommute) # label(axiom). [clausify(616)].
% 10.97/10.95 4943 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),B) = B # label(fact_min__max_Oinf_Oidem) # label(axiom). [clausify(617)].
% 10.97/10.95 4944 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),D),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),D),hAPP(hAPP(c_Set_Oinsert(A),C),B)) # label(fact_min__max_Ofold__inf__insert) # label(axiom). [clausify(618)].
% 10.97/10.95 4945 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),B)) # label(fact_min__max_Oinf__le1) # label(axiom). [clausify(619)].
% 10.97/10.95 4946 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),C)) # label(fact_min__max_Oinf__le2) # label(axiom). [clausify(620)].
% 10.97/10.95 4947 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = B # label(fact_min__max_Ole__iff__inf) # label(axiom). [clausify(621)].
% 10.97/10.95 4948 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) != B # label(fact_min__max_Ole__iff__inf) # label(axiom). [clausify(621)].
% 10.97/10.95 4949 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_min__max_Ole__inf__iff) # label(axiom). [clausify(622)].
% 10.97/10.95 4950 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_min__max_Ole__inf__iff) # label(axiom). [clausify(622)].
% 10.97/10.95 4951 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_min__max_Ole__inf__iff) # label(axiom). [clausify(622)].
% 10.97/10.95 4952 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)),C)) # label(fact_min__max_Ole__infI1) # label(axiom). [clausify(623)].
% 10.97/10.95 4953 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),B)),C)) # label(fact_min__max_Ole__infI2) # label(axiom). [clausify(624)].
% 10.97/10.95 4954 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C) = B # label(fact_min__max_Oinf__absorb1) # label(axiom). [clausify(625)].
% 10.97/10.95 4955 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),B) = B # label(fact_min__max_Oinf__absorb2) # label(axiom). [clausify(626)].
% 10.97/10.95 4956 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) # label(fact_min__max_Ole__infI) # label(axiom). [clausify(627)].
% 10.97/10.95 4957 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) # label(fact_min__max_Oinf__greatest) # label(axiom). [clausify(628)].
% 10.97/10.95 4958 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),E))) # label(fact_min__max_Oinf__mono) # label(axiom). [clausify(629)].
% 10.97/10.95 4959 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_min__max_Ole__infE) # label(axiom). [clausify(630)].
% 10.97/10.95 4960 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_min__max_Ole__infE) # label(axiom). [clausify(630)].
% 10.97/10.95 4961 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_min__le__iff__disj) # label(axiom). [clausify(631)].
% 10.97/10.95 4962 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_min__le__iff__disj) # label(axiom). [clausify(631)].
% 10.97/10.95 4963 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_min__le__iff__disj) # label(axiom). [clausify(631)].
% 10.97/10.95 4964 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_min__less__iff__disj) # label(axiom). [clausify(632)].
% 10.97/10.95 4965 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_min__less__iff__disj) # label(axiom). [clausify(632)].
% 10.97/10.95 4966 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_min__less__iff__disj) # label(axiom). [clausify(632)].
% 10.97/10.95 4967 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_min__less__iff__conj) # label(axiom). [clausify(633)].
% 10.97/10.95 4968 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_min__less__iff__conj) # label(axiom). [clausify(633)].
% 10.97/10.95 4969 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_min__less__iff__conj) # label(axiom). [clausify(633)].
% 10.97/10.95 4970 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),B)),C)) # label(fact_min__max_Oless__infI2) # label(axiom). [clausify(634)].
% 10.97/10.95 4971 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)),C)) # label(fact_min__max_Oless__infI1) # label(axiom). [clausify(635)].
% 10.97/10.95 4972 -class_Lattices_Osemilattice__inf(A) | -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omin(A) = c_Lattices_Osemilattice__inf__class_Oinf(A) # label(fact_inf__min) # label(axiom). [clausify(640)].
% 10.97/10.95 4973 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),D),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))) # label(fact_min__max_Ofold__inf__le__inf) # label(axiom). [clausify(643)].
% 10.97/10.95 4974 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B)),C)) # label(fact_min__max_Ofold1__belowI) # label(axiom). [clausify(663)].
% 10.97/10.95 4975 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B)),C)) | hBOOL(hAPP(hAPP(c_member(A),f45(C,B,A)),B)) # label(fact_fold1__below__iff) # label(axiom). [clausify(664)].
% 10.97/10.95 4976 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),f45(C,B,A)),C)) # label(fact_fold1__below__iff) # label(axiom). [clausify(664)].
% 10.97/10.95 4977 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B)),C)) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),C)) # label(fact_fold1__below__iff) # label(axiom). [clausify(664)].
% 10.97/10.95 4978 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B))) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_min__max_Obelow__fold1__iff) # label(axiom). [clausify(665)].
% 10.97/10.95 4979 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B))) | hBOOL(hAPP(hAPP(c_member(A),f46(C,B,A)),B)) # label(fact_min__max_Obelow__fold1__iff) # label(axiom). [clausify(665)].
% 10.97/10.95 4980 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),f46(C,B,A))) # label(fact_min__max_Obelow__fold1__iff) # label(axiom). [clausify(665)].
% 10.97/10.95 4981 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B)),C)) | hBOOL(hAPP(hAPP(c_member(A),f47(C,B,A)),B)) # label(fact_fold1__strict__below__iff) # label(axiom). [clausify(666)].
% 10.97/10.95 4982 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),f47(C,B,A)),C)) # label(fact_fold1__strict__below__iff) # label(axiom). [clausify(666)].
% 10.97/10.95 4983 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B)),C)) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_fold1__strict__below__iff) # label(axiom). [clausify(666)].
% 10.97/10.95 4984 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B))) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_strict__below__fold1__iff) # label(axiom). [clausify(667)].
% 10.97/10.95 4985 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B))) | hBOOL(hAPP(hAPP(c_member(A),f48(C,B,A)),B)) # label(fact_strict__below__fold1__iff) # label(axiom). [clausify(667)].
% 10.97/10.95 4986 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),f48(C,B,A))) # label(fact_strict__below__fold1__iff) # label(axiom). [clausify(667)].
% 10.97/10.95 4987 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(A,B) = C # label(fact_Min_Oremove) # label(axiom). [clausify(684)].
% 10.97/10.95 4988 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_Min_Oremove) # label(axiom). [clausify(684)].
% 10.97/10.95 4989 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B) = C # label(fact_min__max_OInf__fin_Oremove) # label(axiom). [clausify(686)].
% 10.97/10.95 4990 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_min__max_OInf__fin_Oremove) # label(axiom). [clausify(686)].
% 10.97/10.95 4991 -class_Orderings_Olinorder(A) | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) = B # label(fact_Min_Osingleton) # label(axiom). [clausify(711)].
% 10.97/10.95 4992 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)) # label(fact_min__max_OInf__fin_Oin__idem) # label(axiom). [clausify(712)].
% 10.97/10.95 4993 -class_Orderings_Olinorder(A) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) = B # label(fact_min__max_OInf__fin_Osingleton) # label(axiom). [clausify(714)].
% 10.97/10.95 4994 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Big__Operators_Olinorder__class_OMin(A,B)),C)) # label(fact_Min__le) # label(axiom). [clausify(715)].
% 10.97/10.95 4995 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_member(A),c_Big__Operators_Olinorder__class_OMin(A,B)),B)) # label(fact_Min__in) # label(axiom). [clausify(716)].
% 10.97/10.95 4996 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olinorder__class_OMin(A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olinorder__class_OMin(A,B)) # label(fact_Min_Oin__idem) # label(axiom). [clausify(717)].
% 10.97/10.95 4997 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B) = hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B) # label(fact_min__max_OInf__fin_OF__eq) # label(axiom). [clausify(718)].
% 10.97/10.95 4998 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Big__Operators_Olinorder__class_OMin(A,B) = hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omin(A)),B) # label(fact_Min_OF__eq) # label(axiom). [clausify(720)].
% 10.97/10.95 4999 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)) # label(fact_min__max_OInf__fin_Oinsert__idem) # label(axiom). [clausify(721)].
% 10.97/10.95 5000 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),C)),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)) # label(fact_min__max_OInf__fin_Osubset__idem) # label(axiom). [clausify(722)].
% 10.97/10.95 5001 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),C)) # label(fact_min__max_OInf__fin_Ounion__idem) # label(axiom). [clausify(723)].
% 10.97/10.95 5002 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),B),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Big__Operators_Olinorder__class_OMin(A,C)),c_Big__Operators_Olinorder__class_OMin(A,B))) # label(fact_Min__antimono) # label(axiom). [clausify(724)].
% 10.97/10.95 5003 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),C),B) # label(fact_min__max_OInf__fin_Oeq__fold__idem_H) # label(axiom). [clausify(725)].
% 10.97/10.95 5004 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olinorder__class_OMin(A,B)) # label(fact_Min__insert) # label(axiom). [clausify(726)].
% 10.97/10.95 5005 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Big__Operators_Olinorder__class_OMin(A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olinorder__class_OMin(A,C)),c_Big__Operators_Olinorder__class_OMin(A,B)) # label(fact_Min_Osubset__idem) # label(axiom). [clausify(727)].
% 10.97/10.95 5006 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olinorder__class_OMin(A,B)),c_Big__Operators_Olinorder__class_OMin(A,C)) # label(fact_Min__Un) # label(axiom). [clausify(728)].
% 10.97/10.95 5007 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),C),B) # label(fact_Min_Oeq__fold__idem_H) # label(axiom). [clausify(729)].
% 10.97/10.95 5008 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)) # label(fact_min__max_OInf__fin_Oinsert) # label(axiom). [clausify(732)].
% 10.97/10.95 5009 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = C # label(fact_min__max_OInf__fin_Oinsert__remove) # label(axiom). [clausify(733)].
% 10.97/10.95 5010 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_min__max_OInf__fin_Oinsert__remove) # label(axiom). [clausify(733)].
% 10.97/10.95 5011 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C))),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),C)) # label(fact_min__max_OInf__fin_Ounion__inter) # label(axiom). [clausify(734)].
% 10.97/10.95 5012 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),C)) # label(fact_min__max_OInf__fin_Ounion__disjoint) # label(axiom). [clausify(735)].
% 10.97/10.95 5013 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),C),B) # label(fact_min__max_OInf__fin_Oeq__fold_H) # label(axiom). [clausify(736)].
% 10.97/10.95 5014 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olinorder__class_OMin(A,B)) # label(fact_Min_Oinsert) # label(axiom). [clausify(737)].
% 10.97/10.95 5015 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = C # label(fact_Min_Oinsert__remove) # label(axiom). [clausify(738)].
% 10.97/10.95 5016 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_Min_Oinsert__remove) # label(axiom). [clausify(738)].
% 10.97/10.95 5017 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C))),c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olinorder__class_OMin(A,B)),c_Big__Operators_Olinorder__class_OMin(A,C)) # label(fact_Min_Ounion__inter) # label(axiom). [clausify(739)].
% 10.97/10.95 5018 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olinorder__class_OMin(A,B)),c_Big__Operators_Olinorder__class_OMin(A,C)) # label(fact_Min_Ounion__disjoint) # label(axiom). [clausify(740)].
% 10.97/10.95 5019 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olinorder__class_OMin(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),C),B) # label(fact_Min_Oeq__fold_H) # label(axiom). [clausify(741)].
% 10.97/10.95 5020 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),f53(B,A)),f54(B,A))),hAPP(hAPP(c_Set_Oinsert(A),f53(B,A)),hAPP(hAPP(c_Set_Oinsert(A),f54(B,A)),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(A),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)),B)) # label(fact_min__max_OInf__fin_Oclosed) # label(axiom). [clausify(747)].
% 10.97/10.95 5021 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),f55(B,A)),f56(B,A))),hAPP(hAPP(c_Set_Oinsert(A),f55(B,A)),hAPP(hAPP(c_Set_Oinsert(A),f56(B,A)),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(A),c_Big__Operators_Olinorder__class_OMin(A,B)),B)) # label(fact_Min_Oclosed) # label(axiom). [clausify(748)].
% 10.97/10.95 5022 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Complete__Lattice_OSup__class_OSup(A,C))) | hBOOL(hAPP(hAPP(c_member(A),f64(C,B,A)),C)) # label(fact_less__Sup__iff) # label(axiom). [clausify(832)].
% 10.97/10.95 5023 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Complete__Lattice_OSup__class_OSup(A,C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),f64(C,B,A))) # label(fact_less__Sup__iff) # label(axiom). [clausify(832)].
% 10.97/10.95 5024 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Complete__Lattice_OSup__class_OSup(A,C))) | -hBOOL(hAPP(hAPP(c_member(A),D),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_less__Sup__iff) # label(axiom). [clausify(832)].
% 10.97/10.95 5025 -class_Orderings_Olinorder(A) | c_Finite__Set_Ofun__left__comm__idem(A,A,c_Orderings_Oord__class_Omin(A)) # label(fact_min__max_Ofun__left__comm__idem__inf) # label(axiom). [clausify(913)].
% 10.97/10.95 5026 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f100(C,D,B,A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C)),hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),C),B))) # label(fact_min__max_Oinf__le__fold__inf) # label(axiom). [clausify(1151)].
% 10.97/10.95 5027 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),f100(D,C,B,A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)),hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omin(A)),D),B))) # label(fact_min__max_Oinf__le__fold__inf) # label(axiom). [clausify(1151)].
% 10.97/10.95 5028 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f102(C,B,A)),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olinorder__class_OMin(A,B) = C # label(fact_Min__eqI) # label(axiom). [clausify(1153)].
% 10.97/10.95 5029 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),f102(C,B,A))) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olinorder__class_OMin(A,B) = C # label(fact_Min__eqI) # label(axiom). [clausify(1153)].
% 10.97/10.95 5030 -class_Int_Onumber(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),C)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) # label(fact_le__number__of__eq__not__less) # label(axiom). [clausify(1168)].
% 10.97/10.95 5031 -class_Int_Onumber(A) | -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),C)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) # label(fact_le__number__of__eq__not__less) # label(axiom). [clausify(1168)].
% 10.97/10.95 5032 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Complete__Lattice_OInf__class_OInf(A,B)),C)) | hBOOL(hAPP(hAPP(c_member(A),f153(C,B,A)),B)) # label(fact_Inf__less__iff) # label(axiom). [clausify(2106)].
% 10.97/10.95 5033 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Complete__Lattice_OInf__class_OInf(A,B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),f153(C,B,A)),C)) # label(fact_Inf__less__iff) # label(axiom). [clausify(2106)].
% 10.97/10.95 5034 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Complete__Lattice_OInf__class_OInf(A,B)),C)) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_Inf__less__iff) # label(axiom). [clausify(2106)].
% 10.97/10.95 5035 -class_Orderings_Olinorder(A) | c_Orderings_Oord_Omax(A,hAPP(c_COMBC(A,A,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(A))) = c_Orderings_Oord__class_Omin(A) # label(fact_dual__max) # label(axiom). [clausify(2422)].
% 10.97/10.95 5036 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OlessThan(A),B) != hAPP(c_SetInterval_Oord__class_OlessThan(A),C) | B = C # label(fact_lessThan__eq__iff) # label(axiom). [clausify(2436)].
% 10.97/10.95 5037 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OlessThan(A),B) = hAPP(c_SetInterval_Oord__class_OlessThan(A),C) | B != C # label(fact_lessThan__eq__iff) # label(axiom). [clausify(2436)].
% 10.97/10.95 5038 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)),hAPP(c_SetInterval_Oord__class_OlessThan(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_lessThan__subset__iff) # label(axiom). [clausify(2440)].
% 10.97/10.95 5039 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)),hAPP(c_SetInterval_Oord__class_OlessThan(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_lessThan__subset__iff) # label(axiom). [clausify(2440)].
% 10.97/10.95 5040 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)),hAPP(c_SetInterval_Oord__class_OlessThan(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_lessThan__strict__subset__iff) # label(axiom). [clausify(2442)].
% 10.97/10.95 5041 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)),hAPP(c_SetInterval_Oord__class_OlessThan(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_lessThan__strict__subset__iff) # label(axiom). [clausify(2442)].
% 10.97/10.95 5042 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_le__max__iff__disj) # label(axiom). [clausify(2464)].
% 10.97/10.95 5043 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_le__max__iff__disj) # label(axiom). [clausify(2464)].
% 10.97/10.95 5044 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_le__max__iff__disj) # label(axiom). [clausify(2464)].
% 10.97/10.95 5045 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_min__max_Ole__supE) # label(axiom). [clausify(2465)].
% 10.97/10.95 5046 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_min__max_Ole__supE) # label(axiom). [clausify(2465)].
% 10.97/10.95 5047 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),E))) # label(fact_min__max_Osup__mono) # label(axiom). [clausify(2466)].
% 10.97/10.95 5048 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),C)) # label(fact_min__max_Osup__least) # label(axiom). [clausify(2467)].
% 10.97/10.95 5049 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),C)) # label(fact_min__max_Ole__supI) # label(axiom). [clausify(2468)].
% 10.97/10.95 5050 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B) = C # label(fact_min__max_Osup__absorb1) # label(axiom). [clausify(2469)].
% 10.97/10.95 5051 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = C # label(fact_min__max_Osup__absorb2) # label(axiom). [clausify(2470)].
% 10.97/10.95 5052 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C))) # label(fact_min__max_Ole__supI2) # label(axiom). [clausify(2471)].
% 10.97/10.95 5053 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) # label(fact_min__max_Ole__supI1) # label(axiom). [clausify(2472)].
% 10.97/10.95 5054 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_min__max_Ole__sup__iff) # label(axiom). [clausify(2473)].
% 10.97/10.95 5055 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_min__max_Ole__sup__iff) # label(axiom). [clausify(2473)].
% 10.97/10.95 5056 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_min__max_Ole__sup__iff) # label(axiom). [clausify(2473)].
% 10.97/10.95 5057 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = C # label(fact_min__max_Ole__iff__sup) # label(axiom). [clausify(2474)].
% 10.97/10.95 5058 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) != C # label(fact_min__max_Ole__iff__sup) # label(axiom). [clausify(2474)].
% 10.97/10.95 5059 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B))) # label(fact_le__maxI2) # label(axiom). [clausify(2475)].
% 10.97/10.95 5060 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C))) # label(fact_le__maxI1) # label(axiom). [clausify(2476)].
% 10.97/10.95 5061 -class_Orderings_Olinorder(A) | c_Finite__Set_Ofun__left__comm__idem(A,A,c_Orderings_Oord__class_Omax(A)) # label(fact_min__max_Ofun__left__comm__idem__sup) # label(axiom). [clausify(2477)].
% 10.97/10.95 5062 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) # label(fact_min__max_Oless__supI1) # label(axiom). [clausify(2479)].
% 10.97/10.95 5063 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C))) # label(fact_min__max_Oless__supI2) # label(axiom). [clausify(2480)].
% 10.97/10.95 5064 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_less__max__iff__disj) # label(axiom). [clausify(2481)].
% 10.97/10.95 5065 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_less__max__iff__disj) # label(axiom). [clausify(2481)].
% 10.97/10.95 5066 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_less__max__iff__disj) # label(axiom). [clausify(2481)].
% 10.97/10.95 5067 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_max__less__iff__conj) # label(axiom). [clausify(2482)].
% 10.97/10.95 5068 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_max__less__iff__conj) # label(axiom). [clausify(2482)].
% 10.97/10.95 5069 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_max__less__iff__conj) # label(axiom). [clausify(2482)].
% 10.97/10.95 5070 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B) = B # label(fact_min__max_Osup_Oidem) # label(axiom). [clausify(2484)].
% 10.97/10.95 5071 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B) # label(fact_min__max_Osup_Ocommute) # label(axiom). [clausify(2485)].
% 10.97/10.95 5072 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B) # label(fact_min__max_Osup__commute) # label(axiom). [clausify(2486)].
% 10.97/10.95 5073 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) # label(fact_min__max_Osup_Oleft__idem) # label(axiom). [clausify(2487)].
% 10.97/10.95 5074 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C) # label(fact_min__max_Osup__left__idem) # label(axiom). [clausify(2488)].
% 10.97/10.95 5075 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)) # label(fact_min__max_Osup_Oleft__commute) # label(axiom). [clausify(2489)].
% 10.97/10.95 5076 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)) # label(fact_min__max_Osup__left__commute) # label(axiom). [clausify(2490)].
% 10.97/10.95 5077 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) # label(fact_min__max_Osup_Oassoc) # label(axiom). [clausify(2491)].
% 10.97/10.95 5078 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) # label(fact_min__max_Osup__assoc) # label(axiom). [clausify(2492)].
% 10.97/10.95 5079 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B) = B # label(fact_Max_Oidem) # label(axiom). [clausify(2493)].
% 10.97/10.95 5080 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),C) # label(fact_min__max_Oinf__sup__distrib2) # label(axiom). [clausify(2494)].
% 10.97/10.95 5081 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),D) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) # label(fact_min__max_Osup__inf__distrib2) # label(axiom). [clausify(2495)].
% 10.97/10.95 5082 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)) # label(fact_min__max_Oinf__sup__distrib1) # label(axiom). [clausify(2496)].
% 10.97/10.95 5083 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)) # label(fact_min__max_Osup__inf__distrib1) # label(axiom). [clausify(2497)].
% 10.97/10.95 5084 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)) = B # label(fact_min__max_Oinf__sup__absorb) # label(axiom). [clausify(2498)].
% 10.97/10.95 5085 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = B # label(fact_min__max_Osup__inf__absorb) # label(axiom). [clausify(2499)].
% 10.97/10.95 5086 -class_Lattices_Osemilattice__sup(A) | -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(A) = c_Lattices_Osemilattice__sup__class_Osup(A) # label(fact_sup__max) # label(axiom). [clausify(2503)].
% 10.97/10.95 5087 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D))),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)))) # label(fact_min__max_Odistrib__sup__le) # label(axiom). [clausify(2505)].
% 10.97/10.95 5088 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D))),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)))) # label(fact_min__max_Odistrib__inf__le) # label(axiom). [clausify(2506)].
% 10.97/10.95 5089 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),D),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),D),hAPP(hAPP(c_Set_Oinsert(A),C),B)) # label(fact_min__max_Ofold__sup__insert) # label(axiom). [clausify(2513)].
% 10.97/10.95 5090 -class_Orderings_Olinorder(A) | c_Orderings_Oord__class_Omax(A) = c_Orderings_Oord_Omin(A,hAPP(c_COMBC(A,A,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(A))) # label(fact_dual__min) # label(axiom). [clausify(2514)].
% 10.97/10.95 5091 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)),hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),D),B))) # label(fact_min__max_Osup__le__fold__sup) # label(axiom). [clausify(2515)].
% 10.97/10.95 5092 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)) = C # label(fact_min__max_Osup__Inf__absorb) # label(axiom). [clausify(2516)].
% 10.97/10.95 5093 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(A,B) = C # label(fact_Max_Oremove) # label(axiom). [clausify(2517)].
% 10.97/10.95 5094 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_Max_Oremove) # label(axiom). [clausify(2517)].
% 10.97/10.95 5095 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B))) # label(fact_min__max_OInf__le__Sup) # label(axiom). [clausify(2518)].
% 10.97/10.95 5096 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B) = C # label(fact_min__max_OSup__fin_Oremove) # label(axiom). [clausify(2519)].
% 10.97/10.95 5097 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_min__max_OSup__fin_Oremove) # label(axiom). [clausify(2519)].
% 10.97/10.95 5098 -class_Orderings_Olinorder(A) | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) = B # label(fact_Max_Osingleton) # label(axiom). [clausify(2521)].
% 10.97/10.95 5099 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)) # label(fact_min__max_OSup__fin_Oin__idem) # label(axiom). [clausify(2522)].
% 10.97/10.95 5100 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Big__Operators_Olinorder__class_OMax(A,B))) # label(fact_Max__ge) # label(axiom). [clausify(2523)].
% 10.97/10.95 5101 -class_Orderings_Olinorder(A) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) = B # label(fact_min__max_OSup__fin_Osingleton) # label(axiom). [clausify(2524)].
% 10.97/10.95 5102 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_member(A),c_Big__Operators_Olinorder__class_OMax(A,B)),B)) # label(fact_Max__in) # label(axiom). [clausify(2525)].
% 10.97/10.95 5103 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olinorder__class_OMax(A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olinorder__class_OMax(A,B)) # label(fact_Max_Oin__idem) # label(axiom). [clausify(2526)].
% 10.97/10.95 5104 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B) = hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omax(A)),B) # label(fact_min__max_OSup__fin_OF__eq) # label(axiom). [clausify(2527)].
% 10.97/10.95 5105 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Big__Operators_Olinorder__class_OMax(A,B) = hAPP(c_Finite__Set_Ofold1(A,c_Orderings_Oord__class_Omax(A)),B) # label(fact_Max_OF__eq) # label(axiom). [clausify(2528)].
% 10.97/10.95 5106 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)) # label(fact_min__max_OSup__fin_Oinsert__idem) # label(axiom). [clausify(2529)].
% 10.97/10.95 5107 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),C)),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)) # label(fact_min__max_OSup__fin_Osubset__idem) # label(axiom). [clausify(2530)].
% 10.97/10.95 5108 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)) = C # label(fact_min__max_Oinf__Sup__absorb) # label(axiom). [clausify(2531)].
% 10.97/10.95 5109 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),C)) # label(fact_min__max_OSup__fin_Ounion__idem) # label(axiom). [clausify(2532)].
% 10.97/10.96 5110 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),B),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Big__Operators_Olinorder__class_OMax(A,B)),c_Big__Operators_Olinorder__class_OMax(A,C))) # label(fact_Max__mono) # label(axiom). [clausify(2533)].
% 10.97/10.96 5111 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),C),B) # label(fact_min__max_OSup__fin_Oeq__fold__idem_H) # label(axiom). [clausify(2534)].
% 10.97/10.96 5112 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olinorder__class_OMax(A,B)) # label(fact_Max__insert) # label(axiom). [clausify(2535)].
% 10.97/10.96 5113 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Big__Operators_Olinorder__class_OMax(A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olinorder__class_OMax(A,C)),c_Big__Operators_Olinorder__class_OMax(A,B)) # label(fact_Max_Osubset__idem) # label(axiom). [clausify(2536)].
% 10.97/10.96 5114 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olinorder__class_OMax(A,B)),c_Big__Operators_Olinorder__class_OMax(A,C)) # label(fact_Max__Un) # label(axiom). [clausify(2537)].
% 10.97/10.96 5115 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),C),B) # label(fact_Max_Oeq__fold__idem_H) # label(axiom). [clausify(2538)].
% 10.97/10.96 5116 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)) # label(fact_min__max_OSup__fin_Oinsert) # label(axiom). [clausify(2539)].
% 10.97/10.96 5117 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = C # label(fact_min__max_OSup__fin_Oinsert__remove) # label(axiom). [clausify(2540)].
% 10.97/10.96 5118 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_min__max_OSup__fin_Oinsert__remove) # label(axiom). [clausify(2540)].
% 10.97/10.96 5119 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),C)) # label(fact_min__max_OSup__fin_Ounion__disjoint) # label(axiom). [clausify(2541)].
% 10.97/10.96 5120 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C))),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),C)) # label(fact_min__max_OSup__fin_Ounion__inter) # label(axiom). [clausify(2542)].
% 10.97/10.96 5121 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),C),B) # label(fact_min__max_OSup__fin_Oeq__fold_H) # label(axiom). [clausify(2543)].
% 10.97/10.96 5122 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olinorder__class_OMax(A,B)) # label(fact_Max_Oinsert) # label(axiom). [clausify(2544)].
% 10.97/10.96 5123 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = C # label(fact_Max_Oinsert__remove) # label(axiom). [clausify(2545)].
% 10.97/10.96 5124 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_Max_Oinsert__remove) # label(axiom). [clausify(2545)].
% 10.97/10.96 5125 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olinorder__class_OMax(A,B)),c_Big__Operators_Olinorder__class_OMax(A,C)) # label(fact_Max_Ounion__disjoint) # label(axiom). [clausify(2546)].
% 10.97/10.96 5126 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C))),c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olinorder__class_OMax(A,B)),c_Big__Operators_Olinorder__class_OMax(A,C)) # label(fact_Max_Ounion__inter) # label(axiom). [clausify(2547)].
% 10.97/10.96 5127 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olinorder__class_OMax(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),C),B) # label(fact_Max_Oeq__fold_H) # label(axiom). [clausify(2548)].
% 10.97/10.96 5128 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),f184(B,A)),f185(B,A))),hAPP(hAPP(c_Set_Oinsert(A),f184(B,A)),hAPP(hAPP(c_Set_Oinsert(A),f185(B,A)),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(A),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)),B)) # label(fact_min__max_OSup__fin_Oclosed) # label(axiom). [clausify(2549)].
% 10.97/10.96 5129 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),f186(B,A)),f187(B,A))),hAPP(hAPP(c_Set_Oinsert(A),f186(B,A)),hAPP(hAPP(c_Set_Oinsert(A),f187(B,A)),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(A),c_Big__Operators_Olinorder__class_OMax(A,B)),B)) # label(fact_Max_Oclosed) # label(axiom). [clausify(2550)].
% 10.97/10.96 5130 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(C,A),D),E))) | hBOOL(hAPP(hAPP(c_member(C),f199(E,D,C,B,A)),D)) # label(fact_less__SUP__iff) # label(axiom). [clausify(2628)].
% 10.97/10.96 5131 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(C,A),D),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(E,f199(E,D,C,B,A)))) # label(fact_less__SUP__iff) # label(axiom). [clausify(2628)].
% 10.97/10.96 5132 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(C,A),D),E))) | -hBOOL(hAPP(hAPP(c_member(C),F),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(E,F))) # label(fact_less__SUP__iff) # label(axiom). [clausify(2628)].
% 10.97/10.96 5133 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(B,A),C),D)),E)) | hBOOL(hAPP(hAPP(c_member(B),f200(E,D,C,B,A)),C)) # label(fact_INF__less__iff) # label(axiom). [clausify(2629)].
% 10.97/10.96 5134 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(B,A),C),D)),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(D,f200(E,D,C,B,A))),E)) # label(fact_INF__less__iff) # label(axiom). [clausify(2629)].
% 10.97/10.96 5135 -class_Complete__Lattice_Ocomplete__lattice(A) | -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(B,A),C),D)),E)) | -hBOOL(hAPP(hAPP(c_member(B),F),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(D,F)),E)) # label(fact_INF__less__iff) # label(axiom). [clausify(2629)].
% 10.97/10.96 5136 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),E)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,D)),c_SetInterval_Oord__class_OatLeastAtMost(A,C,E)) # label(fact_Int__atLeastAtMost) # label(axiom). [clausify(2681)].
% 10.97/10.96 5137 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OgreaterThanLessThan(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),E)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,D)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,E)) # label(fact_Int__greaterThanLessThan) # label(axiom). [clausify(2730)].
% 10.97/10.96 5138 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C)),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D)) # label(fact_ivl__disj__un_I19_J) # label(axiom). [clausify(2734)].
% 10.97/10.96 5139 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C)),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) # label(fact_ivl__disj__un_I4_J) # label(axiom). [clausify(2735)].
% 10.97/10.96 5140 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(c_SetInterval_Oord__class_OatMost(A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(A),B)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)) # label(fact_ivl__disj__un_I9_J) # label(axiom). [clausify(2741)].
% 10.97/10.96 5141 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatMost(A),B) != hAPP(c_SetInterval_Oord__class_OatMost(A),C) | B = C # label(fact_atMost__eq__iff) # label(axiom). [clausify(2742)].
% 10.97/10.96 5142 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatMost(A),B) = hAPP(c_SetInterval_Oord__class_OatMost(A),C) | B != C # label(fact_atMost__eq__iff) # label(axiom). [clausify(2742)].
% 10.97/10.96 5143 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,D)) # label(fact_ivl__disj__un_I20_J) # label(axiom). [clausify(2747)].
% 10.97/10.96 5144 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | c_SetInterval_Oord__class_OatLeastAtMost(A,B,D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,D)) # label(fact_ivl__disj__un_I22_J) # label(axiom). [clausify(2756)].
% 10.97/10.96 5145 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OgreaterThanAtMost(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),E)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,D)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,E)) # label(fact_Int__greaterThanAtMost) # label(axiom). [clausify(2759)].
% 10.97/10.96 5146 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(A,B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(A),C)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,D)) # label(fact_Int__atLeastAtMostR1) # label(axiom). [clausify(2763)].
% 10.97/10.96 5147 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(A,B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)),hAPP(c_SetInterval_Oord__class_OatMost(A),D)) # label(fact_Int__atLeastAtMostL1) # label(axiom). [clausify(2764)].
% 10.97/10.96 5148 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,D)) # label(fact_ivl__disj__un_I16_J) # label(axiom). [clausify(2768)].
% 10.97/10.96 5149 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatMost(A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) # label(fact_ivl__disj__un_I2_J) # label(axiom). [clausify(2770)].
% 10.97/10.96 5150 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(c_SetInterval_Oord__class_OatMost(A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)) # label(fact_ivl__disj__un_I10_J) # label(axiom). [clausify(2771)].
% 10.97/10.96 5151 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hAPP(c_SetInterval_Oord__class_OlessThan(A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(A),B)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C)) # label(fact_ivl__disj__un_I7_J) # label(axiom). [clausify(2772)].
% 10.97/10.96 5152 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | c_SetInterval_Oord__class_OatLeastAtMost(A,B,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)) # label(fact_ivl__disj__un_I5_J) # label(axiom). [clausify(2773)].
% 10.97/10.96 5153 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,D),E) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C) | D = B # label(fact_atLeastLessThan__eq__iff) # label(axiom). [clausify(2814)].
% 10.97/10.96 5154 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,D),E) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C) | C = E # label(fact_atLeastLessThan__eq__iff) # label(axiom). [clausify(2814)].
% 10.97/10.96 5155 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,D),E) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C) | D != B | C != E # label(fact_atLeastLessThan__eq__iff) # label(axiom). [clausify(2814)].
% 10.97/10.96 5156 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,D),E) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | B = D # label(fact_atLeastLessThan__inj_I1_J) # label(axiom). [clausify(2815)].
% 10.97/10.96 5157 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,D),E) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | E = C # label(fact_atLeastLessThan__inj_I2_J) # label(axiom). [clausify(2816)].
% 10.97/10.96 5158 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,D),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),B)) # label(fact_atLeastLessThan__subset__iff) # label(axiom). [clausify(2828)].
% 10.97/10.96 5159 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,D),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),E)) # label(fact_atLeastLessThan__subset__iff) # label(axiom). [clausify(2828)].
% 10.97/10.96 5160 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) # label(fact_ivl__disj__un_I17_J) # label(axiom). [clausify(2830)].
% 10.97/10.96 5161 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),D)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C)) # label(fact_ivl__diff) # label(axiom). [clausify(2832)].
% 10.97/10.96 5162 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | c_SetInterval_Oord__class_OatLeastAtMost(A,B,D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C)),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D)) # label(fact_ivl__disj__un_I21_J) # label(axiom). [clausify(2841)].
% 10.97/10.96 5163 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),D),E)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),D)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),E)) # label(fact_Int__atLeastLessThan) # label(axiom). [clausify(2843)].
% 10.97/10.96 5164 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(c_SetInterval_Oord__class_OlessThan(A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C)) # label(fact_ivl__disj__un_I8_J) # label(axiom). [clausify(2844)].
% 10.97/10.96 5165 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) # label(fact_ivl__disj__un_I15_J) # label(axiom). [clausify(2851)].
% 10.97/10.96 5166 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | c_SetInterval_Oord__class_OatLeastAtMost(A,B,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C)),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))) # label(fact_ivl__disj__un_I6_J) # label(axiom). [clausify(2853)].
% 10.97/10.96 5167 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C)) # label(fact_ivl__disj__un_I3_J) # label(axiom). [clausify(2854)].
% 10.97/10.96 5168 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),D) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,D)) # label(fact_ivl__disj__un_I18_J) # label(axiom). [clausify(2855)].
% 10.97/10.96 5169 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatLeast(A),B) != hAPP(c_SetInterval_Oord__class_OatLeast(A),C) | B = C # label(fact_atLeast__eq__iff) # label(axiom). [clausify(2910)].
% 10.97/10.96 5170 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatLeast(A),B) = hAPP(c_SetInterval_Oord__class_OatLeast(A),C) | B != C # label(fact_atLeast__eq__iff) # label(axiom). [clausify(2910)].
% 10.97/10.96 5171 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OlessThan(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(A),B)) # label(fact_Compl__atLeast) # label(axiom). [clausify(2983)].
% 10.97/10.96 5172 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatLeast(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)) # label(fact_Compl__lessThan) # label(axiom). [clausify(2984)].
% 10.97/10.96 5173 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeast(A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),C)),hAPP(c_SetInterval_Oord__class_OatLeast(A),C)) # label(fact_ivl__disj__un_I14_J) # label(axiom). [clausify(2992)].
% 10.97/10.96 5174 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),D) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,D)),hAPP(c_SetInterval_Oord__class_OatLeast(A),C)) # label(fact_Int__atLeastAtMostL2) # label(axiom). [clausify(2994)].
% 10.97/10.96 5175 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeastAtMost(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C),D) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(A),B)),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D)) # label(fact_Int__atLeastAtMostR2) # label(axiom). [clausify(2995)].
% 10.97/10.96 5176 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C)),hAPP(c_SetInterval_Oord__class_OatLeast(A),C)) # label(fact_ivl__disj__un_I12_J) # label(axiom). [clausify(3006)].
% 10.97/10.96 5177 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B) != hAPP(c_SetInterval_Oord__class_OgreaterThan(A),C) | B = C # label(fact_greaterThan__eq__iff) # label(axiom). [clausify(3020)].
% 10.97/10.96 5178 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B) = hAPP(c_SetInterval_Oord__class_OgreaterThan(A),C) | B != C # label(fact_greaterThan__eq__iff) # label(axiom). [clausify(3020)].
% 10.97/10.96 5179 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B)),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_greaterThan__subset__iff) # label(axiom). [clausify(3029)].
% 10.97/10.96 5180 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B)),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_greaterThan__subset__iff) # label(axiom). [clausify(3029)].
% 10.97/10.96 5181 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(A),B)) # label(fact_Compl__atMost) # label(axiom). [clausify(3033)].
% 10.97/10.96 5182 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatMost(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(A,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B)) # label(fact_Compl__greaterThan) # label(axiom). [clausify(3034)].
% 10.97/10.96 5183 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),C)) # label(fact_ivl__disj__un_I11_J) # label(axiom). [clausify(3040)].
% 10.97/10.96 5184 -class_Orderings_Olinorder(A) | hAPP(c_SetInterval_Oord__class_OatLeast(A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B)) # label(fact_ivl__disj__un_I1_J) # label(axiom). [clausify(3046)].
% 10.97/10.96 5185 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeast(A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),C)) # label(fact_ivl__disj__un_I13_J) # label(axiom). [clausify(3047)].
% 10.97/10.96 5186 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(B,f269(C,B,A))),hAPP(B,f270(C,B,A))) != hAPP(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),f269(C,B,A)),f270(C,B,A))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(c_Set_Oimage(A,A,B),C)) = hAPP(B,c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),C)) # label(fact_min__max_OSup__fin_Ohom__commute) # label(axiom). [clausify(3076)].
% 10.97/10.96 5187 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(B,f271(C,B,A))),hAPP(B,f272(C,B,A))) != hAPP(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),f271(C,B,A)),f272(C,B,A))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(c_Set_Oimage(A,A,B),C)) = hAPP(B,c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),C)) # label(fact_min__max_OInf__fin_Ohom__commute) # label(axiom). [clausify(3077)].
% 10.97/10.96 5188 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(B,f273(C,B,A))),hAPP(B,f274(C,B,A))) != hAPP(B,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),f273(C,B,A)),f274(C,B,A))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olinorder__class_OMax(A,hAPP(c_Set_Oimage(A,A,B),C)) = hAPP(B,c_Big__Operators_Olinorder__class_OMax(A,C)) # label(fact_Max_Ohom__commute) # label(axiom). [clausify(3078)].
% 10.97/10.96 5189 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(B,f275(C,B,A))),hAPP(B,f276(C,B,A))) != hAPP(B,hAPP(hAPP(c_Orderings_Oord__class_Omin(A),f275(C,B,A)),f276(C,B,A))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olinorder__class_OMin(A,hAPP(c_Set_Oimage(A,A,B),C)) = hAPP(B,c_Big__Operators_Olinorder__class_OMin(A,C)) # label(fact_Min_Ohom__commute) # label(axiom). [clausify(3079)].
% 10.97/10.96 5190 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(A,tc_HOL_Obool)),tc_fun(A,tc_HOL_Obool),A),hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(A))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_fun(A,tc_HOL_Obool)),tc_fun(A,tc_fun(A,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool))),tc_fun(tc_fun(A,tc_fun(A,tc_HOL_Obool)),tc_fun(A,tc_fun(A,tc_HOL_Obool))),A),c_COMBS(A,tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(A,tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool))),A),hAPP(c_COMBB(tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),A),c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(A,tc_HOL_Obool)),tc_fun(A,tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),A),hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_fun(A,A)),tc_fun(A,tc_fun(A,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_fun(A,A)),tc_fun(A,tc_fun(A,tc_HOL_Obool))),A),c_COMBB(tc_fun(A,A),tc_fun(A,tc_HOL_Obool),A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),A),c_COMBB(A,tc_HOL_Obool,A)),c_fequal))),c_Orderings_Oord__class_Omin(A)))))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),A),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B)))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C))))))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),C)) # label(fact_min__max_Oinf__Sup2__distrib) # label(axiom). [clausify(3212)].
% 10.97/10.96 5191 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(A)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),A),c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj)),hAPP(hAPP(c_COMBC(A,tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),A),c_COMBB(A,tc_HOL_Obool,A)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(A),C))))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B))))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),C),c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),B)) # label(fact_min__max_Oinf__Sup1__distrib) # label(axiom). [clausify(3213)].
% 10.97/10.96 5192 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(A)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),A),c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj)),hAPP(hAPP(c_COMBC(A,tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),A),c_COMBB(A,tc_HOL_Obool,A)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(A),C))))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B))))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)) # label(fact_min__max_Osup__Inf1__distrib) # label(axiom). [clausify(3231)].
% 10.97/10.96 5193 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(A,tc_HOL_Obool)),tc_fun(A,tc_HOL_Obool),A),hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(A))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_fun(A,tc_HOL_Obool)),tc_fun(A,tc_fun(A,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool))),tc_fun(tc_fun(A,tc_fun(A,tc_HOL_Obool)),tc_fun(A,tc_fun(A,tc_HOL_Obool))),A),c_COMBS(A,tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(A,tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool))),A),hAPP(c_COMBB(tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),A),c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(A,tc_HOL_Obool)),tc_fun(A,tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),A),hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_fun(A,A)),tc_fun(A,tc_fun(A,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_fun(A,A)),tc_fun(A,tc_fun(A,tc_HOL_Obool))),A),c_COMBB(tc_fun(A,A),tc_fun(A,tc_HOL_Obool),A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),A),c_COMBB(A,tc_HOL_Obool,A)),c_fequal))),c_Orderings_Oord__class_Omax(A)))))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),A),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B)))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C))))))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),B)),c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),C)) # label(fact_min__max_Osup__Inf2__distrib) # label(axiom). [clausify(3232)].
% 10.97/10.96 5194 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f354(C,D,B,A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),C),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C))) # label(fact_min__max_Ofold__sup__le__sup) # label(axiom). [clausify(3464)].
% 10.97/10.96 5195 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),f354(C,D,B,A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Orderings_Oord__class_Omax(A)),C),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C))) # label(fact_min__max_Ofold__sup__le__sup) # label(axiom). [clausify(3464)].
% 10.97/10.96 5196 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f355(C,B,A)),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olinorder__class_OMax(A,B) = C # label(fact_Max__eqI) # label(axiom). [clausify(3465)].
% 10.97/10.96 5197 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),f355(C,B,A)),C)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Big__Operators_Olinorder__class_OMax(A,B) = C # label(fact_Max__eqI) # label(axiom). [clausify(3465)].
% 10.97/10.96 5198 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_List_Olinorder__class_Osorted__list__of__set(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))) = c_List_Oremove1(A,C,c_List_Olinorder__class_Osorted__list__of__set(A,B)) # label(fact_sorted__list__of__set__remove) # label(axiom). [clausify(3868)].
% 10.97/10.96 5199 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted__list__of__set(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))) = c_List_Olist_ONil(A) # label(fact_sorted__list__of__set__empty) # label(axiom). [clausify(3870)].
% 10.97/10.96 5200 -class_Orderings_Olinorder(A) | c_Big__Operators_Olinorder__class_OMin(A,hAPP(c_List_Oset(A),hAPP(hAPP(c_List_Olist_OCons(A),B),C))) = hAPP(c_List_Ofoldl(A,A,c_Orderings_Oord__class_Omin(A),B),C) # label(fact_Min__fin__set__fold) # label(axiom). [clausify(4007)].
% 10.97/10.96 5201 -class_Orderings_Olinorder(A) | c_Big__Operators_Olinorder__class_OMax(A,hAPP(c_List_Oset(A),hAPP(hAPP(c_List_Olist_OCons(A),B),C))) = hAPP(c_List_Ofoldl(A,A,c_Orderings_Oord__class_Omax(A),B),C) # label(fact_Max__fin__set__fold) # label(axiom). [clausify(4008)].
% 10.97/10.96 5202 -class_Orderings_Olinorder(A) | c_Big__Operators_Olattice_OInf__fin(A,c_Orderings_Oord__class_Omin(A),hAPP(c_List_Oset(A),hAPP(hAPP(c_List_Olist_OCons(A),B),C))) = hAPP(c_List_Ofoldl(A,A,c_Orderings_Oord__class_Omin(A),B),C) # label(fact_min__max_OInf__fin__set__fold) # label(axiom). [clausify(4009)].
% 10.97/10.96 5203 -class_Orderings_Olinorder(A) | c_Big__Operators_Olattice_OSup__fin(A,c_Orderings_Oord__class_Omax(A),hAPP(c_List_Oset(A),hAPP(hAPP(c_List_Olist_OCons(A),B),C))) = hAPP(c_List_Ofoldl(A,A,c_Orderings_Oord__class_Omax(A),B),C) # label(fact_min__max_OSup__fin__set__fold) # label(axiom). [clausify(4010)].
% 10.97/10.96 5204 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_List_Olinorder__class_Osorted__list__of__set(A,hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),C),c_List_Olinorder__class_Osorted__list__of__set(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) # label(fact_sorted__list__of__set__insert) # label(axiom). [clausify(4014)].
% 10.97/10.96 5205 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),c_List_Olist_ONil(B)) = hAPP(hAPP(c_List_Olist_OCons(B),D),c_List_Olist_ONil(B)) # label(fact_insort__key_Osimps_I1_J) # label(axiom). [clausify(4016)].
% 10.97/10.96 5206 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(B,C)),hAPP(B,D))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),C),hAPP(hAPP(c_List_Olist_OCons(E),D),F)) = hAPP(hAPP(c_List_Olist_OCons(E),C),hAPP(hAPP(c_List_Olist_OCons(E),D),F)) # label(fact_insort__key_Osimps_I2_J) # label(axiom). [clausify(4017)].
% 10.97/10.96 5207 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(B,C)),hAPP(B,D))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),C),hAPP(hAPP(c_List_Olist_OCons(E),D),F)) = hAPP(hAPP(c_List_Olist_OCons(E),D),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),C),F)) # label(fact_insort__key_Osimps_I2_J) # label(axiom). [clausify(4017)].
% 10.97/10.96 5208 -class_Orderings_Olinorder(A) | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),E)) # label(fact_length__insort) # label(axiom). [clausify(4018)].
% 10.97/10.96 5209 -class_Orderings_Olinorder(A) | hAPP(B,C) = hAPP(B,D) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),D),F)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),D),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),C),F)) # label(fact_insort__key__left__comm) # label(axiom). [clausify(4019)].
% 10.97/10.96 5210 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),C),D)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),D)) # label(fact_insort__left__comm) # label(axiom). [clausify(4020)].
% 10.97/10.96 5211 -class_Orderings_Olinorder(A) | c_Finite__Set_Ofun__left__comm(A,tc_List_Olist(A),c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A))) # label(fact_fun__left__comm__insort) # label(axiom). [clausify(4021)].
% 10.97/10.96 5212 -class_Orderings_Olinorder(A) | hAPP(c_List_Oset(B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E)) = hAPP(hAPP(c_Set_Oinsert(B),D),hAPP(c_List_Oset(B),E)) # label(fact_set__insort) # label(axiom). [clausify(4022)].
% 10.97/10.96 5213 -class_Orderings_Olinorder(A) | c_List_Oremove1(A,B,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),C)) = C # label(fact_remove1__insort) # label(axiom). [clausify(4023)].
% 10.97/10.96 5214 -class_Orderings_Olinorder(A) | c_List_Olist_ONil(B) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E) # label(fact_insort__not__Nil) # label(axiom). [clausify(4024)].
% 10.97/10.96 5215 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_List_Odistinct(B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E))) | -hBOOL(hAPP(hAPP(c_member(B),D),hAPP(c_List_Oset(B),E))) # label(fact_distinct__insort) # label(axiom). [clausify(4025)].
% 10.97/10.96 5216 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_List_Odistinct(B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E))) | hBOOL(hAPP(c_List_Odistinct(B),E)) # label(fact_distinct__insort) # label(axiom). [clausify(4025)].
% 10.97/10.96 5217 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_List_Odistinct(B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E))) | hBOOL(hAPP(hAPP(c_member(B),D),hAPP(c_List_Oset(B),E))) | -hBOOL(hAPP(c_List_Odistinct(B),E)) # label(fact_distinct__insort) # label(axiom). [clausify(4025)].
% 10.97/10.96 5218 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_member(A),hAPP(B,C)),hAPP(c_Set_Oimage(D,A,B),hAPP(c_List_Oset(D),E)))) | c_List_Olinorder__class_Oinsort__insert__key(D,A,B,C,E) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,A,B),C),E) # label(fact_insort__insert__insort__key) # label(axiom). [clausify(4026)].
% 10.97/10.96 5219 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | c_List_Olinorder__class_Oinsort__insert__key(A,A,c_COMBI(A),B,C) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),C) # label(fact_insort__insert__insort) # label(axiom). [clausify(4027)].
% 10.97/10.96 5220 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_List_Odistinct(B),C)) | hBOOL(hAPP(c_List_Odistinct(B),c_List_Olinorder__class_Oinsort__insert__key(B,A,D,E,C))) # label(fact_distinct__insort__insert) # label(axiom). [clausify(4028)].
% 10.97/10.96 5221 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | c_List_Olinorder__class_Oinsort__insert__key(A,A,c_COMBI(A),B,C) = C # label(fact_insort__insert__triv) # label(axiom). [clausify(4029)].
% 10.97/10.96 5222 -class_Orderings_Olinorder(A) | hAPP(c_List_Oset(A),c_List_Olinorder__class_Oinsort__insert__key(A,A,c_COMBI(A),B,C)) = hAPP(hAPP(c_Set_Oinsert(A),B),hAPP(c_List_Oset(A),C)) # label(fact_set__insort__insert) # label(axiom). [clausify(4030)].
% 10.97/10.96 5223 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_member(A),hAPP(B,C)),hAPP(c_Set_Oimage(D,A,B),hAPP(c_List_Oset(D),E)))) | c_List_Olinorder__class_Oinsort__insert__key(D,A,B,C,E) = E # label(fact_insort__insert__key__triv) # label(axiom). [clausify(4031)].
% 10.97/10.96 5224 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osort__key(A,A,c_COMBI(A),c_List_Oremdups(A,B)) = c_List_Olinorder__class_Osorted__list__of__set(A,hAPP(c_List_Oset(A),B)) # label(fact_sorted__list__of__set__sort__remdups) # label(axiom). [clausify(4218)].
% 10.97/10.96 5225 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osort__key(B,A,C,c_List_Olist_ONil(B)) = c_List_Olist_ONil(B) # label(fact_sort__key__simps_I1_J) # label(axiom). [clausify(4219)].
% 10.97/10.96 5226 -class_Orderings_Olinorder(A) | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),c_List_Olinorder__class_Osort__key(B,A,C,D)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),D) # label(fact_length__sort) # label(axiom). [clausify(4222)].
% 10.97/10.96 5227 -class_Orderings_Olinorder(A) | hAPP(c_List_Oset(B),c_List_Olinorder__class_Osort__key(B,A,C,D)) = hAPP(c_List_Oset(B),D) # label(fact_set__sort) # label(axiom). [clausify(4223)].
% 10.97/10.96 5228 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_List_Odistinct(B),c_List_Olinorder__class_Osort__key(B,A,C,D))) | hBOOL(hAPP(c_List_Odistinct(B),D)) # label(fact_distinct__sort) # label(axiom). [clausify(4224)].
% 10.97/10.96 5229 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_List_Odistinct(B),c_List_Olinorder__class_Osort__key(B,A,C,D))) | -hBOOL(hAPP(c_List_Odistinct(B),D)) # label(fact_distinct__sort) # label(axiom). [clausify(4224)].
% 10.97/10.96 5230 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osort__key(B,A,C,hAPP(hAPP(c_List_Olist_OCons(B),D),E)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),c_List_Olinorder__class_Osort__key(B,A,C,E)) # label(fact_sort__key__simps_I2_J) # label(axiom). [clausify(4232)].
% 10.97/10.96 5231 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osort__key(A,A,c_COMBI(A),B) = hAPP(c_List_Ofoldl(tc_List_Olist(A),A,hAPP(c_COMBC(A,tc_List_Olist(A),tc_List_Olist(A)),c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A))),c_List_Olist_ONil(A)),B) # label(fact_sort__foldl__insort) # label(axiom). [clausify(4234)].
% 10.97/10.96 5232 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osort__key(B,A,C,hAPP(c_List_Ofilter(B,D),E)) = hAPP(c_List_Ofilter(B,D),c_List_Olinorder__class_Osort__key(B,A,C,E)) # label(fact_filter__sort) # label(axiom). [clausify(4242)].
% 10.97/10.96 5233 -class_Orderings_Olinorder(A) | hBOOL(hAPP(B,C)) | hAPP(c_List_Ofilter(D,B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,A,E),C),F)) = hAPP(c_List_Ofilter(D,B),F) # label(fact_filter__insort__triv) # label(axiom). [clausify(4251)].
% 10.97/10.96 5234 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_member(B),C),hAPP(c_List_Oset(B),D))) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),E),D)) | hAPP(c_List_Ohd(B),hAPP(c_List_Ofilter(B,hAPP(hAPP(c_COMBB(A,tc_HOL_Obool,B),hAPP(c_fequal,hAPP(E,C))),E)),D)) != C | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,E),C),c_List_Oremove1(B,C,D)) = D # label(fact_insort__key__remove1) # label(axiom). [clausify(4324)].
% 10.97/10.96 5235 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,c_List_Olist_ONil(A)) # label(fact_sorted_ONil) # label(axiom). [clausify(4325)].
% 10.97/10.96 5236 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),c_List_Olist_ONil(A))) # label(fact_sorted__single) # label(axiom). [clausify(4326)].
% 10.97/10.96 5237 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,c_List_Olinorder__class_Osort__key(A,A,c_COMBI(A),B)) # label(fact_sorted__sort) # label(axiom). [clausify(4328)].
% 10.97/10.96 5238 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,c_List_Olinorder__class_Oinsort__insert__key(A,A,c_COMBI(A),C,B)) # label(fact_sorted__insort__insert) # label(axiom). [clausify(4329)].
% 10.97/10.96 5239 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Odrop(A),C),B)) # label(fact_sorted__drop) # label(axiom). [clausify(4330)].
% 10.97/10.96 5240 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Otake(A),C),B)) # label(fact_sorted__take) # label(axiom). [clausify(4332)].
% 10.97/10.96 5241 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,c_List_Oremove1(A,C,B)) # label(fact_sorted__remove1) # label(axiom). [clausify(4333)].
% 10.97/10.96 5242 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,hAPP(c_List_Otl(A),B)) # label(fact_sorted__tl) # label(axiom). [clausify(4334)].
% 10.97/10.96 5243 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),C)) | c_List_Olinorder__class_Osorted(A,C) # label(fact_sorted__insort) # label(axiom). [clausify(4335)].
% 10.97/10.96 5244 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),C)) | -c_List_Olinorder__class_Osorted(A,C) # label(fact_sorted__insort) # label(axiom). [clausify(4335)].
% 10.97/10.96 5245 -class_Orderings_Olinorder(A) | c_List_Olist_ONil(A) = B | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,c_List_Obutlast(A,B)) # label(fact_sorted__butlast) # label(axiom). [clausify(4336)].
% 10.97/10.96 5246 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,c_List_Olist_ONil(A)) # label(fact_sorted_Oequations_I1_J) # label(axiom). [clausify(4337)].
% 10.97/10.96 5247 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_sorted__many__eq) # label(axiom). [clausify(4338)].
% 10.97/10.96 5248 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),D))) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),C),D)) # label(fact_sorted__many__eq) # label(axiom). [clausify(4338)].
% 10.97/10.96 5249 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),C),D)) # label(fact_sorted__many__eq) # label(axiom). [clausify(4338)].
% 10.97/10.96 5250 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),C),D)) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),D))) # label(fact_sorted__many) # label(axiom). [clausify(4339)].
% 10.97/10.96 5251 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,c_List_Oremdups(A,B)) # label(fact_sorted__remdups) # label(axiom). [clausify(4340)].
% 10.97/10.96 5252 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | -hBOOL(hAPP(c_List_Odistinct(A),B)) | -c_List_Olinorder__class_Osorted(A,C) | -hBOOL(hAPP(c_List_Odistinct(A),C)) | hAPP(c_List_Oset(A),B) != hAPP(c_List_Oset(A),C) | B = C # label(fact_sorted__distinct__set__unique) # label(axiom). [clausify(4341)].
% 10.97/10.96 5253 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),c_List_Olinorder__class_Osort__key(B,A,C,D))) # label(fact_sorted__sort__key) # label(axiom). [clausify(4342)].
% 10.97/10.96 5254 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),D)) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),c_List_Olinorder__class_Oinsort__insert__key(B,A,C,E,D))) # label(fact_sorted__insort__insert__key) # label(axiom). [clausify(4343)].
% 10.97/10.96 5255 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),D)) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),c_List_Oremove1(B,E,D))) # label(fact_sorted__map__remove1) # label(axiom). [clausify(4344)].
% 10.97/10.96 5256 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E))) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),E)) # label(fact_sorted__insort__key) # label(axiom). [clausify(4345)].
% 10.97/10.96 5257 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E))) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),E)) # label(fact_sorted__insort__key) # label(axiom). [clausify(4345)].
% 10.97/10.96 5258 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),hAPP(c_List_Ofilter(B,hAPP(hAPP(c_COMBC(B,A,tc_HOL_Obool),hAPP(hAPP(c_COMBB(A,tc_fun(A,tc_HOL_Obool),B),c_fequal),C)),hAPP(D,E))),E))) # label(fact_sorted__map__same) # label(axiom). [clausify(4346)].
% 10.97/10.96 5259 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),D)) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),hAPP(c_List_Ofilter(B,E),D))) # label(fact_sorted__filter) # label(axiom). [clausify(4347)].
% 10.97/10.96 5260 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),hAPP(B,C))),C)) # label(fact_sorted__same) # label(axiom). [clausify(4348)].
% 10.97/10.96 5261 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) | c_List_Olinorder__class_Osorted(A,C) # label(fact_sorted__Cons) # label(axiom). [clausify(4349)].
% 10.97/10.96 5262 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) | -hBOOL(hAPP(hAPP(c_member(A),D),hAPP(c_List_Oset(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_sorted__Cons) # label(axiom). [clausify(4349)].
% 10.97/10.96 5263 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) | -c_List_Olinorder__class_Osorted(A,C) | hBOOL(hAPP(hAPP(c_member(A),f448(C,B,A)),hAPP(c_List_Oset(A),C))) # label(fact_sorted__Cons) # label(axiom). [clausify(4349)].
% 10.97/10.96 5264 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) | -c_List_Olinorder__class_Osorted(A,C) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),f448(C,B,A))) # label(fact_sorted__Cons) # label(axiom). [clausify(4349)].
% 10.97/10.96 5265 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Oappend(A),B),C)) | c_List_Olinorder__class_Osorted(A,B) # label(fact_sorted__append) # label(axiom). [clausify(4350)].
% 10.97/10.96 5266 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Oappend(A),B),C)) | c_List_Olinorder__class_Osorted(A,C) # label(fact_sorted__append) # label(axiom). [clausify(4350)].
% 10.97/10.96 5267 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Oappend(A),B),C)) | -hBOOL(hAPP(hAPP(c_member(A),D),hAPP(c_List_Oset(A),B))) | -hBOOL(hAPP(hAPP(c_member(A),E),hAPP(c_List_Oset(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),E)) # label(fact_sorted__append) # label(axiom). [clausify(4350)].
% 10.97/10.96 5268 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Oappend(A),B),C)) | -c_List_Olinorder__class_Osorted(A,B) | -c_List_Olinorder__class_Osorted(A,C) | hBOOL(hAPP(hAPP(c_member(A),f449(C,B,A)),hAPP(c_List_Oset(A),B))) # label(fact_sorted__append) # label(axiom). [clausify(4350)].
% 10.97/10.96 5269 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Oappend(A),B),C)) | -c_List_Olinorder__class_Osorted(A,B) | -c_List_Olinorder__class_Osorted(A,C) | hBOOL(hAPP(hAPP(c_member(A),f450(C,B,A)),hAPP(c_List_Oset(A),C))) # label(fact_sorted__append) # label(axiom). [clausify(4350)].
% 10.97/10.96 5270 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Oappend(A),B),C)) | -c_List_Olinorder__class_Osorted(A,B) | -c_List_Olinorder__class_Osorted(A,C) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),f449(C,B,A)),f450(C,B,A))) # label(fact_sorted__append) # label(axiom). [clausify(4350)].
% 10.97/10.96 5271 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),D)) | -hBOOL(hAPP(E,F)) | hAPP(c_List_Ofilter(B,E),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),F),D)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),F),hAPP(c_List_Ofilter(B,E),D)) # label(fact_filter__insort) # label(axiom). [clausify(4351)].
% 10.97/10.96 5272 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) | -hBOOL(hAPP(hAPP(c_member(A),D),hAPP(c_List_Oset(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_sorted_Oequations_I2_J) # label(axiom). [clausify(4352)].
% 10.97/10.96 5273 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) | c_List_Olinorder__class_Osorted(A,C) # label(fact_sorted_Oequations_I2_J) # label(axiom). [clausify(4352)].
% 10.97/10.96 5274 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) | hBOOL(hAPP(hAPP(c_member(A),f451(C,B,A)),hAPP(c_List_Oset(A),C))) | -c_List_Olinorder__class_Osorted(A,C) # label(fact_sorted_Oequations_I2_J) # label(axiom). [clausify(4352)].
% 10.97/10.96 5275 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),f451(C,B,A))) | -c_List_Olinorder__class_Osorted(A,C) # label(fact_sorted_Oequations_I2_J) # label(axiom). [clausify(4352)].
% 10.97/10.96 5276 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(c_List_Oset(A),c_List_Olinorder__class_Osorted__list__of__set(A,B)) = B # label(fact_sorted__list__of__set) # label(axiom). [clausify(4353)].
% 10.97/10.96 5277 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_List_Olinorder__class_Osorted(A,c_List_Olinorder__class_Osorted__list__of__set(A,B)) # label(fact_sorted__list__of__set) # label(axiom). [clausify(4353)].
% 10.97/10.96 5278 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Osorted__list__of__set(A,B))) # label(fact_sorted__list__of__set) # label(axiom). [clausify(4353)].
% 10.97/10.96 5279 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | -c_List_Olinorder__class_Osorted(A,C) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),c_List_Oremove1(A,B,C)) = C # label(fact_insort__remove1) # label(axiom). [clausify(4354)].
% 10.97/10.96 5280 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_List_Onth(A),B),C)),hAPP(hAPP(c_List_Onth(A),B),D))) # label(fact_sorted__nth__mono) # label(axiom). [clausify(4355)].
% 10.97/10.96 5281 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),D),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_List_Onth(A),B),D)),hAPP(hAPP(c_List_Onth(A),B),C))) # label(fact_sorted__equals__nth__mono) # label(axiom). [clausify(4356)].
% 10.97/10.96 5282 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,B) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f452(B,A)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B))) # label(fact_sorted__equals__nth__mono) # label(axiom). [clausify(4356)].
% 10.97/10.96 5283 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,B) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f453(B,A)),f452(B,A))) # label(fact_sorted__equals__nth__mono) # label(axiom). [clausify(4356)].
% 10.97/10.96 5284 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_List_Onth(A),B),f453(B,A))),hAPP(hAPP(c_List_Onth(A),B),f452(B,A)))) # label(fact_sorted__equals__nth__mono) # label(axiom). [clausify(4356)].
% 10.97/10.96 5285 -class_Orderings_Olinorder(A) | -c_Fun_Oinj__on(B,A,C,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,tc_HOL_Obool)),hAPP(c_List_Oset(B),D)),hAPP(c_List_Oset(B),E))) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),D)) | -hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Omap(B,A),C),D))) | -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Omap(B,A),C),E)) | -hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Omap(B,A),C),E))) | hAPP(c_List_Oset(B),D) != hAPP(c_List_Oset(B),E) | D = E # label(fact_map__sorted__distinct__set__unique) # label(axiom). [clausify(4357)].
% 10.97/10.96 5286 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(c_List_Orev(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_List_Onth(A),B),D)),hAPP(hAPP(c_List_Onth(A),B),C))) # label(fact_sorted__rev__nth__mono) # label(axiom). [clausify(4393)].
% 10.97/10.96 5287 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(c_List_Orev(A),B)) | c_List_Olist_ONil(A) != B | c_List_Ofoldr(A,A,c_Orderings_Oord__class_Omax(A),B,C) = C # label(fact_foldr__max__sorted) # label(axiom). [clausify(4394)].
% 10.97/10.96 5288 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(c_List_Orev(A),B)) | c_List_Olist_ONil(A) = B | c_List_Ofoldr(A,A,c_Orderings_Oord__class_Omax(A),B,C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_List_Onth(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),C) # label(fact_foldr__max__sorted) # label(axiom). [clausify(4394)].
% 10.97/10.96 5289 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,c_List_OtakeWhile(A,C,B)) # label(fact_sorted__takeWhile) # label(axiom). [clausify(4398)].
% 10.97/10.96 5290 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,hAPP(c_List_Orev(A),hAPP(hAPP(c_List_Omap(B,A),C),D))) | c_List_OtakeWhile(B,hAPP(hAPP(c_COMBB(A,tc_HOL_Obool,B),hAPP(c_Orderings_Oord__class_Oless(A),E)),C),D) = hAPP(c_List_Ofilter(B,hAPP(hAPP(c_COMBB(A,tc_HOL_Obool,B),hAPP(c_Orderings_Oord__class_Oless(A),E)),C)),D) # label(fact_filter__equals__takeWhile__sorted__rev) # label(axiom). [clausify(4415)].
% 10.97/10.96 5291 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olinorder__class_Osorted(A,c_List_OdropWhile(A,C,B)) # label(fact_sorted__dropWhile) # label(axiom). [clausify(4422)].
% 10.97/10.96 5292 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f457(B,A)),f458(B,A))) | c_List_Olinorder__class_Osorted(A,B) # label(fact_sorted__nth__monoI) # label(axiom). [clausify(4435)].
% 10.97/10.96 5293 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f458(B,A)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B))) | c_List_Olinorder__class_Osorted(A,B) # label(fact_sorted__nth__monoI) # label(axiom). [clausify(4435)].
% 10.97/10.96 5294 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_List_Onth(A),B),f457(B,A))),hAPP(hAPP(c_List_Onth(A),B),f458(B,A)))) | c_List_Olinorder__class_Osorted(A,B) # label(fact_sorted__nth__monoI) # label(axiom). [clausify(4435)].
% 10.97/10.96 5295 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olist_ONil(A) = B | hAPP(hAPP(c_List_Olist_OCons(A),f463(B,A)),f462(B,A)) = B # label(fact_sorted_Osimps) # label(axiom). [clausify(4439)].
% 10.97/10.96 5296 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olist_ONil(A) = B | -hBOOL(hAPP(hAPP(c_member(A),C),hAPP(c_List_Oset(A),f462(B,A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),f463(B,A)),C)) # label(fact_sorted_Osimps) # label(axiom). [clausify(4439)].
% 10.97/10.96 5297 -class_Orderings_Olinorder(A) | -c_List_Olinorder__class_Osorted(A,B) | c_List_Olist_ONil(A) = B | c_List_Olinorder__class_Osorted(A,f462(B,A)) # label(fact_sorted_Osimps) # label(axiom). [clausify(4439)].
% 10.97/10.96 5298 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,B) | c_List_Olist_ONil(A) != B # label(fact_sorted_Osimps) # label(axiom). [clausify(4439)].
% 10.97/10.96 5299 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,B) | hAPP(hAPP(c_List_Olist_OCons(A),C),D) != B | hBOOL(hAPP(hAPP(c_member(A),f464(B,A,D,C)),hAPP(c_List_Oset(A),D))) | -c_List_Olinorder__class_Osorted(A,D) # label(fact_sorted_Osimps) # label(axiom). [clausify(4439)].
% 10.97/10.96 5300 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(A,B) | hAPP(hAPP(c_List_Olist_OCons(A),C),D) != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),f464(B,A,D,C))) | -c_List_Olinorder__class_Osorted(A,D) # label(fact_sorted_Osimps) # label(axiom). [clausify(4439)].
% 10.97/10.96 5301 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(c_List_Oset(A),f473(B,A)) = B # label(fact_finite__sorted__distinct__unique) # label(axiom). [clausify(4467)].
% 10.97/10.96 5302 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_List_Olinorder__class_Osorted(A,f473(B,A)) # label(fact_finite__sorted__distinct__unique) # label(axiom). [clausify(4467)].
% 10.97/10.96 5303 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(c_List_Odistinct(A),f473(B,A))) # label(fact_finite__sorted__distinct__unique) # label(axiom). [clausify(4467)].
% 10.97/10.96 5304 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(c_List_Oset(A),C) != B | -c_List_Olinorder__class_Osorted(A,C) | -hBOOL(hAPP(c_List_Odistinct(A),C)) | C = f473(B,A) # label(fact_finite__sorted__distinct__unique) # label(axiom). [clausify(4467)].
% 10.97/10.96 5305 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_member(B),f475(C,D,E,B,A)),hAPP(c_List_Oset(B),E))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,D),C),E) = hAPP(hAPP(c_List_Olist_OCons(B),C),E) # label(fact_insort__is__Cons) # label(axiom). [clausify(4469)].
% 10.97/10.96 5306 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(B,C)),hAPP(B,f475(C,B,D,E,A)))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),C),D) = hAPP(hAPP(c_List_Olist_OCons(E),C),D) # label(fact_insort__is__Cons) # label(axiom). [clausify(4469)].
% 10.97/10.96 5307 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_member(A),f485(B,C,A)),hAPP(c_List_Oset(A),C))) | -c_List_Olinorder__class_Osorted(A,C) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) # label(fact_sorted_OCons) # label(axiom). [clausify(4477)].
% 10.97/10.96 5308 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),f485(B,C,A))) | -c_List_Olinorder__class_Osorted(A,C) | c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)) # label(fact_sorted_OCons) # label(axiom). [clausify(4477)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),A)). [resolve(4907,a,4908,a)].
% 10.97/10.96 Derived: A = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(4907,a,4910,a)].
% 10.97/10.96 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(4907,a,4911,a)].
% 10.97/10.96 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(4907,a,4912,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(4907,a,4914,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),A)). [resolve(4907,a,4921,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),A)). [resolve(4907,a,4922,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | B = A. [resolve(4907,a,4928,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | B != A. [resolve(4907,a,4929,a)].
% 10.97/10.96 Derived: c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),B)),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A))). [resolve(4907,a,4933,a)].
% 10.97/10.96 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),A) = A. [resolve(4907,a,4934,a)].
% 10.97/10.96 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C)). [resolve(4907,a,4935,a)].
% 10.97/10.96 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),C)). [resolve(4907,a,4937,a)].
% 10.97/10.96 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B). [resolve(4907,a,4939,a)].
% 10.97/10.96 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),A). [resolve(4907,a,4941,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),C),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),C),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)). [resolve(4907,a,4944,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),A)). [resolve(4907,a,4945,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),B)). [resolve(4907,a,4946,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B) = A. [resolve(4907,a,4947,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B) != A. [resolve(4907,a,4948,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(4907,a,4949,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(4907,a,4950,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(4907,a,4951,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),C)),B)). [resolve(4907,a,4952,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),C),A)),B)). [resolve(4907,a,4953,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),A) = A. [resolve(4907,a,4955,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),D))). [resolve(4907,a,4958,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)). [resolve(4907,a,4961,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(4907,a,4964,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(4907,a,4965,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(4907,a,4966,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(4907,a,4967,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(4907,a,4968,a)].
% 10.97/10.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(4907,a,4969,a)].
% 10.97/10.96 Derived: -class_Lattices_Osemilattice__inf(tc_Int_Oint) | c_Orderings_Oord__class_Omin(tc_Int_Oint) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Int_Oint). [resolve(4907,a,4972,b)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),C),A)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C))). [resolve(4907,a,4973,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A)),B)). [resolve(4907,a,4974,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f45(B,A,tc_Int_Oint)),A)). [resolve(4907,a,4975,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),f45(B,A,tc_Int_Oint)),B)). [resolve(4907,a,4976,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),B)). [resolve(4907,a,4977,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),C),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)). [resolve(4907,a,4978,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f46(B,A,tc_Int_Oint)),A)). [resolve(4907,a,4979,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),f46(B,A,tc_Int_Oint))). [resolve(4907,a,4980,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f47(B,A,tc_Int_Oint)),A)). [resolve(4907,a,4981,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),f47(B,A,tc_Int_Oint)),B)). [resolve(4907,a,4982,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(4907,a,4983,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),C),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(4907,a,4984,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f48(B,A,tc_Int_Oint)),A)). [resolve(4907,a,4985,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),f48(B,A,tc_Int_Oint))). [resolve(4907,a,4986,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A) = B. [resolve(4907,a,4987,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,4988,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A) = B. [resolve(4907,a,4989,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,4990,a)].
% 10.97/10.96 Derived: c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) = A. [resolve(4907,a,4991,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)). [resolve(4907,a,4992,a)].
% 10.97/10.96 Derived: c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) = A. [resolve(4907,a,4993,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)),B)). [resolve(4907,a,4994,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)),A)). [resolve(4907,a,4995,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)). [resolve(4907,a,4996,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A) = hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A). [resolve(4907,a,4997,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A) = hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),A). [resolve(4907,a,4998,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)). [resolve(4907,a,4999,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),B)),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)). [resolve(4907,a,5000,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),B)). [resolve(4907,a,5001,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,B)),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A))). [resolve(4907,a,5002,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),B),A). [resolve(4907,a,5003,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)). [resolve(4907,a,5004,a)].
% 10.97/10.96 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,B)),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)). [resolve(4907,a,5005,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,B)). [resolve(4907,a,5006,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),B),A). [resolve(4907,a,5007,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = B. [resolve(4907,a,5009,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,5010,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B))),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),B)). [resolve(4907,a,5011,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = B. [resolve(4907,a,5015,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,5016,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B))),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,B)). [resolve(4907,a,5017,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),f53(A,tc_Int_Oint)),f54(A,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),f53(A,tc_Int_Oint)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),f54(A,tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)),A)). [resolve(4907,a,5020,a)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Complete__Lattice_OSup__class_OSup(tc_Int_Oint,B))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f64(B,A,tc_Int_Oint)),B)). [resolve(4907,a,5022,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Complete__Lattice_OSup__class_OSup(tc_Int_Oint,B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),f64(B,A,tc_Int_Oint))). [resolve(4907,a,5023,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Complete__Lattice_OSup__class_OSup(tc_Int_Oint,B))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(4907,a,5024,b)].
% 10.97/10.97 Derived: c_Finite__Set_Ofun__left__comm__idem(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)). [resolve(4907,a,5025,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f100(B,C,A,tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),C),B)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),B),A))). [resolve(4907,a,5026,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),f100(C,B,A,tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint)),C),A))). [resolve(4907,a,5027,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f102(B,A,tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A) = B. [resolve(4907,a,5028,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),f102(B,A,tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A) = B. [resolve(4907,a,5029,a)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Complete__Lattice_OInf__class_OInf(tc_Int_Oint,A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f153(B,A,tc_Int_Oint)),A)). [resolve(4907,a,5032,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Complete__Lattice_OInf__class_OInf(tc_Int_Oint,A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),f153(B,A,tc_Int_Oint)),B)). [resolve(4907,a,5033,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Complete__Lattice_OInf__class_OInf(tc_Int_Oint,A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(4907,a,5034,b)].
% 10.97/10.97 Derived: c_Orderings_Oord_Omax(tc_Int_Oint,hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))) = c_Orderings_Oord__class_Omin(tc_Int_Oint). [resolve(4907,a,5035,a)].
% 10.97/10.97 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A) != hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),B) | A = B. [resolve(4907,a,5036,a)].
% 10.97/10.97 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),B) | A != B. [resolve(4907,a,5037,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(4907,a,5038,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(4907,a,5039,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(4907,a,5040,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(4907,a,5041,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(4907,a,5042,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(4907,a,5043,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(4907,a,5044,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(4907,a,5045,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)). [resolve(4907,a,5046,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),D))). [resolve(4907,a,5047,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)),B)). [resolve(4907,a,5048,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),A) = B. [resolve(4907,a,5050,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B) = B. [resolve(4907,a,5051,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B) != B. [resolve(4907,a,5058,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),A))). [resolve(4907,a,5059,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B))). [resolve(4907,a,5060,a)].
% 10.97/10.97 Derived: c_Finite__Set_Ofun__left__comm__idem(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)). [resolve(4907,a,5061,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C))). [resolve(4907,a,5062,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),C),B))). [resolve(4907,a,5063,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(4907,a,5064,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(4907,a,5067,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(4907,a,5068,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(4907,a,5069,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),A) = A. [resolve(4907,a,5070,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),A). [resolve(4907,a,5071,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B). [resolve(4907,a,5073,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)). [resolve(4907,a,5075,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C)). [resolve(4907,a,5077,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)),B). [resolve(4907,a,5080,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C)). [resolve(4907,a,5081,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C)). [resolve(4907,a,5082,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)). [resolve(4907,a,5083,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)) = A. [resolve(4907,a,5084,a)].
% 10.97/10.97 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)) = A. [resolve(4907,a,5085,a)].
% 10.97/10.97 Derived: -class_Lattices_Osemilattice__sup(tc_Int_Oint) | c_Orderings_Oord__class_Omax(tc_Int_Oint) = c_Lattices_Osemilattice__sup__class_Osup(tc_Int_Oint). [resolve(4907,a,5086,b)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C))),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)))). [resolve(4907,a,5087,a)].
% 10.97/10.97 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),C))),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C)))). [resolve(4907,a,5088,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),C),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),C),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)). [resolve(4907,a,5089,a)].
% 10.97/10.97 Derived: c_Orderings_Oord__class_Omax(tc_Int_Oint) = c_Orderings_Oord_Omin(tc_Int_Oint,hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))). [resolve(4907,a,5090,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),C)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),C),A))). [resolve(4907,a,5091,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)) = B. [resolve(4907,a,5092,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A) = B. [resolve(4907,a,5093,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,5094,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A))). [resolve(4907,a,5095,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A) = B. [resolve(4907,a,5096,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,5097,a)].
% 10.97/10.97 Derived: c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) = A. [resolve(4907,a,5098,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)). [resolve(4907,a,5099,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A))). [resolve(4907,a,5100,a)].
% 10.97/10.97 Derived: c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) = A. [resolve(4907,a,5101,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)),A)). [resolve(4907,a,5102,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)). [resolve(4907,a,5103,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A) = hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),A). [resolve(4907,a,5104,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A) = hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),A). [resolve(4907,a,5105,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)). [resolve(4907,a,5106,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),B)),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)). [resolve(4907,a,5107,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)) = B. [resolve(4907,a,5108,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),B)). [resolve(4907,a,5109,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,B))). [resolve(4907,a,5110,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),B),A). [resolve(4907,a,5111,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)). [resolve(4907,a,5112,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,B)),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)). [resolve(4907,a,5113,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,B)). [resolve(4907,a,5114,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),B),A). [resolve(4907,a,5115,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = B. [resolve(4907,a,5117,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,5118,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B))),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),B)). [resolve(4907,a,5120,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = B. [resolve(4907,a,5123,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,5124,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B))),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,B)). [resolve(4907,a,5126,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),f184(A,tc_Int_Oint)),f185(A,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),f184(A,tc_Int_Oint)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),f185(A,tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)),A)). [resolve(4907,a,5128,a)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Int_Oint),C),D))) | hBOOL(hAPP(hAPP(c_member(B),f199(D,C,B,A,tc_Int_Oint)),C)). [resolve(4907,a,5130,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Int_Oint),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(D,f199(D,C,B,A,tc_Int_Oint)))). [resolve(4907,a,5131,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Int_Oint),C),D))) | -hBOOL(hAPP(hAPP(c_member(B),E),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(D,E))). [resolve(4907,a,5132,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Int_Oint),B),C)),D)) | hBOOL(hAPP(hAPP(c_member(A),f200(D,C,B,A,tc_Int_Oint)),B)). [resolve(4907,a,5133,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Int_Oint),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(C,f200(D,C,B,A,tc_Int_Oint))),D)). [resolve(4907,a,5134,b)].
% 10.97/10.97 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Int_Oint),B),C)),D)) | -hBOOL(hAPP(hAPP(c_member(A),E),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(C,E)),D)). [resolve(4907,a,5135,b)].
% 10.97/10.97 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,C)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,B,D)). [resolve(4907,a,5136,a)].
% 10.97/10.97 Derived: c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,C)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,B,D)). [resolve(4907,a,5137,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,B,C)). [resolve(4907,a,5138,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))). [resolve(4907,a,5139,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),A)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B)). [resolve(4907,a,5140,a)].
% 10.97/10.97 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),A) != hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),B) | A = B. [resolve(4907,a,5141,a)].
% 10.97/10.97 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),A) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),B) | A != B. [resolve(4907,a,5142,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,B,C)). [resolve(4907,a,5143,a)].
% 10.97/10.97 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,B,C)). [resolve(4907,a,5144,a)].
% 10.97/10.97 Derived: c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,C)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,B,D)). [resolve(4907,a,5145,a)].
% 10.97/10.97 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,C)). [resolve(4907,a,5146,a)].
% 10.97/10.97 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),C)). [resolve(4907,a,5147,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,B,C)). [resolve(4907,a,5148,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))). [resolve(4907,a,5149,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B)). [resolve(4907,a,5150,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),A)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B)). [resolve(4907,a,5151,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B)). [resolve(4907,a,5152,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C),D) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B) | C = A. [resolve(4907,a,5153,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C),D) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B) | B = D. [resolve(4907,a,5154,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C),D) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B) | C != A | B != D. [resolve(4907,a,5155,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),A)). [resolve(4907,a,5158,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),D)). [resolve(4907,a,5159,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,B),C)). [resolve(4907,a,5160,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,B),C) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B)). [resolve(4907,a,5161,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,B,C)). [resolve(4907,a,5162,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,B),D)). [resolve(4907,a,5163,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B)). [resolve(4907,a,5164,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,B),C)). [resolve(4907,a,5165,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))). [resolve(4907,a,5166,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B)). [resolve(4907,a,5167,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,B,C)). [resolve(4907,a,5168,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A) != hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),B) | A = B. [resolve(4907,a,5169,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),B) | A != B. [resolve(4907,a,5170,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A)). [resolve(4907,a,5171,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)). [resolve(4907,a,5172,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,A),B)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),B)). [resolve(4907,a,5173,a)].
% 10.97/10.98 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,C)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),B)). [resolve(4907,a,5174,a)].
% 10.97/10.98 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,B,C)). [resolve(4907,a,5175,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,A,B)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),B)). [resolve(4907,a,5176,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A) != hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),B) | A = B. [resolve(4907,a,5177,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),B) | A != B. [resolve(4907,a,5178,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),A)). [resolve(4907,a,5179,a)].
% 10.97/10.98 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),A)). [resolve(4907,a,5180,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),A)). [resolve(4907,a,5181,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A)). [resolve(4907,a,5182,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),B)). [resolve(4907,a,5183,a)].
% 10.97/10.98 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A)). [resolve(4907,a,5184,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,A,B)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),B)). [resolve(4907,a,5185,a)].
% 10.97/10.98 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(A,f269(B,A,tc_Int_Oint))),hAPP(A,f270(B,A,tc_Int_Oint))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),f269(B,A,tc_Int_Oint)),f270(B,A,tc_Int_Oint))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,A),B)) = hAPP(A,c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),B)). [resolve(4907,a,5186,a)].
% 10.97/10.98 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(A,f271(B,A,tc_Int_Oint))),hAPP(A,f272(B,A,tc_Int_Oint))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),f271(B,A,tc_Int_Oint)),f272(B,A,tc_Int_Oint))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,A),B)) = hAPP(A,c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),B)). [resolve(4907,a,5187,a)].
% 10.97/10.98 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(A,f273(B,A,tc_Int_Oint))),hAPP(A,f274(B,A,tc_Int_Oint))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),f273(B,A,tc_Int_Oint)),f274(B,A,tc_Int_Oint))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,A),B)) = hAPP(A,c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,B)). [resolve(4907,a,5188,a)].
% 10.97/10.98 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(A,f275(B,A,tc_Int_Oint))),hAPP(A,f276(B,A,tc_Int_Oint))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),f275(B,A,tc_Int_Oint)),f276(B,A,tc_Int_Oint))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,A),B)) = hAPP(A,c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,B)). [resolve(4907,a,5189,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool))),tc_fun(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Int_Oint,tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool))),tc_Int_Oint),hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Int_Oint),hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool))),tc_Int_Oint),c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint)),c_fequal))),c_Orderings_Oord__class_Omin(tc_Int_Oint)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Int_Oint)),A)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Int_Oint)),B))))))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),B)). [resolve(4907,a,5190,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Int_Oint)),A))))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),B),c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A)). [resolve(4907,a,5191,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Int_Oint)),A))))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),B),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)). [resolve(4907,a,5192,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool))),tc_fun(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Int_Oint,tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool))),tc_Int_Oint),hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Int_Oint),hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool))),tc_Int_Oint),c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint)),c_fequal))),c_Orderings_Oord__class_Omax(tc_Int_Oint)))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Int_Oint)),A)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Int_Oint)),B))))))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A)),c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),B)). [resolve(4907,a,5193,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f354(B,C,A,tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),B),A)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),C),B))). [resolve(4907,a,5194,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),f354(B,C,A,tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint)),B),A)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),C),B))). [resolve(4907,a,5195,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f355(B,A,tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A) = B. [resolve(4907,a,5196,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),f355(B,A,tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A) = B. [resolve(4907,a,5197,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))))) = c_List_Oremove1(tc_Int_Oint,B,c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,A)). [resolve(4907,a,5198,a)].
% 10.97/10.98 Derived: c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) = c_List_Olist_ONil(tc_Int_Oint). [resolve(4907,a,5199,a)].
% 10.97/10.98 Derived: c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(c_List_Oset(tc_Int_Oint),hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B))) = hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B). [resolve(4907,a,5200,a)].
% 10.97/10.98 Derived: c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(c_List_Oset(tc_Int_Oint),hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B))) = hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B). [resolve(4907,a,5201,a)].
% 10.97/10.98 Derived: c_Big__Operators_Olattice_OInf__fin(tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(c_List_Oset(tc_Int_Oint),hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B))) = hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B). [resolve(4907,a,5202,a)].
% 10.97/10.98 Derived: c_Big__Operators_Olattice_OSup__fin(tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(c_List_Oset(tc_Int_Oint),hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B))) = hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B). [resolve(4907,a,5203,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),B),c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))). [resolve(4907,a,5204,a)].
% 10.97/10.98 Derived: hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),c_List_Olist_ONil(A)) = hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)). [resolve(4907,a,5205,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(A,B)),hAPP(A,C))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Int_Oint,A),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)) = hAPP(hAPP(c_List_Olist_OCons(D),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)). [resolve(4907,a,5206,a)].
% 10.97/10.98 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(A,B)),hAPP(A,C))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Int_Oint,A),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)) = hAPP(hAPP(c_List_Olist_OCons(D),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Int_Oint,A),B),E)). [resolve(4907,a,5207,a)].
% 10.97/10.98 Derived: hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),D)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),D)). [resolve(4907,a,5208,a)].
% 10.97/10.98 Derived: hAPP(A,B) = hAPP(A,C) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Int_Oint,A),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Int_Oint,A),C),E)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Int_Oint,A),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Int_Oint,A),B),E)). [resolve(4907,a,5209,a)].
% 10.97/10.98 Derived: hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),B),C)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),A),C)). [resolve(4907,a,5210,a)].
% 10.97/10.98 Derived: c_Finite__Set_Ofun__left__comm(tc_Int_Oint,tc_List_Olist(tc_Int_Oint),c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint))). [resolve(4907,a,5211,a)].
% 10.97/10.98 Derived: hAPP(c_List_Oset(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),D)) = hAPP(hAPP(c_Set_Oinsert(A),C),hAPP(c_List_Oset(A),D)). [resolve(4907,a,5212,a)].
% 10.97/10.98 Derived: c_List_Oremove1(tc_Int_Oint,A,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),A),B)) = B. [resolve(4907,a,5213,a)].
% 10.97/10.98 Derived: c_List_Olist_ONil(A) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),D). [resolve(4907,a,5214,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),D))) | -hBOOL(hAPP(hAPP(c_member(A),C),hAPP(c_List_Oset(A),D))). [resolve(4907,a,5215,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),D))) | hBOOL(hAPP(c_List_Odistinct(A),D)). [resolve(4907,a,5216,a)].
% 10.97/10.98 Derived: hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),D))) | hBOOL(hAPP(hAPP(c_member(A),C),hAPP(c_List_Oset(A),D))) | -hBOOL(hAPP(c_List_Odistinct(A),D)). [resolve(4907,a,5217,a)].
% 10.97/10.98 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(A,B)),hAPP(c_Set_Oimage(C,tc_Int_Oint,A),hAPP(c_List_Oset(C),D)))) | c_List_Olinorder__class_Oinsort__insert__key(C,tc_Int_Oint,A,B,D) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(C,tc_Int_Oint,A),B),D). [resolve(4907,a,5218,a)].
% 10.97/10.98 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),hAPP(c_List_Oset(tc_Int_Oint),B))) | c_List_Olinorder__class_Oinsort__insert__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint),A,B) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),A),B). [resolve(4907,a,5219,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(c_List_Odistinct(A),B)) | hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Oinsort__insert__key(A,tc_Int_Oint,C,D,B))). [resolve(4907,a,5220,a)].
% 10.97/10.98 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),hAPP(c_List_Oset(tc_Int_Oint),B))) | c_List_Olinorder__class_Oinsort__insert__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint),A,B) = B. [resolve(4907,a,5221,a)].
% 10.97/10.98 Derived: hAPP(c_List_Oset(tc_Int_Oint),c_List_Olinorder__class_Oinsort__insert__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint),A,B)) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),hAPP(c_List_Oset(tc_Int_Oint),B)). [resolve(4907,a,5222,a)].
% 11.04/10.98 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(A,B)),hAPP(c_Set_Oimage(C,tc_Int_Oint,A),hAPP(c_List_Oset(C),D)))) | c_List_Olinorder__class_Oinsort__insert__key(C,tc_Int_Oint,A,B,D) = D. [resolve(4907,a,5223,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint),c_List_Oremdups(tc_Int_Oint,A)) = c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,hAPP(c_List_Oset(tc_Int_Oint),A)). [resolve(4907,a,5224,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,c_List_Olist_ONil(A)) = c_List_Olist_ONil(A). [resolve(4907,a,5225,a)].
% 11.04/10.98 Derived: hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,C)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C). [resolve(4907,a,5226,a)].
% 11.04/10.98 Derived: hAPP(c_List_Oset(A),c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,C)) = hAPP(c_List_Oset(A),C). [resolve(4907,a,5227,a)].
% 11.04/10.98 Derived: -hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,C))) | hBOOL(hAPP(c_List_Odistinct(A),C)). [resolve(4907,a,5228,a)].
% 11.04/10.98 Derived: hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,C))) | -hBOOL(hAPP(c_List_Odistinct(A),C)). [resolve(4907,a,5229,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,D)). [resolve(4907,a,5230,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint),A) = hAPP(c_List_Ofoldl(tc_List_Olist(tc_Int_Oint),tc_Int_Oint,hAPP(c_COMBC(tc_Int_Oint,tc_List_Olist(tc_Int_Oint),tc_List_Olist(tc_Int_Oint)),c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint))),c_List_Olist_ONil(tc_Int_Oint)),A). [resolve(4907,a,5231,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,hAPP(c_List_Ofilter(A,C),D)) = hAPP(c_List_Ofilter(A,C),c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,D)). [resolve(4907,a,5232,a)].
% 11.04/10.98 Derived: hBOOL(hAPP(A,B)) | hAPP(c_List_Ofilter(C,A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(C,tc_Int_Oint,D),B),E)) = hAPP(c_List_Ofilter(C,A),E). [resolve(4907,a,5233,a)].
% 11.04/10.98 Derived: -hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),D),C)) | hAPP(c_List_Ohd(A),hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,A),hAPP(c_fequal,hAPP(D,B))),D)),C)) != B | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,D),B),c_List_Oremove1(A,B,C)) = C. [resolve(4907,a,5234,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Olist_ONil(tc_Int_Oint)). [resolve(4907,a,5235,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),c_List_Olist_ONil(tc_Int_Oint))). [resolve(4907,a,5236,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Olinorder__class_Osort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint),A)). [resolve(4907,a,5237,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Olinorder__class_Oinsort__insert__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint),B,A)). [resolve(4907,a,5238,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Odrop(tc_Int_Oint),B),A)). [resolve(4907,a,5239,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Otake(tc_Int_Oint),B),A)). [resolve(4907,a,5240,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oremove1(tc_Int_Oint,B,A)). [resolve(4907,a,5241,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(c_List_Otl(tc_Int_Oint),A)). [resolve(4907,a,5242,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),A),B)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,B). [resolve(4907,a,5243,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),A),B)) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B). [resolve(4907,a,5244,a)].
% 11.04/10.98 Derived: c_List_Olist_ONil(tc_Int_Oint) = A | -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Obutlast(tc_Int_Oint,A)). [resolve(4907,a,5245,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(4907,a,5247,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),B),C))) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),B),C)). [resolve(4907,a,5248,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),B),C)). [resolve(4907,a,5249,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oremdups(tc_Int_Oint,A)). [resolve(4907,a,5251,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | -hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),A)) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | -hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),B)) | hAPP(c_List_Oset(tc_Int_Oint),A) != hAPP(c_List_Oset(tc_Int_Oint),B) | A = B. [resolve(4907,a,5252,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),c_List_Olinorder__class_Osort__key(A,tc_Int_Oint,B,C))). [resolve(4907,a,5253,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),C)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),c_List_Olinorder__class_Oinsort__insert__key(A,tc_Int_Oint,B,D,C))). [resolve(4907,a,5254,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),C)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),c_List_Oremove1(A,D,C))). [resolve(4907,a,5255,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),D))) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D)). [resolve(4907,a,5256,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),C),D))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D)). [resolve(4907,a,5257,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),A),c_fequal),B)),hAPP(C,D))),D))). [resolve(4907,a,5258,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),C)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),hAPP(c_List_Ofilter(A,D),C))). [resolve(4907,a,5259,a)].
% 11.04/10.98 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(c_List_Ofilter(tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),hAPP(A,B))),B)). [resolve(4907,a,5260,a)].
% 11.04/10.98 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,B). [resolve(4907,a,5261,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),C),hAPP(c_List_Oset(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(4907,a,5262,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f448(B,A,tc_Int_Oint)),hAPP(c_List_Oset(tc_Int_Oint),B))). [resolve(4907,a,5263,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),f448(B,A,tc_Int_Oint))). [resolve(4907,a,5264,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Oappend(tc_Int_Oint),A),B)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,A). [resolve(4907,a,5265,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Oappend(tc_Int_Oint),A),B)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,B). [resolve(4907,a,5266,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Oappend(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),C),hAPP(c_List_Oset(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),D),hAPP(c_List_Oset(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),D)). [resolve(4907,a,5267,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Oappend(tc_Int_Oint),A),B)) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f449(B,A,tc_Int_Oint)),hAPP(c_List_Oset(tc_Int_Oint),A))). [resolve(4907,a,5268,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Oappend(tc_Int_Oint),A),B)) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f450(B,A,tc_Int_Oint)),hAPP(c_List_Oset(tc_Int_Oint),B))). [resolve(4907,a,5269,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Oappend(tc_Int_Oint),A),B)) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),f449(B,A,tc_Int_Oint)),f450(B,A,tc_Int_Oint))). [resolve(4907,a,5270,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),C)) | -hBOOL(hAPP(D,E)) | hAPP(c_List_Ofilter(A,D),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),E),C)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,B),E),hAPP(c_List_Ofilter(A,D),C)). [resolve(4907,a,5271,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f451(B,A,tc_Int_Oint)),hAPP(c_List_Oset(tc_Int_Oint),B))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B). [resolve(4907,a,5274,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),f451(B,A,tc_Int_Oint))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B). [resolve(4907,a,5275,a)].
% 11.04/10.99 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hAPP(c_List_Oset(tc_Int_Oint),c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,A)) = A. [resolve(4907,a,5276,a)].
% 11.04/10.99 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,A)). [resolve(4907,a,5277,a)].
% 11.04/10.99 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Olinorder__class_Osorted__list__of__set(tc_Int_Oint,A))). [resolve(4907,a,5278,a)].
% 11.04/10.99 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),hAPP(c_List_Oset(tc_Int_Oint),B))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Int_Oint,tc_Int_Oint,c_COMBI(tc_Int_Oint)),A),c_List_Oremove1(tc_Int_Oint,A,B)) = B. [resolve(4907,a,5279,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Int_Oint)),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),B)),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),C))). [resolve(4907,a,5280,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f452(A,tc_Int_Oint)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Int_Oint)),A))). [resolve(4907,a,5282,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f453(A,tc_Int_Oint)),f452(A,tc_Int_Oint))). [resolve(4907,a,5283,a)].
% 11.04/10.99 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),f453(A,tc_Int_Oint))),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),f452(A,tc_Int_Oint)))). [resolve(4907,a,5284,a)].
% 11.04/10.99 Derived: -c_Fun_Oinj__on(A,tc_Int_Oint,B,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_List_Oset(A),C)),hAPP(c_List_Oset(A),D))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),C)) | -hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),C))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D)) | -hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D))) | hAPP(c_List_Oset(A),C) != hAPP(c_List_Oset(A),D) | C = D. [resolve(4907,a,5285,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(c_List_Orev(tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Int_Oint)),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),C)),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),B))). [resolve(4907,a,5286,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(c_List_Orev(tc_Int_Oint),A)) | c_List_Olist_ONil(tc_Int_Oint) != A | c_List_Ofoldr(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A,B) = B. [resolve(4907,a,5287,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(c_List_Orev(tc_Int_Oint),A)) | c_List_Olist_ONil(tc_Int_Oint) = A | c_List_Ofoldr(tc_Int_Oint,tc_Int_Oint,c_Orderings_Oord__class_Omax(tc_Int_Oint),A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B). [resolve(4907,a,5288,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_OtakeWhile(tc_Int_Oint,B,A)). [resolve(4907,a,5289,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(c_List_Orev(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),C))) | c_List_OtakeWhile(A,hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,A),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),D)),B),C) = hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,A),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),D)),B)),C). [resolve(4907,a,5290,a)].
% 11.04/10.99 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_OdropWhile(tc_Int_Oint,B,A)). [resolve(4907,a,5291,a)].
% 11.04/10.99 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f457(A,tc_Int_Oint)),f458(A,tc_Int_Oint))) | c_List_Olinorder__class_Osorted(tc_Int_Oint,A). [resolve(4907,a,5292,a)].
% 11.04/10.99 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f458(A,tc_Int_Oint)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Int_Oint)),A))) | c_List_Olinorder__class_Osorted(tc_Int_Oint,A). [resolve(4907,a,5293,a)].
% 11.04/11.01 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),f457(A,tc_Int_Oint))),hAPP(hAPP(c_List_Onth(tc_Int_Oint),A),f458(A,tc_Int_Oint)))) | c_List_Olinorder__class_Osorted(tc_Int_Oint,A). [resolve(4907,a,5294,a)].
% 11.04/11.01 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olist_ONil(tc_Int_Oint) = A | hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),f463(A,tc_Int_Oint)),f462(A,tc_Int_Oint)) = A. [resolve(4907,a,5295,a)].
% 11.04/11.01 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olist_ONil(tc_Int_Oint) = A | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),hAPP(c_List_Oset(tc_Int_Oint),f462(A,tc_Int_Oint)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),f463(A,tc_Int_Oint)),B)). [resolve(4907,a,5296,a)].
% 11.04/11.01 Derived: -c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olist_ONil(tc_Int_Oint) = A | c_List_Olinorder__class_Osorted(tc_Int_Oint,f462(A,tc_Int_Oint)). [resolve(4907,a,5297,a)].
% 11.04/11.01 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | c_List_Olist_ONil(tc_Int_Oint) != A. [resolve(4907,a,5298,a)].
% 11.04/11.01 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),B),C) != A | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f464(A,tc_Int_Oint,C,B)),hAPP(c_List_Oset(tc_Int_Oint),C))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,C). [resolve(4907,a,5299,a)].
% 11.04/11.01 Derived: c_List_Olinorder__class_Osorted(tc_Int_Oint,A) | hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),B),C) != A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),f464(A,tc_Int_Oint,C,B))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,C). [resolve(4907,a,5300,a)].
% 11.04/11.01 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hAPP(c_List_Oset(tc_Int_Oint),f473(A,tc_Int_Oint)) = A. [resolve(4907,a,5301,a)].
% 11.04/11.01 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_List_Olinorder__class_Osorted(tc_Int_Oint,f473(A,tc_Int_Oint)). [resolve(4907,a,5302,a)].
% 11.04/11.01 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),f473(A,tc_Int_Oint))). [resolve(4907,a,5303,a)].
% 11.04/11.01 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hAPP(c_List_Oset(tc_Int_Oint),B) != A | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | -hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),B)) | B = f473(A,tc_Int_Oint). [resolve(4907,a,5304,a)].
% 11.04/11.01 Derived: hBOOL(hAPP(hAPP(c_member(A),f475(B,C,D,A,tc_Int_Oint)),hAPP(c_List_Oset(A),D))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Int_Oint,C),B),D) = hAPP(hAPP(c_List_Olist_OCons(A),B),D). [resolve(4907,a,5305,a)].
% 11.04/11.01 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(A,B)),hAPP(A,f475(B,A,C,D,tc_Int_Oint)))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Int_Oint,A),B),C) = hAPP(hAPP(c_List_Olist_OCons(D),B),C). [resolve(4907,a,5306,a)].
% 11.04/11.01 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),f485(A,B,tc_Int_Oint)),hAPP(c_List_Oset(tc_Int_Oint),B))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)). [resolve(4907,a,5307,a)].
% 11.04/11.01 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),f485(A,B,tc_Int_Oint))) | -c_List_Olinorder__class_Osorted(tc_Int_Oint,B) | c_List_Olinorder__class_Osorted(tc_Int_Oint,hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)). [resolve(4907,a,5308,a)].
% 11.04/11.01 5309 class_Orderings_Olinorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Olinorder) # label(axiom). [assumption].
% 11.04/11.01 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),A)). [resolve(5309,a,4908,a)].
% 11.04/11.01 Derived: A = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5309,a,4910,a)].
% 11.04/11.01 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)). [resolve(5309,a,4911,a)].
% 11.04/11.02 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5309,a,4912,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),A)). [resolve(5309,a,4914,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),A)). [resolve(5309,a,4921,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),A)). [resolve(5309,a,4922,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | B = A. [resolve(5309,a,4928,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | B != A. [resolve(5309,a,4929,a)].
% 11.04/11.02 Derived: c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),B)),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A))). [resolve(5309,a,4933,a)].
% 11.04/11.02 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),A) = A. [resolve(5309,a,4934,a)].
% 11.04/11.02 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C)). [resolve(5309,a,4935,a)].
% 11.04/11.02 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),C)). [resolve(5309,a,4937,a)].
% 11.04/11.02 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B). [resolve(5309,a,4939,a)].
% 11.04/11.02 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),A). [resolve(5309,a,4941,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),C),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),C),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)). [resolve(5309,a,4944,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),A)). [resolve(5309,a,4945,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),B)). [resolve(5309,a,4946,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B) = A. [resolve(5309,a,4947,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B) != A. [resolve(5309,a,4948,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5309,a,4949,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5309,a,4950,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5309,a,4951,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),C)),B)). [resolve(5309,a,4952,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),C),A)),B)). [resolve(5309,a,4953,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),A) = A. [resolve(5309,a,4955,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),D))). [resolve(5309,a,4958,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5309,a,4961,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5309,a,4964,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5309,a,4965,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5309,a,4966,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5309,a,4967,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5309,a,4968,a)].
% 11.04/11.02 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5309,a,4969,a)].
% 11.04/11.02 Derived: -class_Lattices_Osemilattice__inf(tc_Nat_Onat) | c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat). [resolve(5309,a,4972,b)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),C),A)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C))). [resolve(5309,a,4973,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A)),B)). [resolve(5309,a,4974,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f45(B,A,tc_Nat_Onat)),A)). [resolve(5309,a,4975,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f45(B,A,tc_Nat_Onat)),B)). [resolve(5309,a,4976,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),B)). [resolve(5309,a,4977,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),C),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5309,a,4978,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A))) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f46(B,A,tc_Nat_Onat)),A)). [resolve(5309,a,4979,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),f46(B,A,tc_Nat_Onat))). [resolve(5309,a,4980,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f47(B,A,tc_Nat_Onat)),A)). [resolve(5309,a,4981,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f47(B,A,tc_Nat_Onat)),B)). [resolve(5309,a,4982,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),B)). [resolve(5309,a,4983,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),C),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5309,a,4984,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A))) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f48(B,A,tc_Nat_Onat)),A)). [resolve(5309,a,4985,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),f48(B,A,tc_Nat_Onat))). [resolve(5309,a,4986,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A) = B. [resolve(5309,a,4987,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,4988,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A) = B. [resolve(5309,a,4989,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,4990,a)].
% 11.04/11.02 Derived: c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) = A. [resolve(5309,a,4991,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)). [resolve(5309,a,4992,a)].
% 11.04/11.02 Derived: c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) = A. [resolve(5309,a,4993,a)].
% 11.04/11.02 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A)),B)). [resolve(5309,a,4994,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A)),A)). [resolve(5309,a,4995,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A)). [resolve(5309,a,4996,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A) = hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A). [resolve(5309,a,4997,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A) = hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),A). [resolve(5309,a,4998,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)). [resolve(5309,a,4999,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),B)),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)). [resolve(5309,a,5000,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),B)). [resolve(5309,a,5001,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,B)),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A))). [resolve(5309,a,5002,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),B),A). [resolve(5309,a,5003,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A)). [resolve(5309,a,5004,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,B)),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A)). [resolve(5309,a,5005,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A)),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,B)). [resolve(5309,a,5006,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),B),A). [resolve(5309,a,5007,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = B. [resolve(5309,a,5009,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,5010,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B))),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),B)). [resolve(5309,a,5011,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = B. [resolve(5309,a,5015,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,5016,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B))),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A)),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,B)). [resolve(5309,a,5017,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),f53(A,tc_Nat_Onat)),f54(A,tc_Nat_Onat))),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),f53(A,tc_Nat_Onat)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),f54(A,tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)),A)). [resolve(5309,a,5020,a)].
% 11.04/11.03 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Complete__Lattice_OSup__class_OSup(tc_Nat_Onat,B))) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f64(B,A,tc_Nat_Onat)),B)). [resolve(5309,a,5022,b)].
% 11.04/11.03 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Complete__Lattice_OSup__class_OSup(tc_Nat_Onat,B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),f64(B,A,tc_Nat_Onat))). [resolve(5309,a,5023,b)].
% 11.04/11.03 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Complete__Lattice_OSup__class_OSup(tc_Nat_Onat,B))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5309,a,5024,b)].
% 11.04/11.03 Derived: c_Finite__Set_Ofun__left__comm__idem(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)). [resolve(5309,a,5025,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f100(B,C,A,tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),B),A))). [resolve(5309,a,5026,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),f100(C,B,A,tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)),C),A))). [resolve(5309,a,5027,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f102(B,A,tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A) = B. [resolve(5309,a,5028,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),f102(B,A,tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A) = B. [resolve(5309,a,5029,a)].
% 11.04/11.03 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Complete__Lattice_OInf__class_OInf(tc_Nat_Onat,A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f153(B,A,tc_Nat_Onat)),A)). [resolve(5309,a,5032,b)].
% 11.04/11.03 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Complete__Lattice_OInf__class_OInf(tc_Nat_Onat,A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f153(B,A,tc_Nat_Onat)),B)). [resolve(5309,a,5033,b)].
% 11.04/11.03 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Complete__Lattice_OInf__class_OInf(tc_Nat_Onat,A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),B)). [resolve(5309,a,5034,b)].
% 11.04/11.03 Derived: c_Orderings_Oord_Omax(tc_Nat_Onat,hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat))) = c_Orderings_Oord__class_Omin(tc_Nat_Onat). [resolve(5309,a,5035,a)].
% 11.04/11.03 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A) != hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B) | A = B. [resolve(5309,a,5036,a)].
% 11.04/11.03 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B) | A != B. [resolve(5309,a,5037,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5309,a,5038,a)].
% 11.04/11.03 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5309,a,5039,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5309,a,5040,a)].
% 11.04/11.03 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5309,a,5041,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5309,a,5042,a)].
% 11.04/11.03 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5309,a,5043,a)].
% 11.04/11.03 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5309,a,5044,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5309,a,5045,a)].
% 11.04/11.03 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5309,a,5046,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),D))). [resolve(5309,a,5047,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),C)),B)). [resolve(5309,a,5048,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),A) = B. [resolve(5309,a,5050,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B) = B. [resolve(5309,a,5051,a)].
% 11.04/11.04 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B) != B. [resolve(5309,a,5058,a)].
% 11.04/11.04 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),A))). [resolve(5309,a,5059,a)].
% 11.04/11.04 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B))). [resolve(5309,a,5060,a)].
% 11.04/11.04 Derived: c_Finite__Set_Ofun__left__comm__idem(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)). [resolve(5309,a,5061,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C))). [resolve(5309,a,5062,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),C),B))). [resolve(5309,a,5063,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5309,a,5064,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5309,a,5067,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5309,a,5068,a)].
% 11.04/11.04 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5309,a,5069,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),A) = A. [resolve(5309,a,5070,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),A). [resolve(5309,a,5071,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B). [resolve(5309,a,5073,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),C)). [resolve(5309,a,5075,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C)). [resolve(5309,a,5077,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),C)),B). [resolve(5309,a,5080,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C)). [resolve(5309,a,5081,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C)). [resolve(5309,a,5082,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),C)). [resolve(5309,a,5083,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)) = A. [resolve(5309,a,5084,a)].
% 11.04/11.04 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)) = A. [resolve(5309,a,5085,a)].
% 11.04/11.04 Derived: -class_Lattices_Osemilattice__sup(tc_Nat_Onat) | c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat). [resolve(5309,a,5086,b)].
% 11.04/11.04 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C))),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),C)))). [resolve(5309,a,5087,a)].
% 11.04/11.04 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),C))),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C)))). [resolve(5309,a,5088,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),C),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),C),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)). [resolve(5309,a,5089,a)].
% 11.04/11.04 Derived: c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Orderings_Oord_Omin(tc_Nat_Onat,hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat))). [resolve(5309,a,5090,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),C)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),C),A))). [resolve(5309,a,5091,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)) = B. [resolve(5309,a,5092,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A) = B. [resolve(5309,a,5093,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,5094,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A))). [resolve(5309,a,5095,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A) = B. [resolve(5309,a,5096,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,5097,a)].
% 11.04/11.04 Derived: c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) = A. [resolve(5309,a,5098,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)). [resolve(5309,a,5099,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A))). [resolve(5309,a,5100,a)].
% 11.04/11.04 Derived: c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) = A. [resolve(5309,a,5101,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A)),A)). [resolve(5309,a,5102,a)].
% 11.04/11.04 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A)). [resolve(5309,a,5103,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A) = hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),A). [resolve(5309,a,5104,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A) = hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),A). [resolve(5309,a,5105,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)). [resolve(5309,a,5106,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),B)),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)). [resolve(5309,a,5107,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)) = B. [resolve(5309,a,5108,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),B)). [resolve(5309,a,5109,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A)),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,B))). [resolve(5309,a,5110,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),B),A). [resolve(5309,a,5111,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A)). [resolve(5309,a,5112,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,B)),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A)). [resolve(5309,a,5113,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A)),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,B)). [resolve(5309,a,5114,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),B),A). [resolve(5309,a,5115,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = B. [resolve(5309,a,5117,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,5118,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B))),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),B)). [resolve(5309,a,5120,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = B. [resolve(5309,a,5123,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,5124,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B))),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A)),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,B)). [resolve(5309,a,5126,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),f184(A,tc_Nat_Onat)),f185(A,tc_Nat_Onat))),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),f184(A,tc_Nat_Onat)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),f185(A,tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)),A)). [resolve(5309,a,5128,a)].
% 11.04/11.05 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Nat_Onat),C),D))) | hBOOL(hAPP(hAPP(c_member(B),f199(D,C,B,A,tc_Nat_Onat)),C)). [resolve(5309,a,5130,b)].
% 11.04/11.05 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Nat_Onat),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(D,f199(D,C,B,A,tc_Nat_Onat)))). [resolve(5309,a,5131,b)].
% 11.04/11.05 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Nat_Onat),C),D))) | -hBOOL(hAPP(hAPP(c_member(B),E),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(D,E))). [resolve(5309,a,5132,b)].
% 11.04/11.05 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Nat_Onat),B),C)),D)) | hBOOL(hAPP(hAPP(c_member(A),f200(D,C,B,A,tc_Nat_Onat)),B)). [resolve(5309,a,5133,b)].
% 11.04/11.05 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Nat_Onat),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(C,f200(D,C,B,A,tc_Nat_Onat))),D)). [resolve(5309,a,5134,b)].
% 11.04/11.05 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Nat_Onat),B),C)),D)) | -hBOOL(hAPP(hAPP(c_member(A),E),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(C,E)),D)). [resolve(5309,a,5135,b)].
% 11.04/11.05 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,C)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,D)). [resolve(5309,a,5136,a)].
% 11.04/11.05 Derived: c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,C)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,B,D)). [resolve(5309,a,5137,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)). [resolve(5309,a,5138,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). [resolve(5309,a,5139,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),A)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B)). [resolve(5309,a,5140,a)].
% 11.04/11.05 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),A) != hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),B) | A = B. [resolve(5309,a,5141,a)].
% 11.04/11.05 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),A) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),B) | A != B. [resolve(5309,a,5142,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,B,C)). [resolve(5309,a,5143,a)].
% 11.04/11.05 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,B,C)). [resolve(5309,a,5144,a)].
% 11.04/11.05 Derived: c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,C)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,B,D)). [resolve(5309,a,5145,a)].
% 11.04/11.05 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,C)). [resolve(5309,a,5146,a)].
% 11.04/11.05 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),C)). [resolve(5309,a,5147,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,B,C)). [resolve(5309,a,5148,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). [resolve(5309,a,5149,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)). [resolve(5309,a,5150,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),A)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B)). [resolve(5309,a,5151,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B)). [resolve(5309,a,5152,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B) | C = A. [resolve(5309,a,5153,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B) | B = D. [resolve(5309,a,5154,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B) | C != A | B != D. [resolve(5309,a,5155,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),A)). [resolve(5309,a,5158,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),D)). [resolve(5309,a,5159,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C)). [resolve(5309,a,5160,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)). [resolve(5309,a,5161,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)). [resolve(5309,a,5162,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),D)). [resolve(5309,a,5163,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)). [resolve(5309,a,5164,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C)). [resolve(5309,a,5165,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))). [resolve(5309,a,5166,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B)). [resolve(5309,a,5167,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,B,C)). [resolve(5309,a,5168,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),A) != hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),B) | A = B. [resolve(5309,a,5169,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),A) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),B) | A != B. [resolve(5309,a,5170,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),A)). [resolve(5309,a,5171,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A)). [resolve(5309,a,5172,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),B)). [resolve(5309,a,5173,a)].
% 11.04/11.06 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,C)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),B)). [resolve(5309,a,5174,a)].
% 11.04/11.06 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),A)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)). [resolve(5309,a,5175,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,A,B)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),B)). [resolve(5309,a,5176,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A) != hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),B) | A = B. [resolve(5309,a,5177,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),B) | A != B. [resolve(5309,a,5178,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),A)). [resolve(5309,a,5179,a)].
% 11.04/11.06 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),A)). [resolve(5309,a,5180,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),A)). [resolve(5309,a,5181,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A)). [resolve(5309,a,5182,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),B)). [resolve(5309,a,5183,a)].
% 11.04/11.06 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),A)). [resolve(5309,a,5184,a)].
% 11.04/11.06 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),B)). [resolve(5309,a,5185,a)].
% 11.04/11.07 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(A,f269(B,A,tc_Nat_Onat))),hAPP(A,f270(B,A,tc_Nat_Onat))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),f269(B,A,tc_Nat_Onat)),f270(B,A,tc_Nat_Onat))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,A),B)) = hAPP(A,c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),B)). [resolve(5309,a,5186,a)].
% 11.04/11.07 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(A,f271(B,A,tc_Nat_Onat))),hAPP(A,f272(B,A,tc_Nat_Onat))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),f271(B,A,tc_Nat_Onat)),f272(B,A,tc_Nat_Onat))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,A),B)) = hAPP(A,c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),B)). [resolve(5309,a,5187,a)].
% 11.04/11.07 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(A,f273(B,A,tc_Nat_Onat))),hAPP(A,f274(B,A,tc_Nat_Onat))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),f273(B,A,tc_Nat_Onat)),f274(B,A,tc_Nat_Onat))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,A),B)) = hAPP(A,c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,B)). [resolve(5309,a,5188,a)].
% 11.04/11.07 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(A,f275(B,A,tc_Nat_Onat))),hAPP(A,f276(B,A,tc_Nat_Onat))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),f275(B,A,tc_Nat_Onat)),f276(B,A,tc_Nat_Onat))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,A),B)) = hAPP(A,c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,B)). [resolve(5309,a,5189,a)].
% 11.04/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat)),c_fequal))),c_Orderings_Oord__class_Omin(tc_Nat_Onat)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),A)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),B))))))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),B)). [resolve(5309,a,5190,a)].
% 11.04/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),A))))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),B),c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A)). [resolve(5309,a,5191,a)].
% 11.04/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),A))))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),B),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)). [resolve(5309,a,5192,a)].
% 11.04/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat)),c_fequal))),c_Orderings_Oord__class_Omax(tc_Nat_Onat)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),A)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),B))))))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A)),c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),B)). [resolve(5309,a,5193,a)].
% 11.13/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f354(B,C,A,tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),B),A)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),C),B))). [resolve(5309,a,5194,a)].
% 11.13/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f354(B,C,A,tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),B),A)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),C),B))). [resolve(5309,a,5195,a)].
% 11.13/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f355(B,A,tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A) = B. [resolve(5309,a,5196,a)].
% 11.13/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f355(B,A,tc_Nat_Onat)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A) = B. [resolve(5309,a,5197,a)].
% 11.13/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))) = c_List_Oremove1(tc_Nat_Onat,B,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,A)). [resolve(5309,a,5198,a)].
% 11.13/11.07 Derived: c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(tc_Nat_Onat). [resolve(5309,a,5199,a)].
% 11.13/11.07 Derived: c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(c_List_Oset(tc_Nat_Onat),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B))) = hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B). [resolve(5309,a,5200,a)].
% 11.13/11.07 Derived: c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(c_List_Oset(tc_Nat_Onat),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B))) = hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B). [resolve(5309,a,5201,a)].
% 11.13/11.07 Derived: c_Big__Operators_Olattice_OInf__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_List_Oset(tc_Nat_Onat),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B))) = hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),B). [resolve(5309,a,5202,a)].
% 11.13/11.07 Derived: c_Big__Operators_Olattice_OSup__fin(tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_List_Oset(tc_Nat_Onat),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B))) = hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),B). [resolve(5309,a,5203,a)].
% 11.13/11.07 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),B),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))). [resolve(5309,a,5204,a)].
% 11.13/11.07 Derived: hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),c_List_Olist_ONil(A)) = hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)). [resolve(5309,a,5205,a)].
% 11.13/11.07 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(A,B)),hAPP(A,C))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Nat_Onat,A),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)) = hAPP(hAPP(c_List_Olist_OCons(D),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)). [resolve(5309,a,5206,a)].
% 11.13/11.08 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(A,B)),hAPP(A,C))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Nat_Onat,A),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)) = hAPP(hAPP(c_List_Olist_OCons(D),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Nat_Onat,A),B),E)). [resolve(5309,a,5207,a)].
% 11.13/11.08 Derived: hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),D)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),D)). [resolve(5309,a,5208,a)].
% 11.13/11.08 Derived: hAPP(A,B) = hAPP(A,C) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Nat_Onat,A),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Nat_Onat,A),C),E)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Nat_Onat,A),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Nat_Onat,A),B),E)). [resolve(5309,a,5209,a)].
% 11.13/11.08 Derived: hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),B),C)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),A),C)). [resolve(5309,a,5210,a)].
% 11.13/11.08 Derived: c_Finite__Set_Ofun__left__comm(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat))). [resolve(5309,a,5211,a)].
% 11.13/11.08 Derived: hAPP(c_List_Oset(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),D)) = hAPP(hAPP(c_Set_Oinsert(A),C),hAPP(c_List_Oset(A),D)). [resolve(5309,a,5212,a)].
% 11.13/11.08 Derived: c_List_Oremove1(tc_Nat_Onat,A,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),A),B)) = B. [resolve(5309,a,5213,a)].
% 11.13/11.08 Derived: c_List_Olist_ONil(A) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),D). [resolve(5309,a,5214,a)].
% 11.13/11.08 Derived: -hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),D))) | -hBOOL(hAPP(hAPP(c_member(A),C),hAPP(c_List_Oset(A),D))). [resolve(5309,a,5215,a)].
% 11.13/11.08 Derived: -hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),D))) | hBOOL(hAPP(c_List_Odistinct(A),D)). [resolve(5309,a,5216,a)].
% 11.13/11.08 Derived: hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),D))) | hBOOL(hAPP(hAPP(c_member(A),C),hAPP(c_List_Oset(A),D))) | -hBOOL(hAPP(c_List_Odistinct(A),D)). [resolve(5309,a,5217,a)].
% 11.13/11.08 Derived: hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(A,B)),hAPP(c_Set_Oimage(C,tc_Nat_Onat,A),hAPP(c_List_Oset(C),D)))) | c_List_Olinorder__class_Oinsort__insert__key(C,tc_Nat_Onat,A,B,D) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(C,tc_Nat_Onat,A),B),D). [resolve(5309,a,5218,a)].
% 11.13/11.08 Derived: hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),hAPP(c_List_Oset(tc_Nat_Onat),B))) | c_List_Olinorder__class_Oinsort__insert__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat),A,B) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),A),B). [resolve(5309,a,5219,a)].
% 11.13/11.08 Derived: -hBOOL(hAPP(c_List_Odistinct(A),B)) | hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Oinsort__insert__key(A,tc_Nat_Onat,C,D,B))). [resolve(5309,a,5220,a)].
% 11.13/11.08 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),hAPP(c_List_Oset(tc_Nat_Onat),B))) | c_List_Olinorder__class_Oinsort__insert__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat),A,B) = B. [resolve(5309,a,5221,a)].
% 11.13/11.08 Derived: hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Oinsort__insert__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat),A,B)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),hAPP(c_List_Oset(tc_Nat_Onat),B)). [resolve(5309,a,5222,a)].
% 11.13/11.08 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(A,B)),hAPP(c_Set_Oimage(C,tc_Nat_Onat,A),hAPP(c_List_Oset(C),D)))) | c_List_Olinorder__class_Oinsort__insert__key(C,tc_Nat_Onat,A,B,D) = D. [resolve(5309,a,5223,a)].
% 11.13/11.08 Derived: c_List_Olinorder__class_Osort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat),c_List_Oremdups(tc_Nat_Onat,A)) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_List_Oset(tc_Nat_Onat),A)). [resolve(5309,a,5224,a)].
% 11.13/11.08 Derived: c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,c_List_Olist_ONil(A)) = c_List_Olist_ONil(A). [resolve(5309,a,5225,a)].
% 11.13/11.08 Derived: hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,C)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C). [resolve(5309,a,5226,a)].
% 11.13/11.08 Derived: hAPP(c_List_Oset(A),c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,C)) = hAPP(c_List_Oset(A),C). [resolve(5309,a,5227,a)].
% 11.13/11.08 Derived: -hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,C))) | hBOOL(hAPP(c_List_Odistinct(A),C)). [resolve(5309,a,5228,a)].
% 11.13/11.08 Derived: hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,C))) | -hBOOL(hAPP(c_List_Odistinct(A),C)). [resolve(5309,a,5229,a)].
% 11.13/11.08 Derived: c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,D)). [resolve(5309,a,5230,a)].
% 11.13/11.08 Derived: c_List_Olinorder__class_Osort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat),A) = hAPP(c_List_Ofoldl(tc_List_Olist(tc_Nat_Onat),tc_Nat_Onat,hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(tc_Nat_Onat)),c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat))),c_List_Olist_ONil(tc_Nat_Onat)),A). [resolve(5309,a,5231,a)].
% 11.13/11.08 Derived: c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,hAPP(c_List_Ofilter(A,C),D)) = hAPP(c_List_Ofilter(A,C),c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,D)). [resolve(5309,a,5232,a)].
% 11.13/11.08 Derived: hBOOL(hAPP(A,B)) | hAPP(c_List_Ofilter(C,A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(C,tc_Nat_Onat,D),B),E)) = hAPP(c_List_Ofilter(C,A),E). [resolve(5309,a,5233,a)].
% 11.13/11.08 Derived: -hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),D),C)) | hAPP(c_List_Ohd(A),hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,A),hAPP(c_fequal,hAPP(D,B))),D)),C)) != B | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,D),B),c_List_Oremove1(A,B,C)) = C. [resolve(5309,a,5234,a)].
% 11.13/11.08 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat)). [resolve(5309,a,5235,a)].
% 11.13/11.08 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),c_List_Olist_ONil(tc_Nat_Onat))). [resolve(5309,a,5236,a)].
% 11.13/11.08 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat),A)). [resolve(5309,a,5237,a)].
% 11.13/11.08 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Oinsort__insert__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat),B,A)). [resolve(5309,a,5238,a)].
% 11.13/11.08 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),B),A)). [resolve(5309,a,5239,a)].
% 11.13/11.08 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Otake(tc_Nat_Onat),B),A)). [resolve(5309,a,5240,a)].
% 11.13/11.08 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oremove1(tc_Nat_Onat,B,A)). [resolve(5309,a,5241,a)].
% 11.13/11.08 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Otl(tc_Nat_Onat),A)). [resolve(5309,a,5242,a)].
% 11.13/11.08 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),A),B)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,B). [resolve(5309,a,5243,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),A),B)) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B). [resolve(5309,a,5244,a)].
% 11.14/11.09 Derived: c_List_Olist_ONil(tc_Nat_Onat) = A | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Obutlast(tc_Nat_Onat,A)). [resolve(5309,a,5245,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5309,a,5247,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),B),C))) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),B),C)). [resolve(5309,a,5248,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),B),C)). [resolve(5309,a,5249,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oremdups(tc_Nat_Onat,A)). [resolve(5309,a,5251,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | -hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),A)) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | -hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),B)) | hAPP(c_List_Oset(tc_Nat_Onat),A) != hAPP(c_List_Oset(tc_Nat_Onat),B) | A = B. [resolve(5309,a,5252,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),c_List_Olinorder__class_Osort__key(A,tc_Nat_Onat,B,C))). [resolve(5309,a,5253,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),C)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),c_List_Olinorder__class_Oinsort__insert__key(A,tc_Nat_Onat,B,D,C))). [resolve(5309,a,5254,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),C)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),c_List_Oremove1(A,D,C))). [resolve(5309,a,5255,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),D))) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),D)). [resolve(5309,a,5256,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),C),D))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),D)). [resolve(5309,a,5257,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),A),c_fequal),B)),hAPP(C,D))),D))). [resolve(5309,a,5258,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),C)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),hAPP(c_List_Ofilter(A,D),C))). [resolve(5309,a,5259,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Ofilter(tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal),hAPP(A,B))),B)). [resolve(5309,a,5260,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,B). [resolve(5309,a,5261,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),C),hAPP(c_List_Oset(tc_Nat_Onat),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5309,a,5262,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f448(B,A,tc_Nat_Onat)),hAPP(c_List_Oset(tc_Nat_Onat),B))). [resolve(5309,a,5263,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),f448(B,A,tc_Nat_Onat))). [resolve(5309,a,5264,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),A),B)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,A). [resolve(5309,a,5265,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),A),B)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,B). [resolve(5309,a,5266,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),C),hAPP(c_List_Oset(tc_Nat_Onat),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),D),hAPP(c_List_Oset(tc_Nat_Onat),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)). [resolve(5309,a,5267,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),A),B)) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f449(B,A,tc_Nat_Onat)),hAPP(c_List_Oset(tc_Nat_Onat),A))). [resolve(5309,a,5268,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),A),B)) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f450(B,A,tc_Nat_Onat)),hAPP(c_List_Oset(tc_Nat_Onat),B))). [resolve(5309,a,5269,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),A),B)) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f449(B,A,tc_Nat_Onat)),f450(B,A,tc_Nat_Onat))). [resolve(5309,a,5270,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),C)) | -hBOOL(hAPP(D,E)) | hAPP(c_List_Ofilter(A,D),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),E),C)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,B),E),hAPP(c_List_Ofilter(A,D),C)). [resolve(5309,a,5271,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f451(B,A,tc_Nat_Onat)),hAPP(c_List_Oset(tc_Nat_Onat),B))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B). [resolve(5309,a,5274,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),f451(B,A,tc_Nat_Onat))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B). [resolve(5309,a,5275,a)].
% 11.14/11.09 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hAPP(c_List_Oset(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,A)) = A. [resolve(5309,a,5276,a)].
% 11.14/11.09 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,A)). [resolve(5309,a,5277,a)].
% 11.14/11.09 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,A))). [resolve(5309,a,5278,a)].
% 11.14/11.09 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),hAPP(c_List_Oset(tc_Nat_Onat),B))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Nat_Onat,tc_Nat_Onat,c_COMBI(tc_Nat_Onat)),A),c_List_Oremove1(tc_Nat_Onat,A,B)) = B. [resolve(5309,a,5279,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),B)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),C))). [resolve(5309,a,5280,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f452(A,tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),A))). [resolve(5309,a,5282,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f453(A,tc_Nat_Onat)),f452(A,tc_Nat_Onat))). [resolve(5309,a,5283,a)].
% 11.14/11.09 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),f453(A,tc_Nat_Onat))),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),f452(A,tc_Nat_Onat)))). [resolve(5309,a,5284,a)].
% 11.14/11.09 Derived: -c_Fun_Oinj__on(A,tc_Nat_Onat,B,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_List_Oset(A),C)),hAPP(c_List_Oset(A),D))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),C)) | -hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),C))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),D)) | -hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),D))) | hAPP(c_List_Oset(A),C) != hAPP(c_List_Oset(A),D) | C = D. [resolve(5309,a,5285,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),C)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),B))). [resolve(5309,a,5286,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),A)) | c_List_Olist_ONil(tc_Nat_Onat) != A | c_List_Ofoldr(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A,B) = B. [resolve(5309,a,5287,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),A)) | c_List_Olist_ONil(tc_Nat_Onat) = A | c_List_Ofoldr(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat),A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B). [resolve(5309,a,5288,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_OtakeWhile(tc_Nat_Onat,B,A)). [resolve(5309,a,5289,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),C))) | c_List_OtakeWhile(A,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,A),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),D)),B),C) = hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,A),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),D)),B)),C). [resolve(5309,a,5290,a)].
% 11.14/11.09 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_OdropWhile(tc_Nat_Onat,B,A)). [resolve(5309,a,5291,a)].
% 11.14/11.09 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f457(A,tc_Nat_Onat)),f458(A,tc_Nat_Onat))) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,A). [resolve(5309,a,5292,a)].
% 11.14/11.09 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f458(A,tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),A))) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,A). [resolve(5309,a,5293,a)].
% 11.18/11.13 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),f457(A,tc_Nat_Onat))),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),A),f458(A,tc_Nat_Onat)))) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,A). [resolve(5309,a,5294,a)].
% 11.18/11.13 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olist_ONil(tc_Nat_Onat) = A | hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),f463(A,tc_Nat_Onat)),f462(A,tc_Nat_Onat)) = A. [resolve(5309,a,5295,a)].
% 11.18/11.13 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olist_ONil(tc_Nat_Onat) = A | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),hAPP(c_List_Oset(tc_Nat_Onat),f462(A,tc_Nat_Onat)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f463(A,tc_Nat_Onat)),B)). [resolve(5309,a,5296,a)].
% 11.18/11.13 Derived: -c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olist_ONil(tc_Nat_Onat) = A | c_List_Olinorder__class_Osorted(tc_Nat_Onat,f462(A,tc_Nat_Onat)). [resolve(5309,a,5297,a)].
% 11.18/11.13 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | c_List_Olist_ONil(tc_Nat_Onat) != A. [resolve(5309,a,5298,a)].
% 11.18/11.13 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),B),C) != A | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f464(A,tc_Nat_Onat,C,B)),hAPP(c_List_Oset(tc_Nat_Onat),C))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,C). [resolve(5309,a,5299,a)].
% 11.18/11.13 Derived: c_List_Olinorder__class_Osorted(tc_Nat_Onat,A) | hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),B),C) != A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),f464(A,tc_Nat_Onat,C,B))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,C). [resolve(5309,a,5300,a)].
% 11.18/11.13 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hAPP(c_List_Oset(tc_Nat_Onat),f473(A,tc_Nat_Onat)) = A. [resolve(5309,a,5301,a)].
% 11.18/11.13 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,f473(A,tc_Nat_Onat)). [resolve(5309,a,5302,a)].
% 11.18/11.13 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),f473(A,tc_Nat_Onat))). [resolve(5309,a,5303,a)].
% 11.18/11.13 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hAPP(c_List_Oset(tc_Nat_Onat),B) != A | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | -hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),B)) | B = f473(A,tc_Nat_Onat). [resolve(5309,a,5304,a)].
% 11.18/11.13 Derived: hBOOL(hAPP(hAPP(c_member(A),f475(B,C,D,A,tc_Nat_Onat)),hAPP(c_List_Oset(A),D))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Nat_Onat,C),B),D) = hAPP(hAPP(c_List_Olist_OCons(A),B),D). [resolve(5309,a,5305,a)].
% 11.18/11.13 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(A,B)),hAPP(A,f475(B,A,C,D,tc_Nat_Onat)))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Nat_Onat,A),B),C) = hAPP(hAPP(c_List_Olist_OCons(D),B),C). [resolve(5309,a,5306,a)].
% 11.18/11.13 Derived: hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),f485(A,B,tc_Nat_Onat)),hAPP(c_List_Oset(tc_Nat_Onat),B))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)). [resolve(5309,a,5307,a)].
% 11.18/11.13 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),f485(A,B,tc_Nat_Onat))) | -c_List_Olinorder__class_Osorted(tc_Nat_Onat,B) | c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)). [resolve(5309,a,5308,a)].
% 11.18/11.13 5310 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) # label(axiom). [assumption].
% 11.18/11.13 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,4908,a)].
% 11.18/11.13 Derived: A = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,4910,a)].
% 11.18/11.13 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,4911,a)].
% 11.18/11.14 Derived: A != B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,4912,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,4914,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,4921,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,4922,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | B = A. [resolve(5310,a,4928,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | B != A. [resolve(5310,a,4929,a)].
% 11.18/11.14 Derived: c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),B)),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A))). [resolve(5310,a,4933,a)].
% 11.18/11.14 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),A) = A. [resolve(5310,a,4934,a)].
% 11.18/11.14 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,4935,a)].
% 11.18/11.14 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,4937,a)].
% 11.18/11.14 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B). [resolve(5310,a,4939,a)].
% 11.18/11.14 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),A). [resolve(5310,a,4941,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),C),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),C),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,4944,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),A)). [resolve(5310,a,4945,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),B)). [resolve(5310,a,4946,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B) = A. [resolve(5310,a,4947,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B) != A. [resolve(5310,a,4948,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,4949,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,4950,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,4951,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),C)),B)). [resolve(5310,a,4952,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),C),A)),B)). [resolve(5310,a,4953,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),A) = A. [resolve(5310,a,4955,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(5310,a,4958,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,4961,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,4964,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,4965,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,4966,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,4967,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,4968,a)].
% 11.18/11.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,4969,a)].
% 11.18/11.14 Derived: -class_Lattices_Osemilattice__inf(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Code__Numeral_Ocode__numeral). [resolve(5310,a,4972,b)].
% 11.18/11.14 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),C),A)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(5310,a,4973,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A)),B)). [resolve(5310,a,4974,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f45(B,A,tc_Code__Numeral_Ocode__numeral)),A)). [resolve(5310,a,4975,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),f45(B,A,tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5310,a,4976,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),B)). [resolve(5310,a,4977,a)].
% 11.18/11.14 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),C),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,4978,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A))) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f46(B,A,tc_Code__Numeral_Ocode__numeral)),A)). [resolve(5310,a,4979,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),f46(B,A,tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,4980,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f47(B,A,tc_Code__Numeral_Ocode__numeral)),A)). [resolve(5310,a,4981,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),f47(B,A,tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5310,a,4982,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),B)). [resolve(5310,a,4983,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),C),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,4984,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A))) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f48(B,A,tc_Code__Numeral_Ocode__numeral)),A)). [resolve(5310,a,4985,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),f48(B,A,tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,4986,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A) = B. [resolve(5310,a,4987,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,4988,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A) = B. [resolve(5310,a,4989,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,4990,a)].
% 11.18/11.15 Derived: c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) = A. [resolve(5310,a,4991,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,4992,a)].
% 11.18/11.15 Derived: c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) = A. [resolve(5310,a,4993,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A)),B)). [resolve(5310,a,4994,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A)),A)). [resolve(5310,a,4995,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,4996,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A). [resolve(5310,a,4997,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A) = hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),A). [resolve(5310,a,4998,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,4999,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B)),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5000,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5001,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,B)),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A))). [resolve(5310,a,5002,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),B),A). [resolve(5310,a,5003,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5004,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,B)),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5005,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A)),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,B)). [resolve(5310,a,5006,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),B),A). [resolve(5310,a,5007,a)].
% 11.18/11.15 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = B. [resolve(5310,a,5009,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,5010,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B))),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5011,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = B. [resolve(5310,a,5015,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,5016,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B))),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A)),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,B)). [resolve(5310,a,5017,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),f53(A,tc_Code__Numeral_Ocode__numeral)),f54(A,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),f53(A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),f54(A,tc_Code__Numeral_Ocode__numeral)),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)),A)). [resolve(5310,a,5020,a)].
% 11.18/11.16 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),c_Complete__Lattice_OSup__class_OSup(tc_Code__Numeral_Ocode__numeral,B))) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f64(B,A,tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5310,a,5022,b)].
% 11.18/11.16 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),c_Complete__Lattice_OSup__class_OSup(tc_Code__Numeral_Ocode__numeral,B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),f64(B,A,tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,5023,b)].
% 11.18/11.16 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),c_Complete__Lattice_OSup__class_OSup(tc_Code__Numeral_Ocode__numeral,B))) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5024,b)].
% 11.18/11.16 Derived: c_Finite__Set_Ofun__left__comm__idem(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)). [resolve(5310,a,5025,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f100(B,C,A,tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),C),B)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),B),A))). [resolve(5310,a,5026,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),f100(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)),C),A))). [resolve(5310,a,5027,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f102(B,A,tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A) = B. [resolve(5310,a,5028,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),f102(B,A,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A) = B. [resolve(5310,a,5029,a)].
% 11.18/11.16 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Complete__Lattice_OInf__class_OInf(tc_Code__Numeral_Ocode__numeral,A)),B)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f153(B,A,tc_Code__Numeral_Ocode__numeral)),A)). [resolve(5310,a,5032,b)].
% 11.18/11.16 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Complete__Lattice_OInf__class_OInf(tc_Code__Numeral_Ocode__numeral,A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),f153(B,A,tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5310,a,5033,b)].
% 11.18/11.16 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Complete__Lattice_OInf__class_OInf(tc_Code__Numeral_Ocode__numeral,A)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),C),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),B)). [resolve(5310,a,5034,b)].
% 11.18/11.16 Derived: c_Orderings_Oord_Omax(tc_Code__Numeral_Ocode__numeral,hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral))) = c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral). [resolve(5310,a,5035,a)].
% 11.18/11.16 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A) != hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),B) | A = B. [resolve(5310,a,5036,a)].
% 11.18/11.16 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),B) | A != B. [resolve(5310,a,5037,a)].
% 11.18/11.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,5038,a)].
% 11.18/11.16 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,5039,a)].
% 11.18/11.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,5040,a)].
% 11.18/11.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,5041,a)].
% 11.18/11.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5042,a)].
% 11.18/11.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,5043,a)].
% 11.18/11.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5044,a)].
% 11.18/11.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5045,a)].
% 11.18/11.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,5046,a)].
% 11.18/11.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(5310,a,5047,a)].
% 11.18/11.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),C)),B)). [resolve(5310,a,5048,a)].
% 11.18/11.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),A) = B. [resolve(5310,a,5050,a)].
% 11.18/11.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B) = B. [resolve(5310,a,5051,a)].
% 11.18/11.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B) != B. [resolve(5310,a,5058,a)].
% 11.18/11.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),A))). [resolve(5310,a,5059,a)].
% 11.18/11.18 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5310,a,5060,a)].
% 11.18/11.18 Derived: c_Finite__Set_Ofun__left__comm__idem(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)). [resolve(5310,a,5061,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(5310,a,5062,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(5310,a,5063,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5064,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5067,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,5068,a)].
% 11.18/11.18 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,5069,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),A) = A. [resolve(5310,a,5070,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),A). [resolve(5310,a,5071,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B). [resolve(5310,a,5073,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5075,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,5077,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),C),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(5310,a,5080,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,5081,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,5082,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5083,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)) = A. [resolve(5310,a,5084,a)].
% 11.18/11.18 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)) = A. [resolve(5310,a,5085,a)].
% 11.18/11.18 Derived: -class_Lattices_Osemilattice__sup(tc_Code__Numeral_Ocode__numeral) | c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral) = c_Lattices_Osemilattice__sup__class_Osup(tc_Code__Numeral_Ocode__numeral). [resolve(5310,a,5086,b)].
% 11.18/11.18 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C))),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),C)))). [resolve(5310,a,5087,a)].
% 11.18/11.18 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),C))),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C)))). [resolve(5310,a,5088,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),C),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),C),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,5089,a)].
% 11.18/11.18 Derived: c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral) = c_Orderings_Oord_Omin(tc_Code__Numeral_Ocode__numeral,hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,5090,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),C)),hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),C),A))). [resolve(5310,a,5091,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)) = B. [resolve(5310,a,5092,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A) = B. [resolve(5310,a,5093,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,5094,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A))). [resolve(5310,a,5095,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A) = B. [resolve(5310,a,5096,a)].
% 11.18/11.18 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,5097,a)].
% 11.18/11.19 Derived: c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) = A. [resolve(5310,a,5098,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5099,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A))). [resolve(5310,a,5100,a)].
% 11.18/11.19 Derived: c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) = A. [resolve(5310,a,5101,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A)),A)). [resolve(5310,a,5102,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5103,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),A). [resolve(5310,a,5104,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A) = hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),A). [resolve(5310,a,5105,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5106,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B)),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5107,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)) = B. [resolve(5310,a,5108,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5109,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A)),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,B))). [resolve(5310,a,5110,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),B),A). [resolve(5310,a,5111,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5112,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,B)),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5113,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A)),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,B)). [resolve(5310,a,5114,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),B),A). [resolve(5310,a,5115,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = B. [resolve(5310,a,5117,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,5118,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B))),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5120,a)].
% 11.18/11.19 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = B. [resolve(5310,a,5123,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,5124,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B) | hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B))),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A)),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,B)). [resolve(5310,a,5126,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),f184(A,tc_Code__Numeral_Ocode__numeral)),f185(A,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),f184(A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),f185(A,tc_Code__Numeral_Ocode__numeral)),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)),A)). [resolve(5310,a,5128,a)].
% 11.18/11.20 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Code__Numeral_Ocode__numeral),C),D))) | hBOOL(hAPP(hAPP(c_member(B),f199(D,C,B,A,tc_Code__Numeral_Ocode__numeral)),C)). [resolve(5310,a,5130,b)].
% 11.18/11.20 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Code__Numeral_Ocode__numeral),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(D,f199(D,C,B,A,tc_Code__Numeral_Ocode__numeral)))). [resolve(5310,a,5131,b)].
% 11.18/11.20 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,tc_Code__Numeral_Ocode__numeral),C),D))) | -hBOOL(hAPP(hAPP(c_member(B),E),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(D,E))). [resolve(5310,a,5132,b)].
% 11.18/11.20 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Code__Numeral_Ocode__numeral),B),C)),D)) | hBOOL(hAPP(hAPP(c_member(A),f200(D,C,B,A,tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5310,a,5133,b)].
% 11.18/11.20 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Code__Numeral_Ocode__numeral),B),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(C,f200(D,C,B,A,tc_Code__Numeral_Ocode__numeral))),D)). [resolve(5310,a,5134,b)].
% 11.18/11.20 Derived: -class_Complete__Lattice_Ocomplete__lattice(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(A,tc_Code__Numeral_Ocode__numeral),B),C)),D)) | -hBOOL(hAPP(hAPP(c_member(A),E),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(C,E)),D)). [resolve(5310,a,5135,b)].
% 11.18/11.20 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,C)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(5310,a,5136,a)].
% 11.18/11.20 Derived: c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,C)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(5310,a,5137,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(5310,a,5138,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,B)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))). [resolve(5310,a,5139,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),A)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(5310,a,5140,a)].
% 11.18/11.20 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),A) != hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),B) | A = B. [resolve(5310,a,5141,a)].
% 11.18/11.20 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),B) | A != B. [resolve(5310,a,5142,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,B)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(5310,a,5143,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,B)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(5310,a,5144,a)].
% 11.18/11.20 Derived: c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,C)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(5310,a,5145,a)].
% 11.18/11.20 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,C)). [resolve(5310,a,5146,a)].
% 11.18/11.20 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,B)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),C)). [resolve(5310,a,5147,a)].
% 11.18/11.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,B)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(5310,a,5148,a)].
% 11.18/11.20 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))). [resolve(5310,a,5149,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(5310,a,5150,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),A)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(5310,a,5151,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(5310,a,5152,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,C),D) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B) | C = A. [resolve(5310,a,5153,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,C),D) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B) | B = D. [resolve(5310,a,5154,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),D)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,C),D) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B) | C != A | B != D. [resolve(5310,a,5155,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),A)). [resolve(5310,a,5158,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),D)). [resolve(5310,a,5159,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,B),C)). [resolve(5310,a,5160,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,B),C) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B)). [resolve(5310,a,5161,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(5310,a,5162,a)].
% 11.28/11.21 Derived: hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,B),D)). [resolve(5310,a,5163,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B)). [resolve(5310,a,5164,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,B),C)). [resolve(5310,a,5165,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))). [resolve(5310,a,5166,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,B)). [resolve(5310,a,5167,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)) | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),C) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,B)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(5310,a,5168,a)].
% 11.28/11.21 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),A) != hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),B) | A = B. [resolve(5310,a,5169,a)].
% 11.28/11.21 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),B) | A != B. [resolve(5310,a,5170,a)].
% 11.28/11.21 Derived: hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5171,a)].
% 11.28/11.21 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5172,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Code__Numeral_Ocode__numeral,A),B)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5173,a)].
% 11.28/11.21 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,C)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5174,a)].
% 11.28/11.21 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B),C) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),A)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(5310,a,5175,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Code__Numeral_Ocode__numeral,A,B)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5176,a)].
% 11.28/11.21 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A) != hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),B) | A = B. [resolve(5310,a,5177,a)].
% 11.28/11.21 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),B) | A != B. [resolve(5310,a,5178,a)].
% 11.28/11.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,5179,a)].
% 11.28/11.22 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,5180,a)].
% 11.28/11.22 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5181,a)].
% 11.28/11.22 Derived: hAPP(c_SetInterval_Oord__class_OatMost(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5182,a)].
% 11.28/11.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Code__Numeral_Ocode__numeral,A,B)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5183,a)].
% 11.28/11.22 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5184,a)].
% 11.28/11.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(c_SetInterval_Oord__class_OatLeast(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Code__Numeral_Ocode__numeral,A,B)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5185,a)].
% 11.28/11.22 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(A,f269(B,A,tc_Code__Numeral_Ocode__numeral))),hAPP(A,f270(B,A,tc_Code__Numeral_Ocode__numeral))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),f269(B,A,tc_Code__Numeral_Ocode__numeral)),f270(B,A,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(c_Set_Oimage(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,A),B)) = hAPP(A,c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5186,a)].
% 11.28/11.22 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(A,f271(B,A,tc_Code__Numeral_Ocode__numeral))),hAPP(A,f272(B,A,tc_Code__Numeral_Ocode__numeral))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),f271(B,A,tc_Code__Numeral_Ocode__numeral)),f272(B,A,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(c_Set_Oimage(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,A),B)) = hAPP(A,c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5187,a)].
% 11.28/11.22 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(A,f273(B,A,tc_Code__Numeral_Ocode__numeral))),hAPP(A,f274(B,A,tc_Code__Numeral_Ocode__numeral))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),f273(B,A,tc_Code__Numeral_Ocode__numeral)),f274(B,A,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(c_Set_Oimage(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,A),B)) = hAPP(A,c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,B)). [resolve(5310,a,5188,a)].
% 11.28/11.22 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(A,f275(B,A,tc_Code__Numeral_Ocode__numeral))),hAPP(A,f276(B,A,tc_Code__Numeral_Ocode__numeral))) != hAPP(A,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),f275(B,A,tc_Code__Numeral_Ocode__numeral)),f276(B,A,tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(c_Set_Oimage(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,A),B)) = hAPP(A,c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,B)). [resolve(5310,a,5189,a)].
% 11.28/11.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(c_Set_OCollect(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),c_COMBS(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBS(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_fconj))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral)),c_fequal))),c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral)))))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_fconj),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Code__Numeral_Ocode__numeral)),A)))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Code__Numeral_Ocode__numeral)),B))))))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5190,a)].
% 11.28/11.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(c_Set_OCollect(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBS(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_fconj)),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B))))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Code__Numeral_Ocode__numeral)),A))))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5191,a)].
% 11.28/11.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(c_Set_OCollect(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBS(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_fconj)),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B))))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Code__Numeral_Ocode__numeral)),A))))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5192,a)].
% 11.28/11.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(c_Set_OCollect(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),c_COMBS(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBS(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_fconj))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral)),c_fequal))),c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)))))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_fconj),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Code__Numeral_Ocode__numeral)),A)))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Code__Numeral_Ocode__numeral)),B))))))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A)),c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5193,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f354(B,C,A,tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),B),A)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(5310,a,5194,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),f354(B,C,A,tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral)),B),A)),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(5310,a,5195,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f355(B,A,tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A) = B. [resolve(5310,a,5196,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),f355(B,A,tc_Code__Numeral_Ocode__numeral)),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A) = B. [resolve(5310,a,5197,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))))) = c_List_Oremove1(tc_Code__Numeral_Ocode__numeral,B,c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5198,a)].
% 11.28/11.23 Derived: c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))) = c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral). [resolve(5310,a,5199,a)].
% 11.28/11.23 Derived: c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B))) = hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B). [resolve(5310,a,5200,a)].
% 11.28/11.23 Derived: c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B))) = hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B). [resolve(5310,a,5201,a)].
% 11.28/11.23 Derived: c_Big__Operators_Olattice_OInf__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B))) = hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),B). [resolve(5310,a,5202,a)].
% 11.28/11.23 Derived: c_Big__Operators_Olattice_OSup__fin(tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B))) = hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),B). [resolve(5310,a,5203,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),B),c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))). [resolve(5310,a,5204,a)].
% 11.28/11.23 Derived: hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),c_List_Olist_ONil(A)) = hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)). [resolve(5310,a,5205,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(A,B)),hAPP(A,C))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Code__Numeral_Ocode__numeral,A),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)) = hAPP(hAPP(c_List_Olist_OCons(D),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)). [resolve(5310,a,5206,a)].
% 11.28/11.23 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(A,B)),hAPP(A,C))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Code__Numeral_Ocode__numeral,A),B),hAPP(hAPP(c_List_Olist_OCons(D),C),E)) = hAPP(hAPP(c_List_Olist_OCons(D),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Code__Numeral_Ocode__numeral,A),B),E)). [resolve(5310,a,5207,a)].
% 11.28/11.23 Derived: hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),D)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),D)). [resolve(5310,a,5208,a)].
% 11.28/11.23 Derived: hAPP(A,B) = hAPP(A,C) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Code__Numeral_Ocode__numeral,A),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Code__Numeral_Ocode__numeral,A),C),E)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Code__Numeral_Ocode__numeral,A),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Code__Numeral_Ocode__numeral,A),B),E)). [resolve(5310,a,5209,a)].
% 11.28/11.23 Derived: hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),B),C)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),A),C)). [resolve(5310,a,5210,a)].
% 11.28/11.23 Derived: c_Finite__Set_Ofun__left__comm(tc_Code__Numeral_Ocode__numeral,tc_List_Olist(tc_Code__Numeral_Ocode__numeral),c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,5211,a)].
% 11.28/11.23 Derived: hAPP(c_List_Oset(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),D)) = hAPP(hAPP(c_Set_Oinsert(A),C),hAPP(c_List_Oset(A),D)). [resolve(5310,a,5212,a)].
% 11.28/11.23 Derived: c_List_Oremove1(tc_Code__Numeral_Ocode__numeral,A,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),A),B)) = B. [resolve(5310,a,5213,a)].
% 11.28/11.23 Derived: c_List_Olist_ONil(A) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),D). [resolve(5310,a,5214,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),D))) | -hBOOL(hAPP(hAPP(c_member(A),C),hAPP(c_List_Oset(A),D))). [resolve(5310,a,5215,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),D))) | hBOOL(hAPP(c_List_Odistinct(A),D)). [resolve(5310,a,5216,a)].
% 11.28/11.23 Derived: hBOOL(hAPP(c_List_Odistinct(A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),D))) | hBOOL(hAPP(hAPP(c_member(A),C),hAPP(c_List_Oset(A),D))) | -hBOOL(hAPP(c_List_Odistinct(A),D)). [resolve(5310,a,5217,a)].
% 11.28/11.23 Derived: hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(A,B)),hAPP(c_Set_Oimage(C,tc_Code__Numeral_Ocode__numeral,A),hAPP(c_List_Oset(C),D)))) | c_List_Olinorder__class_Oinsort__insert__key(C,tc_Code__Numeral_Ocode__numeral,A,B,D) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(C,tc_Code__Numeral_Ocode__numeral,A),B),D). [resolve(5310,a,5218,a)].
% 11.28/11.23 Derived: hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))) | c_List_Olinorder__class_Oinsort__insert__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral),A,B) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),A),B). [resolve(5310,a,5219,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(c_List_Odistinct(A),B)) | hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Oinsort__insert__key(A,tc_Code__Numeral_Ocode__numeral,C,D,B))). [resolve(5310,a,5220,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))) | c_List_Olinorder__class_Oinsort__insert__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral),A,B) = B. [resolve(5310,a,5221,a)].
% 11.28/11.23 Derived: hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),c_List_Olinorder__class_Oinsort__insert__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral),A,B)) = hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5310,a,5222,a)].
% 11.28/11.23 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(A,B)),hAPP(c_Set_Oimage(C,tc_Code__Numeral_Ocode__numeral,A),hAPP(c_List_Oset(C),D)))) | c_List_Olinorder__class_Oinsort__insert__key(C,tc_Code__Numeral_Ocode__numeral,A,B,D) = D. [resolve(5310,a,5223,a)].
% 11.28/11.23 Derived: c_List_Olinorder__class_Osort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral),c_List_Oremdups(tc_Code__Numeral_Ocode__numeral,A)) = c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5224,a)].
% 11.28/11.23 Derived: c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,c_List_Olist_ONil(A)) = c_List_Olist_ONil(A). [resolve(5310,a,5225,a)].
% 11.28/11.24 Derived: hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,C)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C). [resolve(5310,a,5226,a)].
% 11.28/11.24 Derived: hAPP(c_List_Oset(A),c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,C)) = hAPP(c_List_Oset(A),C). [resolve(5310,a,5227,a)].
% 11.28/11.24 Derived: -hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,C))) | hBOOL(hAPP(c_List_Odistinct(A),C)). [resolve(5310,a,5228,a)].
% 11.28/11.24 Derived: hBOOL(hAPP(c_List_Odistinct(A),c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,C))) | -hBOOL(hAPP(c_List_Odistinct(A),C)). [resolve(5310,a,5229,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(5310,a,5230,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_List_Ofoldl(tc_List_Olist(tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_List_Olist(tc_Code__Numeral_Ocode__numeral),tc_List_Olist(tc_Code__Numeral_Ocode__numeral)),c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral))),c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral)),A). [resolve(5310,a,5231,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,hAPP(c_List_Ofilter(A,C),D)) = hAPP(c_List_Ofilter(A,C),c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,D)). [resolve(5310,a,5232,a)].
% 11.28/11.24 Derived: hBOOL(hAPP(A,B)) | hAPP(c_List_Ofilter(C,A),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(C,tc_Code__Numeral_Ocode__numeral,D),B),E)) = hAPP(c_List_Ofilter(C,A),E). [resolve(5310,a,5233,a)].
% 11.28/11.24 Derived: -hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),D),C)) | hAPP(c_List_Ohd(A),hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,A),hAPP(c_fequal,hAPP(D,B))),D)),C)) != B | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,D),B),c_List_Oremove1(A,B,C)) = C. [resolve(5310,a,5234,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral)). [resolve(5310,a,5235,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,5236,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_Olinorder__class_Osort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5237,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_Olinorder__class_Oinsort__insert__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral),B,A)). [resolve(5310,a,5238,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Odrop(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,5239,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Otake(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(5310,a,5240,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_Oremove1(tc_Code__Numeral_Ocode__numeral,B,A)). [resolve(5310,a,5241,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Otl(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5310,a,5242,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),A),B)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B). [resolve(5310,a,5243,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),A),B)) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B). [resolve(5310,a,5244,a)].
% 11.28/11.24 Derived: c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral) = A | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_Obutlast(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5245,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,5247,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),B),C))) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,5248,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5310,a,5249,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_Oremdups(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5251,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | -hBOOL(hAPP(c_List_Odistinct(tc_Code__Numeral_Ocode__numeral),A)) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | -hBOOL(hAPP(c_List_Odistinct(tc_Code__Numeral_Ocode__numeral),B)) | hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),A) != hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B) | A = B. [resolve(5310,a,5252,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),c_List_Olinorder__class_Osort__key(A,tc_Code__Numeral_Ocode__numeral,B,C))). [resolve(5310,a,5253,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),C)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),c_List_Olinorder__class_Oinsort__insert__key(A,tc_Code__Numeral_Ocode__numeral,B,D,C))). [resolve(5310,a,5254,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),C)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),c_List_Oremove1(A,D,C))). [resolve(5310,a,5255,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),D))) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),D)). [resolve(5310,a,5256,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),C),D))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),D)). [resolve(5310,a,5257,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),A),c_fequal),B)),hAPP(C,D))),D))). [resolve(5310,a,5258,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),C)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),hAPP(c_List_Ofilter(A,D),C))). [resolve(5310,a,5259,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Ofilter(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),c_fequal),hAPP(A,B))),B)). [resolve(5310,a,5260,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B). [resolve(5310,a,5261,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),C),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5310,a,5262,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f448(B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))). [resolve(5310,a,5263,a)].
% 11.28/11.24 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),f448(B,A,tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,5264,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Oappend(tc_Code__Numeral_Ocode__numeral),A),B)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A). [resolve(5310,a,5265,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Oappend(tc_Code__Numeral_Ocode__numeral),A),B)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B). [resolve(5310,a,5266,a)].
% 11.28/11.24 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Oappend(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),C),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),A))) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),D),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),D)). [resolve(5310,a,5267,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Oappend(tc_Code__Numeral_Ocode__numeral),A),B)) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f449(B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),A))). [resolve(5310,a,5268,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Oappend(tc_Code__Numeral_Ocode__numeral),A),B)) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f450(B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))). [resolve(5310,a,5269,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Oappend(tc_Code__Numeral_Ocode__numeral),A),B)) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),f449(B,A,tc_Code__Numeral_Ocode__numeral)),f450(B,A,tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,5270,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),C)) | -hBOOL(hAPP(D,E)) | hAPP(c_List_Ofilter(A,D),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),E),C)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,B),E),hAPP(c_List_Ofilter(A,D),C)). [resolve(5310,a,5271,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f451(B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B). [resolve(5310,a,5274,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),f451(B,A,tc_Code__Numeral_Ocode__numeral))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B). [resolve(5310,a,5275,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,A)) = A. [resolve(5310,a,5276,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,A)). [resolve(5310,a,5277,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hBOOL(hAPP(c_List_Odistinct(tc_Code__Numeral_Ocode__numeral),c_List_Olinorder__class_Osorted__list__of__set(tc_Code__Numeral_Ocode__numeral,A))). [resolve(5310,a,5278,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_COMBI(tc_Code__Numeral_Ocode__numeral)),A),c_List_Oremove1(tc_Code__Numeral_Ocode__numeral,A,B)) = B. [resolve(5310,a,5279,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Code__Numeral_Ocode__numeral)),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),C))). [resolve(5310,a,5280,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f452(A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Code__Numeral_Ocode__numeral)),A))). [resolve(5310,a,5282,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f453(A,tc_Code__Numeral_Ocode__numeral)),f452(A,tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,5283,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),f453(A,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),f452(A,tc_Code__Numeral_Ocode__numeral)))). [resolve(5310,a,5284,a)].
% 11.28/11.25 Derived: -c_Fun_Oinj__on(A,tc_Code__Numeral_Ocode__numeral,B,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),hAPP(c_List_Oset(A),C)),hAPP(c_List_Oset(A),D))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),C)) | -hBOOL(hAPP(c_List_Odistinct(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),C))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),D)) | -hBOOL(hAPP(c_List_Odistinct(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),D))) | hAPP(c_List_Oset(A),C) != hAPP(c_List_Oset(A),D) | C = D. [resolve(5310,a,5285,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Orev(tc_Code__Numeral_Ocode__numeral),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Code__Numeral_Ocode__numeral)),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5310,a,5286,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Orev(tc_Code__Numeral_Ocode__numeral),A)) | c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral) != A | c_List_Ofoldr(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A,B) = B. [resolve(5310,a,5287,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Orev(tc_Code__Numeral_Ocode__numeral),A)) | c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral) = A | c_List_Ofoldr(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A,B) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B). [resolve(5310,a,5288,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_OtakeWhile(tc_Code__Numeral_Ocode__numeral,B,A)). [resolve(5310,a,5289,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(c_List_Orev(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),C))) | c_List_OtakeWhile(A,hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,A),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),D)),B),C) = hAPP(c_List_Ofilter(A,hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,A),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),D)),B)),C). [resolve(5310,a,5290,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,c_List_OdropWhile(tc_Code__Numeral_Ocode__numeral,B,A)). [resolve(5310,a,5291,a)].
% 11.28/11.25 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),f457(A,tc_Code__Numeral_Ocode__numeral)),f458(A,tc_Code__Numeral_Ocode__numeral))) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A). [resolve(5310,a,5292,a)].
% 11.28/11.25 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),f458(A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Code__Numeral_Ocode__numeral)),A))) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A). [resolve(5310,a,5293,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),f457(A,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A),f458(A,tc_Code__Numeral_Ocode__numeral)))) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A). [resolve(5310,a,5294,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),f463(A,tc_Code__Numeral_Ocode__numeral)),f462(A,tc_Code__Numeral_Ocode__numeral)) = A. [resolve(5310,a,5295,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral) = A | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),f462(A,tc_Code__Numeral_Ocode__numeral)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),f463(A,tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5310,a,5296,a)].
% 11.28/11.25 Derived: -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral) = A | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,f462(A,tc_Code__Numeral_Ocode__numeral)). [resolve(5310,a,5297,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral) != A. [resolve(5310,a,5298,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),B),C) != A | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f464(A,tc_Code__Numeral_Ocode__numeral,C,B)),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),C))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,C). [resolve(5310,a,5299,a)].
% 11.28/11.25 Derived: c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,A) | hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),B),C) != A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),f464(A,tc_Code__Numeral_Ocode__numeral,C,B))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,C). [resolve(5310,a,5300,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),f473(A,tc_Code__Numeral_Ocode__numeral)) = A. [resolve(5310,a,5301,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,f473(A,tc_Code__Numeral_Ocode__numeral)). [resolve(5310,a,5302,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hBOOL(hAPP(c_List_Odistinct(tc_Code__Numeral_Ocode__numeral),f473(A,tc_Code__Numeral_Ocode__numeral))). [resolve(5310,a,5303,a)].
% 11.28/11.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B) != A | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | -hBOOL(hAPP(c_List_Odistinct(tc_Code__Numeral_Ocode__numeral),B)) | B = f473(A,tc_Code__Numeral_Ocode__numeral). [resolve(5310,a,5304,a)].
% 13.61/13.52 Derived: hBOOL(hAPP(hAPP(c_member(A),f475(B,C,D,A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(A),D))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,tc_Code__Numeral_Ocode__numeral,C),B),D) = hAPP(hAPP(c_List_Olist_OCons(A),B),D). [resolve(5310,a,5305,a)].
% 13.61/13.52 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(A,B)),hAPP(A,f475(B,A,C,D,tc_Code__Numeral_Ocode__numeral)))) | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,tc_Code__Numeral_Ocode__numeral,A),B),C) = hAPP(hAPP(c_List_Olist_OCons(D),B),C). [resolve(5310,a,5306,a)].
% 13.61/13.52 Derived: hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),f485(A,B,tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),B))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,5307,a)].
% 13.61/13.52 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),f485(A,B,tc_Code__Numeral_Ocode__numeral))) | -c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,B) | c_List_Olinorder__class_Osorted(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5310,a,5308,a)].
% 13.61/13.52 5311 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__bot(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__bot) # label(axiom). [clausify(4858)].
% 13.61/13.52 5312 -class_Lattices_Obounded__lattice__bot(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),c_Orderings_Obot__class_Obot(A)),B) = B # label(fact_sup__bot__left) # label(axiom). [clausify(120)].
% 13.61/13.52 5313 -class_Lattices_Obounded__lattice__bot(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),c_Orderings_Obot__class_Obot(A)) = B # label(fact_sup__bot__right) # label(axiom). [clausify(121)].
% 13.61/13.52 5314 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) | c_Orderings_Obot__class_Obot(A) = B # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(122)].
% 13.61/13.52 5315 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) | c_Orderings_Obot__class_Obot(A) = C # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(122)].
% 13.61/13.52 5316 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),C) | c_Orderings_Obot__class_Obot(A) != B | c_Orderings_Obot__class_Obot(A) != C # label(fact_sup__eq__bot__iff) # label(axiom). [clausify(122)].
% 13.61/13.52 5317 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),c_Orderings_Obot__class_Obot(A)),B) # label(fact_inf__bot__left) # label(axiom). [clausify(325)].
% 13.61/13.52 5318 -class_Lattices_Obounded__lattice__bot(A) | c_Orderings_Obot__class_Obot(A) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),c_Orderings_Obot__class_Obot(A)) # label(fact_inf__bot__right) # label(axiom). [clausify(326)].
% 13.61/13.52 Derived: -class_Lattices_Obounded__lattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),c_Orderings_Obot__class_Obot(tc_fun(B,A))),C) = C. [resolve(5311,b,5312,a)].
% 13.61/13.52 Derived: -class_Lattices_Obounded__lattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),c_Orderings_Obot__class_Obot(tc_fun(B,A))) = C. [resolve(5311,b,5313,a)].
% 13.61/13.52 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = C. [resolve(5311,b,5314,a)].
% 13.61/13.52 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = D. [resolve(5311,b,5315,a)].
% 17.79/17.72 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),D) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != C | c_Orderings_Obot__class_Obot(tc_fun(B,A)) != D. [resolve(5311,b,5316,a)].
% 17.79/17.72 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),c_Orderings_Obot__class_Obot(tc_fun(B,A))),C). [resolve(5311,b,5317,a)].
% 17.79/17.72 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Obot__class_Obot(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),c_Orderings_Obot__class_Obot(tc_fun(B,A))). [resolve(5311,b,5318,a)].
% 17.79/17.72 5319 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__bot) # label(axiom). [assumption].
% 17.79/17.72 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),A) = A. [resolve(5319,a,5312,a)].
% 17.79/17.72 Derived: hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = A. [resolve(5319,a,5313,a)].
% 17.79/17.72 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) = A. [resolve(5319,a,5314,a)].
% 17.79/17.72 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) = B. [resolve(5319,a,5315,a)].
% 17.79/17.72 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),B) | c_Orderings_Obot__class_Obot(tc_HOL_Obool) != A | c_Orderings_Obot__class_Obot(tc_HOL_Obool) != B. [resolve(5319,a,5316,a)].
% 17.79/17.72 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),A). [resolve(5319,a,5317,a)].
% 17.79/17.72 Derived: c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),c_Orderings_Obot__class_Obot(tc_HOL_Obool)). [resolve(5319,a,5318,a)].
% 17.79/17.72 5320 class_Groups_Oordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add) # label(axiom). [assumption].
% 17.79/17.72 5321 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(224)].
% 17.79/17.72 5322 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_diff__eq__diff__less__eq) # label(axiom). [clausify(224)].
% 17.79/17.72 5323 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(370)].
% 17.79/17.72 5324 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_diff__eq__diff__less) # label(axiom). [clausify(370)].
% 17.79/17.72 5325 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)),C) # label(fact_min__diff__distrib__left) # label(axiom). [clausify(637)].
% 17.79/17.72 5326 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(960)].
% 17.79/17.72 5327 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__iff__diff__le__0) # label(axiom). [clausify(960)].
% 17.79/17.72 5328 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(961)].
% 17.79/17.72 5329 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__iff__diff__less__0) # label(axiom). [clausify(961)].
% 17.79/17.72 5330 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_le__imp__neg__le) # label(axiom). [clausify(1502)].
% 17.79/17.72 5331 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_neg__le__iff__le) # label(axiom). [clausify(1503)].
% 17.79/17.72 5332 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),B)) # label(fact_neg__le__iff__le) # label(axiom). [clausify(1503)].
% 17.79/17.72 5333 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B)) # label(fact_minus__le__iff) # label(axiom). [clausify(1504)].
% 17.79/17.72 5334 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B)) # label(fact_minus__le__iff) # label(axiom). [clausify(1504)].
% 17.79/17.72 5335 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_le__minus__iff) # label(axiom). [clausify(1505)].
% 17.79/17.72 5336 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_le__minus__iff) # label(axiom). [clausify(1505)].
% 17.79/17.72 5337 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_less__minus__iff) # label(axiom). [clausify(1511)].
% 17.79/17.72 5338 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) # label(fact_less__minus__iff) # label(axiom). [clausify(1511)].
% 17.79/17.72 5339 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B)) # label(fact_minus__less__iff) # label(axiom). [clausify(1512)].
% 17.79/17.72 5340 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B)) # label(fact_minus__less__iff) # label(axiom). [clausify(1512)].
% 17.79/17.72 5341 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_neg__less__iff__less) # label(axiom). [clausify(1513)].
% 17.79/17.72 5342 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) # label(fact_neg__less__iff__less) # label(axiom). [clausify(1513)].
% 17.79/17.72 5343 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(1557)].
% 17.79/17.72 5344 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_neg__0__le__iff__le) # label(axiom). [clausify(1557)].
% 17.79/17.72 5345 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(1559)].
% 17.79/17.72 5346 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__le__0__iff__le) # label(axiom). [clausify(1559)].
% 17.79/17.72 5347 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(1562)].
% 17.79/17.72 5348 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_neg__0__less__iff__less) # label(axiom). [clausify(1562)].
% 17.79/17.72 5349 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(1563)].
% 17.79/17.72 5350 -class_Groups_Oordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__less__0__iff__less) # label(axiom). [clausify(1563)].
% 17.79/17.72 5351 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),f181(D,E,C,B,A)),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(E,D) # label(fact_setsum__nonneg__0) # label(axiom). [clausify(2460)].
% 17.79/17.72 5352 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(D,f181(E,D,C,B,A)))) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C) | -hBOOL(hAPP(hAPP(c_member(B),E),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(D,E) # label(fact_setsum__nonneg__0) # label(axiom). [clausify(2460)].
% 17.79/17.72 5353 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),f182(D,E,F,C,B,A)),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),F),C) != E | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(F,D)),E)) # label(fact_setsum__nonneg__leq__bound) # label(axiom). [clausify(2461)].
% 17.79/17.72 5354 -class_Groups_Oordered__ab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(D,f182(E,F,D,C,B,A)))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C) != F | -hBOOL(hAPP(hAPP(c_member(B),E),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(D,E)),F)) # label(fact_setsum__nonneg__leq__bound) # label(axiom). [clausify(2461)].
% 17.79/17.72 5355 -class_Groups_Oordered__ab__group__add(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),C) # label(fact_max__diff__distrib__left) # label(axiom). [clausify(2483)].
% 17.79/17.72 5356 -class_Groups_Oordered__ab__group__add(A) | c_Fun_Oinj__on(A,A,c_Groups_Ouminus__class_Ouminus(A),B) # label(fact_inj__uminus) # label(axiom). [clausify(2856)].
% 17.79/17.72 5357 -class_Groups_Oordered__ab__group__add(A) | hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),hAPP(c_SetInterval_Oord__class_OatLeast(A),B)) = hAPP(c_SetInterval_Oord__class_OatMost(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) # label(fact_image__uminus__atLeast) # label(axiom). [clausify(2904)].
% 17.79/17.72 5358 -class_Groups_Oordered__ab__group__add(A) | hAPP(c_SetInterval_Oord__class_OatLeast(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) = hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),hAPP(c_SetInterval_Oord__class_OatMost(A),B)) # label(fact_image__uminus__atMost) # label(axiom). [clausify(2905)].
% 17.79/17.72 5359 -class_Groups_Oordered__ab__group__add(A) | c_SetInterval_Oord__class_OatLeastAtMost(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),c_SetInterval_Oord__class_OatLeastAtMost(A,C,B)) # label(fact_image__uminus__atLeastAtMost) # label(axiom). [clausify(2937)].
% 17.79/17.72 5360 -class_Groups_Oordered__ab__group__add(A) | c_SetInterval_Oord__class_OgreaterThanLessThan(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,B)) # label(fact_image__uminus__greaterThanLessThan) # label(axiom). [clausify(2945)].
% 17.79/17.72 5361 -class_Groups_Oordered__ab__group__add(A) | hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) # label(fact_image__uminus__greaterThanAtMost) # label(axiom). [clausify(2978)].
% 17.79/17.72 5362 -class_Groups_Oordered__ab__group__add(A) | c_SetInterval_Oord__class_OgreaterThanAtMost(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),B)) # label(fact_image__uminus__atLeastLessThan) # label(axiom). [clausify(2979)].
% 17.79/17.72 5363 -class_Groups_Oordered__ab__group__add(A) | hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),hAPP(c_SetInterval_Oord__class_OgreaterThan(A),B)) = hAPP(c_SetInterval_Oord__class_OlessThan(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) # label(fact_image__uminus__greaterThan) # label(axiom). [clausify(3041)].
% 17.79/17.72 5364 -class_Groups_Oordered__ab__group__add(A) | hAPP(c_SetInterval_Oord__class_OgreaterThan(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) = hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),hAPP(c_SetInterval_Oord__class_OlessThan(A),B)) # label(fact_image__uminus__lessThan) # label(axiom). [clausify(3042)].
% 17.79/17.72 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(5320,a,5321,a)].
% 17.79/17.72 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(5320,a,5322,a)].
% 17.79/17.72 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(5320,a,5323,a)].
% 17.79/17.72 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(5320,a,5324,a)].
% 17.79/17.72 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),C)),B). [resolve(5320,a,5325,a)].
% 17.79/17.72 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5320,a,5326,a)].
% 17.79/17.72 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5320,a,5327,a)].
% 17.79/17.72 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5320,a,5328,a)].
% 17.79/17.72 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5320,a,5329,a)].
% 17.79/17.72 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))). [resolve(5320,a,5330,a)].
% 17.79/17.72 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),A)). [resolve(5320,a,5331,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),A)). [resolve(5320,a,5333,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))). [resolve(5320,a,5335,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))). [resolve(5320,a,5337,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),A)). [resolve(5320,a,5339,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(5320,a,5341,a)].
% 17.79/17.73 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(5320,a,5342,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5320,a,5343,a)].
% 17.79/17.73 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5320,a,5344,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5320,a,5345,a)].
% 17.79/17.73 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5320,a,5346,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5320,a,5347,a)].
% 17.79/17.73 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5320,a,5348,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5320,a,5349,a)].
% 17.79/17.73 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5320,a,5350,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f181(C,D,B,A,tc_Int_Oint)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(D,C). [resolve(5320,a,5351,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(C,f181(D,C,B,A,tc_Int_Oint)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),B) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(C,D). [resolve(5320,a,5352,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f182(C,D,E,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),E),B) != D | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(E,C)),D)). [resolve(5320,a,5353,a)].
% 17.79/17.73 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(C,f182(D,E,C,B,A,tc_Int_Oint)))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),B) != E | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(C,D)),E)). [resolve(5320,a,5354,a)].
% 17.79/17.73 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)),B). [resolve(5320,a,5355,a)].
% 17.79/17.73 Derived: c_Fun_Oinj__on(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A). [resolve(5320,a,5356,a)].
% 17.79/17.73 Derived: hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),A)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(5320,a,5357,a)].
% 17.79/17.73 Derived: hAPP(c_SetInterval_Oord__class_OatLeast(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Int_Oint),A)). [resolve(5320,a,5358,a)].
% 17.79/17.73 Derived: c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,B,A)). [resolve(5320,a,5359,a)].
% 17.79/17.73 Derived: c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,B,A)). [resolve(5320,a,5360,a)].
% 17.79/17.73 Derived: hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,A,B)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(5320,a,5361,a)].
% 17.79/17.73 Derived: c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,B),A)). [resolve(5320,a,5362,a)].
% 22.10/22.04 Derived: hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),A)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(5320,a,5363,a)].
% 22.10/22.04 Derived: hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Int_Oint),A)). [resolve(5320,a,5364,a)].
% 22.10/22.04 5365 class_Groups_Oab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__group__add) # label(axiom). [assumption].
% 22.10/22.04 5366 -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | E != D | B = C # label(fact_diff__eq__diff__eq) # label(axiom). [clausify(235)].
% 22.10/22.04 5367 -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E) | E = D | B != C # label(fact_diff__eq__diff__eq) # label(axiom). [clausify(235)].
% 22.10/22.04 5368 -class_Groups_Oab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),hAPP(hAPP(c_Set_Oinsert(B),D),c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(E,D)) # label(fact_setsum__diff1) # label(axiom). [clausify(247)].
% 22.10/22.04 5369 -class_Groups_Oab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),hAPP(hAPP(c_Set_Oinsert(B),D),c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) # label(fact_setsum__diff1) # label(axiom). [clausify(247)].
% 22.10/22.04 5370 -class_Groups_Oab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)) # label(fact_setsum__diff) # label(axiom). [clausify(407)].
% 22.10/22.04 5371 -class_Groups_Oab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),D)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,tc_HOL_Obool)),C),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,tc_HOL_Obool)),C),D))) # label(fact_setsum__Un) # label(axiom). [clausify(470)].
% 22.10/22.04 5372 -class_Groups_Oab__group__add(A) | B != C | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B) # label(fact_eq__iff__diff__eq__0) # label(axiom). [clausify(870)].
% 22.10/22.04 5373 -class_Groups_Oab__group__add(A) | B = C | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B) # label(fact_eq__iff__diff__eq__0) # label(axiom). [clausify(870)].
% 22.10/22.04 5374 -class_Groups_Oab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_minus__add__distrib) # label(axiom). [clausify(1514)].
% 22.10/22.05 5375 -class_Groups_Oab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B) # label(fact_minus__diff__eq) # label(axiom). [clausify(1523)].
% 22.10/22.05 5376 -class_Groups_Oab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B) # label(fact_ab__left__minus) # label(axiom). [clausify(1568)].
% 22.10/22.05 5377 -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) # label(fact_ab__diff__minus) # label(axiom). [clausify(1573)].
% 22.10/22.05 5378 -class_Groups_Oab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBB(A,A,B),c_Groups_Ouminus__class_Ouminus(A)),C)),D) # label(fact_setsum__negf) # label(axiom). [clausify(2276)].
% 22.10/22.05 5379 -class_Groups_Oab__group__add(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Ominus__class_Ominus(A)),C)),D)),E) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),E)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),E)) # label(fact_setsum__subtractf) # label(axiom). [clausify(2295)].
% 22.10/22.05 5380 -class_Groups_Oab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(hAPP(c_COMBS(tc_Nat_Onat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(A)),D)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat),D),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(D,B)),hAPP(D,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) # label(fact_setsum__natinterval__difff) # label(axiom). [clausify(2558)].
% 22.10/22.05 5381 -class_Groups_Oab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(hAPP(c_COMBS(tc_Nat_Onat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(A)),D)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat),D),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)) # label(fact_setsum__natinterval__difff) # label(axiom). [clausify(2558)].
% 22.10/22.05 5382 -class_Groups_Oab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),E),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),E),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),D))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),E),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C))) # label(fact_setsum__diff__nat__ivl) # label(axiom). [clausify(2837)].
% 22.10/22.05 5383 -class_Groups_Oab__group__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Ominus__class_Ominus(A)),C)),D)),E)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),C),E))),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),D),E))) # label(fact_listsum__subtractf) # label(axiom). [clausify(4069)].
% 22.10/22.05 5384 -class_Groups_Oab__group__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),hAPP(c_Fun_Ocomp(A,A,B,c_Groups_Ouminus__class_Ouminus(A)),C)),D)) = hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),C),D))) # label(fact_uminus__listsum__map) # label(axiom). [clausify(4093)].
% 22.10/22.05 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | D != C | A = B. [resolve(5365,a,5366,a)].
% 22.10/22.05 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),D) | D = C | A != B. [resolve(5365,a,5367,a)].
% 22.10/22.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(D,C)). [resolve(5365,a,5368,a)].
% 22.10/22.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B). [resolve(5365,a,5369,a)].
% 22.10/22.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)). [resolve(5365,a,5370,a)].
% 22.10/22.05 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))). [resolve(5365,a,5371,a)].
% 22.10/22.05 Derived: A != B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),A). [resolve(5365,a,5372,a)].
% 22.10/22.05 Derived: A = B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),A). [resolve(5365,a,5373,a)].
% 22.10/22.05 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(5365,a,5374,a)].
% 22.10/22.05 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),A). [resolve(5365,a,5375,a)].
% 22.10/22.05 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),A). [resolve(5365,a,5376,a)].
% 22.10/22.05 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B). [resolve(5365,a,5377,a)].
% 22.10/22.05 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),B)),C). [resolve(5365,a,5378,a)].
% 22.10/22.05 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),B)),C)),D) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),D)). [resolve(5365,a,5379,a)].
% 22.10/22.05 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),C)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Nat_Onat),C),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(C,A)),hAPP(C,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). [resolve(5365,a,5380,a)].
% 22.10/22.05 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),C)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Nat_Onat),C),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)). [resolve(5365,a,5381,a)].
% 22.10/22.05 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),C))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B))). [resolve(5365,a,5382,a)].
% 22.10/22.05 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),B)),C)),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),C),D))). [resolve(5365,a,5383,a)].
% 22.10/22.05 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),B)),C)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),C))). [resolve(5365,a,5384,a)].
% 24.28/24.19 5385 class_Rings_Oring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring) # label(axiom). [assumption].
% 24.28/24.19 5386 -class_Rings_Oring(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),hAPP(hAPP(c_Set_Oinsert(B),D),c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(E,D)) # label(fact_setsum__diff1__ring) # label(axiom). [clausify(246)].
% 24.28/24.19 5387 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D) = F # label(fact_eq__add__iff2) # label(axiom). [clausify(476)].
% 24.28/24.19 5388 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D) != F # label(fact_eq__add__iff2) # label(axiom). [clausify(476)].
% 24.28/24.19 5389 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F) = D # label(fact_eq__add__iff1) # label(axiom). [clausify(477)].
% 24.28/24.19 5390 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F) != D # label(fact_eq__add__iff1) # label(axiom). [clausify(477)].
% 24.28/24.19 5391 -class_Int_Onumber(A) | -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),D)) # label(fact_right__diff__distrib__number__of) # label(axiom). [clausify(1172)].
% 24.28/24.19 5392 -class_Int_Onumber(A) | -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),hAPP(c_Int_Onumber__class_Onumber__of(A),D)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Int_Onumber__class_Onumber__of(A),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(c_Int_Onumber__class_Onumber__of(A),D))) # label(fact_left__diff__distrib__number__of) # label(axiom). [clausify(1173)].
% 24.28/24.19 5393 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) # label(fact_minus__mult__minus) # label(axiom). [clausify(1519)].
% 24.28/24.19 5394 -class_Rings_Oring(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_minus__mult__commute) # label(axiom). [clausify(1520)].
% 24.28/24.20 5395 -class_Rings_Oring(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C) # label(fact_minus__mult__left) # label(axiom). [clausify(1521)].
% 24.28/24.20 5396 -class_Rings_Oring(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_minus__mult__right) # label(axiom). [clausify(1522)].
% 24.28/24.20 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) = E. [resolve(5385,a,5387,a)].
% 24.28/24.20 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) != E. [resolve(5385,a,5388,a)].
% 24.28/24.20 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E) = C. [resolve(5385,a,5389,a)].
% 24.28/24.20 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E) != C. [resolve(5385,a,5390,a)].
% 24.28/24.20 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),C)). [resolve(5385,a,5391,b)].
% 24.28/24.20 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),C))). [resolve(5385,a,5392,b)].
% 24.28/24.20 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B). [resolve(5385,a,5393,a)].
% 24.28/24.20 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(5385,a,5394,a)].
% 24.28/24.20 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B). [resolve(5385,a,5395,a)].
% 26.25/26.20 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(5385,a,5396,a)].
% 26.25/26.20 5397 class_Groups_Oab__semigroup__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 26.25/26.20 5398 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,A,c_Groups_Otimes__class_Otimes(A),B,C),D)) | -hBOOL(hAPP(hAPP(c_member(A),E),C)) | hBOOL(hAPP(hAPP(c_member(A),B),C)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,A,c_Groups_Otimes__class_Otimes(A),E,hAPP(hAPP(c_Set_Oinsert(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),C),hAPP(hAPP(c_Set_Oinsert(A),E),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))),D)) # label(fact_fold__graph__permute__diff) # label(axiom). [clausify(248)].
% 26.25/26.20 5399 -class_Groups_Oab__semigroup__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(259)].
% 26.25/26.20 5400 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,A,c_Groups_Otimes__class_Otimes(A),B,C),D)) | hBOOL(hAPP(hAPP(c_member(A),B),C)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(A,A,c_Groups_Otimes__class_Otimes(A),E,hAPP(hAPP(c_Set_Oinsert(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),D))) # label(fact_fold__graph__insert__swap) # label(axiom). [clausify(404)].
% 26.25/26.20 5401 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = C | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | hAPP(c_Finite__Set_Ofold1(A,c_Groups_Otimes__class_Otimes(A)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Finite__Set_Ofold1(A,c_Groups_Otimes__class_Otimes(A)),B)),hAPP(c_Finite__Set_Ofold1(A,c_Groups_Otimes__class_Otimes(A)),C)) # label(fact_fold1__Un) # label(axiom). [clausify(421)].
% 26.25/26.20 5402 -class_Groups_Oab__semigroup__mult(A) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(c_Finite__Set_Ofold1(A,c_Groups_Otimes__class_Otimes(A)),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(c_Finite__Set_Ofold1(A,c_Groups_Otimes__class_Otimes(A)),B)) # label(fact_fold1__insert) # label(axiom). [clausify(423)].
% 26.25/26.20 5403 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),f40(B,A)),f41(B,A))),hAPP(hAPP(c_Set_Oinsert(A),f40(B,A)),hAPP(hAPP(c_Set_Oinsert(A),f41(B,A)),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(A),hAPP(c_Finite__Set_Ofold1(A,c_Groups_Otimes__class_Otimes(A)),B)),B)) # label(fact_fold1__in) # label(axiom). [clausify(479)].
% 26.25/26.20 5404 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(c_Finite__Set_Ofold1(A,c_Groups_Otimes__class_Otimes(A)),hAPP(hAPP(c_Set_Oinsert(A),C),B)) = hAPP(hAPP(c_Finite__Set_Ofold(A,A,c_Groups_Otimes__class_Otimes(A)),C),B) # label(fact_fold1__eq__fold) # label(axiom). [clausify(604)].
% 26.25/26.20 5405 -class_Groups_Oab__semigroup__mult(A) | c_Finite__Set_Ofun__left__comm(A,A,c_Groups_Otimes__class_Otimes(A)) # label(fact_fun__left__comm) # label(axiom). [clausify(700)].
% 26.25/26.20 5406 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(E,D)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Otimes__class_Otimes(A)),E),F),C)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Otimes__class_Otimes(A)),E),F),hAPP(hAPP(c_Set_Oinsert(B),D),C)) # label(fact_fold__image__insert) # label(axiom). [clausify(809)].
% 26.25/26.21 5407 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),f101(D,E,F,C,B,A)),C)) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Otimes__class_Otimes(A)),E),D),C) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Otimes__class_Otimes(A)),F),D),C) # label(fact_fold__image__cong) # label(axiom). [clausify(1152)].
% 26.25/26.21 5408 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(D,f101(E,D,F,C,B,A)) != hAPP(F,f101(E,D,F,C,B,A)) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Otimes__class_Otimes(A)),D),E),C) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Otimes__class_Otimes(A)),F),E),C) # label(fact_fold__image__cong) # label(axiom). [clausify(1152)].
% 26.25/26.21 5409 -class_Groups_Oab__semigroup__mult(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -c_Fun_Oinj__on(B,D,E,C) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,D,c_Groups_Otimes__class_Otimes(A)),F),V6),hAPP(c_Set_Oimage(B,D,E),C)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Otimes__class_Otimes(A)),hAPP(c_Fun_Ocomp(D,A,B,F),E)),V6),C) # label(fact_fold__image__reindex) # label(axiom). [clausify(3415)].
% 26.25/26.21 Derived: -hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Int_Oint,tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint),A,B),C)) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),D),B)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),B)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Int_Oint,tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint),D,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),D),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))),C)). [resolve(5397,a,5398,a)].
% 26.25/26.21 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(5397,a,5399,a)].
% 26.25/26.21 Derived: -hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Int_Oint,tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint),A,B),C)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),B)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Int_Oint,tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint),D,hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),C))). [resolve(5397,a,5400,a)].
% 26.25/26.21 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = B | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B) | hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),A)),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),B)). [resolve(5397,a,5401,a)].
% 26.25/26.21 Derived: c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),A)). [resolve(5397,a,5402,a)].
% 26.30/26.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),f40(A,tc_Int_Oint)),f41(A,tc_Int_Oint))),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),f40(A,tc_Int_Oint)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),f41(A,tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),A)),A)). [resolve(5397,a,5403,a)].
% 26.30/26.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),A)) | hAPP(c_Finite__Set_Ofold1(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Int_Oint,tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),B),A). [resolve(5397,a,5404,a)].
% 26.30/26.22 Derived: c_Finite__Set_Ofun__left__comm(tc_Int_Oint,tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint)). [resolve(5397,a,5405,a)].
% 26.30/26.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(D,C)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),D),E),B)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),D),E),hAPP(hAPP(c_Set_Oinsert(A),C),B)). [resolve(5397,a,5406,a)].
% 26.30/26.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f101(C,D,E,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),D),C),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),E),C),B). [resolve(5397,a,5407,a)].
% 26.30/26.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(C,f101(D,C,E,B,A,tc_Int_Oint)) != hAPP(E,f101(D,C,E,B,A,tc_Int_Oint)) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),C),D),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),E),D),B). [resolve(5397,a,5408,a)].
% 26.30/26.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -c_Fun_Oinj__on(A,C,D,B) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,C,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),E),F),hAPP(c_Set_Oimage(A,C,D),B)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,A,c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Fun_Ocomp(C,tc_Int_Oint,A,E),D)),F),B). [resolve(5397,a,5409,a)].
% 26.30/26.22 5410 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 26.30/26.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A,B),C)) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),D),B)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),B)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),D),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),C)). [resolve(5410,a,5398,a)].
% 26.30/26.22 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(5410,a,5399,a)].
% 26.30/26.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A,B),C)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),B)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D,hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),D),C))). [resolve(5410,a,5400,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = B | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B) | hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),A)),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),B)). [resolve(5410,a,5401,a)].
% 26.33/26.25 Derived: c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),A)). [resolve(5410,a,5402,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),f40(A,tc_Nat_Onat)),f41(A,tc_Nat_Onat))),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),f40(A,tc_Nat_Onat)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),f41(A,tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),A)),A)). [resolve(5410,a,5403,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),A)) | hAPP(c_Finite__Set_Ofold1(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),B),A). [resolve(5410,a,5404,a)].
% 26.33/26.25 Derived: c_Finite__Set_Ofun__left__comm(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)). [resolve(5410,a,5405,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(D,C)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),D),E),B)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),D),E),hAPP(hAPP(c_Set_Oinsert(A),C),B)). [resolve(5410,a,5406,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f101(C,D,E,B,A,tc_Nat_Onat)),B)) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),D),C),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),E),C),B). [resolve(5410,a,5407,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(C,f101(D,C,E,B,A,tc_Nat_Onat)) != hAPP(E,f101(D,C,E,B,A,tc_Nat_Onat)) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),C),D),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),E),D),B). [resolve(5410,a,5408,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -c_Fun_Oinj__on(A,C,D,B) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,C,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),E),F),hAPP(c_Set_Oimage(A,C,D),B)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),hAPP(c_Fun_Ocomp(C,tc_Nat_Onat,A,E),D)),F),B). [resolve(5410,a,5409,a)].
% 26.33/26.25 5411 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) # label(axiom). [assumption].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A,B),C)) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),D),B)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),D,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),D),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))),C)). [resolve(5411,a,5398,a)].
% 26.33/26.25 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5411,a,5399,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A,B),C)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(c_Finite__Set_Ofold__graph(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),D,hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),D),C))). [resolve(5411,a,5400,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),B)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = B | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B) | hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),A)),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5411,a,5401,a)].
% 26.33/26.25 Derived: c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),A)). [resolve(5411,a,5402,a)].
% 26.33/26.25 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),f40(A,tc_Code__Numeral_Ocode__numeral)),f41(A,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),f40(A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),f41(A,tc_Code__Numeral_Ocode__numeral)),c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)))))) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),A)),A)). [resolve(5411,a,5403,a)].
% 32.49/32.44 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),A)) | hAPP(c_Finite__Set_Ofold1(tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Set_Oinsert(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Finite__Set_Ofold(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),B),A). [resolve(5411,a,5404,a)].
% 32.49/32.44 Derived: c_Finite__Set_Ofun__left__comm(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)). [resolve(5411,a,5405,a)].
% 32.49/32.44 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(D,C)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),D),E),B)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),D),E),hAPP(hAPP(c_Set_Oinsert(A),C),B)). [resolve(5411,a,5406,a)].
% 32.49/32.44 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f101(C,D,E,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),D),C),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),E),C),B). [resolve(5411,a,5407,a)].
% 32.49/32.44 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(C,f101(D,C,E,B,A,tc_Code__Numeral_Ocode__numeral)) != hAPP(E,f101(D,C,E,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),C),D),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),E),D),B). [resolve(5411,a,5408,a)].
% 32.49/32.44 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -c_Fun_Oinj__on(A,C,D,B) | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,C,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),E),F),hAPP(c_Set_Oimage(A,C,D),B)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Fun_Ocomp(C,tc_Code__Numeral_Ocode__numeral,A,E),D)),F),B). [resolve(5411,a,5409,a)].
% 32.49/32.44 5412 class_Groups_Ocomm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 32.49/32.44 5413 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)) = C | hBOOL(hAPP(hAPP(c_member(B),f35(D,E,C,B,A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C))) # label(fact_setsum__strict__mono) # label(axiom). [clausify(414)].
% 32.49/32.44 5414 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Oordered__cancel__ab__semigroup__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)) = C | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(D,f35(E,D,C,B,A))),hAPP(E,f35(E,D,C,B,A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C))) # label(fact_setsum__strict__mono) # label(axiom). [clausify(414)].
% 32.49/32.44 5415 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(E,D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),hAPP(hAPP(c_Set_Oinsert(B),D),c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) # label(fact_setsum__diff1_H) # label(axiom). [clausify(415)].
% 32.49/32.44 5416 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(E,D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),hAPP(hAPP(c_Set_Oinsert(B),D),c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) # label(fact_setsum_Oremove) # label(axiom). [clausify(416)].
% 32.49/32.44 5417 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(E,D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Set_Oinsert(B),D),C)) # label(fact_setsum_Oinsert) # label(axiom). [clausify(457)].
% 32.49/32.44 5418 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(E,D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Set_Oinsert(B),D),C)) # label(fact_setsum__insert) # label(axiom). [clausify(458)].
% 32.49/32.44 5419 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),D)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,tc_HOL_Obool)),C),D))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,tc_HOL_Obool)),C),D))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)) # label(fact_setsum__Un__Int) # label(axiom). [clausify(459)].
% 32.49/32.44 5420 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(D,E)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),hAPP(hAPP(c_Set_Oinsert(B),E),c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),hAPP(hAPP(c_Set_Oinsert(B),E),C)) # label(fact_setsum_Oinsert__remove) # label(axiom). [clausify(468)].
% 32.49/32.44 5421 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),D)) | c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,tc_HOL_Obool)),C),D) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,tc_HOL_Obool)),C),D)) # label(fact_setsum__Un__disjoint) # label(axiom). [clausify(469)].
% 32.49/32.44 5422 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B # label(fact_add__0) # label(axiom). [clausify(858)].
% 32.49/32.44 5423 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add_Ocomm__neutral) # label(axiom). [clausify(861)].
% 32.49/32.44 5424 -class_Groups_Ocomm__monoid__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))) # label(fact_setsum__empty) # label(axiom). [clausify(968)].
% 32.49/32.44 5425 -class_Groups_Ocomm__monoid__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))) # label(fact_setsum_Oempty) # label(axiom). [clausify(969)].
% 32.49/32.44 5426 -class_Groups_Ocomm__monoid__add(A) | hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C) # label(fact_setsum_Oinfinite) # label(axiom). [clausify(970)].
% 32.49/32.44 5427 -class_Groups_Ocomm__monoid__add(A) | hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C) # label(fact_setsum__infinite) # label(axiom). [clausify(971)].
% 32.49/32.44 5428 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Oplus__class_Oplus(A)),D),c_Groups_Ozero__class_Ozero(A)),C) # label(fact_setsum_OF__eq) # label(axiom). [clausify(1040)].
% 32.49/32.44 5429 -class_Groups_Ocomm__monoid__add(A) | hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C) # label(fact_setsum_OF__eq) # label(axiom). [clausify(1040)].
% 32.49/32.44 5430 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(A,B,c_Groups_Oplus__class_Oplus(A)),D),c_Groups_Ozero__class_Ozero(A)),C) # label(fact_setsum_Oeq__fold) # label(axiom). [clausify(1041)].
% 32.49/32.44 5431 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),D)) | hBOOL(hAPP(hAPP(c_member(B),f87(E,D,C,B,A)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,tc_HOL_Obool)),C),D))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,tc_HOL_Obool)),C),D)) # label(fact_setsum_Ounion__inter__neutral) # label(axiom). [clausify(1051)].
% 32.49/32.44 5432 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),D)) | c_Groups_Ozero__class_Ozero(A) != hAPP(E,f87(E,D,C,B,A)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,tc_HOL_Obool)),C),D)) # label(fact_setsum_Ounion__inter__neutral) # label(axiom). [clausify(1051)].
% 32.49/32.44 5433 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),D)) | hBOOL(hAPP(hAPP(c_member(B),f88(E,D,C,B,A)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,tc_HOL_Obool)),C),D))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,tc_HOL_Obool)),C),D)) # label(fact_setsum__Un__zero) # label(axiom). [clausify(1052)].
% 32.49/32.44 5434 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),D)) | c_Groups_Ozero__class_Ozero(A) != hAPP(E,f88(E,D,C,B,A)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,tc_HOL_Obool)),C),D)) # label(fact_setsum__Un__zero) # label(axiom). [clausify(1052)].
% 32.49/32.44 5435 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | hBOOL(hAPP(hAPP(c_member(B),f89(E,D,C,B,A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C))) # label(fact_setsum__mono3) # label(axiom). [clausify(1053)].
% 32.49/32.44 5436 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(E,f89(E,D,C,B,A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C))) # label(fact_setsum__mono3) # label(axiom). [clausify(1053)].
% 32.49/32.44 5437 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | hBOOL(hAPP(hAPP(c_member(B),f94(E,D,C,B,A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),D))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) # label(fact_setsum__mono__zero__left) # label(axiom). [clausify(1138)].
% 32.49/32.44 5438 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(E,f94(E,D,C,B,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) # label(fact_setsum__mono__zero__left) # label(axiom). [clausify(1138)].
% 32.49/32.44 5439 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | hBOOL(hAPP(hAPP(c_member(B),f95(E,D,C,B,A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),D))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) # label(fact_setsum__mono__zero__right) # label(axiom). [clausify(1139)].
% 32.49/32.44 5440 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(E,f95(E,D,C,B,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) # label(fact_setsum__mono__zero__right) # label(axiom). [clausify(1139)].
% 32.49/32.44 5441 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Oplus__class_Oplus(A)),D)),E)),C) # label(fact_setsum_Odistrib) # label(axiom). [clausify(2273)].
% 32.49/32.44 5442 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(C,tc_HOL_Obool),A),hAPP(hAPP(c_COMBB(tc_fun(C,A),tc_fun(tc_fun(C,tc_HOL_Obool),A),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A)),hAPP(c_COMBC(C,B,A),D))),E)),F) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A),hAPP(hAPP(c_COMBC(C,tc_fun(B,tc_HOL_Obool),A),hAPP(hAPP(c_COMBB(tc_fun(B,A),tc_fun(tc_fun(B,tc_HOL_Obool),A),C),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A)),D)),F)),E) # label(fact_setsum__commute) # label(axiom). [clausify(2288)].
% 32.49/32.44 5443 -class_Groups_Ocomm__monoid__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_COMBK(A,B),c_Groups_Ozero__class_Ozero(A))),C) # label(fact_setsum__0) # label(axiom). [clausify(2293)].
% 32.49/32.44 5444 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Oplus__class_Oplus(A)),C)),E)),D) # label(fact_setsum__addf) # label(axiom). [clausify(2298)].
% 32.49/32.44 5445 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBS(B,A,tc_fun(A,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),B),c_If(A)),hAPP(c_fequal,D))),E)),c_Groups_Ozero__class_Ozero(A))),C) = hAPP(E,D) # label(fact_setsum__delta_H) # label(axiom). [clausify(2316)].
% 32.49/32.44 5446 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),D),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBS(B,A,tc_fun(A,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),B),c_If(A)),hAPP(c_fequal,D))),E)),c_Groups_Ozero__class_Ozero(A))),C) # label(fact_setsum__delta_H) # label(axiom). [clausify(2316)].
% 32.49/32.44 5447 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBS(B,A,tc_fun(A,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),B),c_If(A)),hAPP(hAPP(c_COMBC(B,B,tc_HOL_Obool),c_fequal),D))),E)),c_Groups_Ozero__class_Ozero(A))),C) = hAPP(E,D) # label(fact_setsum__delta) # label(axiom). [clausify(2317)].
% 32.49/32.44 5448 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),D),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBS(B,A,tc_fun(A,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),B),c_If(A)),hAPP(hAPP(c_COMBC(B,B,tc_HOL_Obool),c_fequal),D))),E)),c_Groups_Ozero__class_Ozero(A))),C) # label(fact_setsum__delta) # label(axiom). [clausify(2317)].
% 32.49/32.44 5449 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBS(B,A,tc_fun(A,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),B),c_If(A)),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),D))),E)),c_Groups_Ozero__class_Ozero(A))),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,tc_HOL_Obool)),C),D)) # label(fact_setsum__restrict__set) # label(axiom). [clausify(2329)].
% 32.49/32.44 5450 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),C))),hAPP(B,C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,C))) # label(fact_setsum__lessThan__Suc) # label(axiom). [clausify(2441)].
% 32.49/32.44 5451 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat),B),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,C),hAPP(c_Nat_OSuc,D))) # label(fact_setsum__shift__bounds__cl__Suc__ivl) # label(axiom). [clausify(2666)].
% 32.49/32.44 5452 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat),B),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),C))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,D,E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),E),C))) # label(fact_setsum__shift__bounds__cl__nat__ivl) # label(axiom). [clausify(2667)].
% 32.49/32.44 5453 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(D,B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)) # label(fact_setsum__head__Suc) # label(axiom). [clausify(2684)].
% 32.49/32.44 5454 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,B)),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,hAPP(c_Nat_OSuc,B))) # label(fact_setsum__cl__ivl__Suc) # label(axiom). [clausify(2685)].
% 32.49/32.44 5455 -class_Groups_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,B)),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,B))),hAPP(D,hAPP(c_Nat_OSuc,B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,hAPP(c_Nat_OSuc,B))) # label(fact_setsum__cl__ivl__Suc) # label(axiom). [clausify(2685)].
% 32.49/32.44 5456 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),E)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),E))) # label(fact_setsum__ub__add__nat) # label(axiom). [clausify(2688)].
% 32.49/32.44 5457 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),C))),hAPP(B,hAPP(c_Nat_OSuc,C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,C))) # label(fact_setsum__atMost__Suc) # label(axiom). [clausify(2760)].
% 32.49/32.44 5458 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(D,B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,B,C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)) # label(fact_setsum__head) # label(axiom). [clausify(2769)].
% 32.49/32.44 5459 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat),B),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,C)),hAPP(c_Nat_OSuc,D))) # label(fact_setsum__shift__bounds__Suc__ivl) # label(axiom). [clausify(2829)].
% 32.49/32.44 5460 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat),B),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),C))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,D),E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),E),C))) # label(fact_setsum__shift__bounds__nat__ivl) # label(axiom). [clausify(2831)].
% 32.49/32.44 5461 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),E),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),E),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),E),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),D)) # label(fact_setsum__add__nat__ivl) # label(axiom). [clausify(2836)].
% 32.49/32.44 5462 -class_Groups_Ocomm__monoid__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),C)) # label(fact_setsum__shift__lb__Suc0__0__upt) # label(axiom). [clausify(2847)].
% 32.49/32.44 5463 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(D,B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)),C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C)) # label(fact_setsum__head__upt__Suc) # label(axiom). [clausify(2848)].
% 32.49/32.44 5464 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),hAPP(c_Nat_OSuc,B))) # label(fact_setsum__op__ivl__Suc) # label(axiom). [clausify(2850)].
% 32.49/32.44 5465 -class_Groups_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),B))),hAPP(D,B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),hAPP(c_Nat_OSuc,B))) # label(fact_setsum__op__ivl__Suc) # label(axiom). [clausify(2850)].
% 32.49/32.44 5466 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,A),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,tc_Int_Oint),B),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,A),B),C) # label(fact_transfer__nat__int__sum__prod_I2_J) # label(axiom). [clausify(2950)].
% 32.49/32.44 5467 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,A),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,tc_Int_Oint),B),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),C) # label(fact_transfer__nat__int__sum__prod_I1_J) # label(axiom). [clausify(2982)].
% 32.49/32.44 5468 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Ocomm__monoid__mult(A) | -c_Nat__Transfer_Onat__set(B) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,A),C),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,A),hAPP(hAPP(c_COMBB(tc_Int_Oint,A,tc_Nat_Onat),C),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),B)) # label(fact_transfer__int__nat__sum__prod_I2_J) # label(axiom). [clausify(3048)].
% 32.49/32.44 5469 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Ocomm__monoid__mult(A) | -c_Nat__Transfer_Onat__set(B) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,A),C),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(hAPP(c_COMBB(tc_Int_Oint,A,tc_Nat_Onat),C),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),B)) # label(fact_transfer__int__nat__sum__prod_I1_J) # label(axiom). [clausify(3074)].
% 32.49/32.44 5470 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Ocomm__monoid__mult(A) | B != C | -c_Nat__Transfer_Onat__set(B) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),f285(D,E,B,C,A))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,A),E),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,A),D),B) # label(fact_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(3084)].
% 32.49/32.44 5471 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Ocomm__monoid__mult(A) | B != C | -c_Nat__Transfer_Onat__set(B) | hAPP(D,f285(E,D,B,C,A)) != hAPP(E,f285(E,D,B,C,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,A),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,A),E),B) # label(fact_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(3084)].
% 32.49/32.44 5472 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Ocomm__monoid__mult(A) | B != C | -c_Nat__Transfer_Onat__set(B) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),f286(D,E,B,C,A))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,A),E),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,A),D),B) # label(fact_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(3085)].
% 32.49/32.44 5473 -class_Groups_Ocomm__monoid__add(A) | -class_Groups_Ocomm__monoid__mult(A) | B != C | -c_Nat__Transfer_Onat__set(B) | hAPP(D,f286(E,D,B,C,A)) != hAPP(E,f286(E,D,B,C,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,A),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,A),E),B) # label(fact_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(3085)].
% 32.49/32.44 5474 -class_Groups_Ocomm__monoid__add(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(B,C),A),hAPP(c_Product__Type_Oprod_Oprod__case(B,C,A),D)),hAPP(hAPP(c_Product__Type_OSigma(B,C),E),hAPP(c_COMBK(tc_fun(C,tc_HOL_Obool),B),F))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(C,tc_HOL_Obool),A),hAPP(hAPP(c_COMBB(tc_fun(C,A),tc_fun(tc_fun(C,tc_HOL_Obool),A),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A)),D)),F)),E) # label(fact_setsum__cartesian__product) # label(axiom). [clausify(3102)].
% 32.49/32.44 5475 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),f297(D,E,F,C,B,A)),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(B,F),A),hAPP(c_Product__Type_Oprod_Oprod__case(B,F,A),D)),hAPP(hAPP(c_Product__Type_OSigma(B,F),C),E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,tc_fun(F,tc_HOL_Obool),A),hAPP(hAPP(c_COMBB(tc_fun(F,A),tc_fun(tc_fun(F,tc_HOL_Obool),A),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(F,A)),D)),E)),C) # label(fact_setsum__Sigma) # label(axiom). [clausify(3139)].
% 32.49/32.44 5476 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(D),hAPP(E,f297(F,E,D,C,B,A)))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(B,D),A),hAPP(c_Product__Type_Oprod_Oprod__case(B,D,A),F)),hAPP(hAPP(c_Product__Type_OSigma(B,D),C),E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,tc_fun(D,tc_HOL_Obool),A),hAPP(hAPP(c_COMBB(tc_fun(D,A),tc_fun(tc_fun(D,tc_HOL_Obool),A),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,A)),F)),E)),C) # label(fact_setsum__Sigma) # label(axiom). [clausify(3139)].
% 32.49/32.44 5477 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(D),E)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,A),hAPP(hAPP(c_COMBS(D,tc_fun(B,tc_HOL_Obool),A),hAPP(hAPP(c_COMBB(tc_fun(B,A),tc_fun(tc_fun(B,tc_HOL_Obool),A),D),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A)),hAPP(c_COMBC(B,D,A),F))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool),D),c_Set_OCollect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool),D),hAPP(c_COMBS(B,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),B),c_fconj),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),C)))),hAPP(c_COMBC(B,D,tc_HOL_Obool),V6))))),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,tc_fun(D,tc_HOL_Obool),A),hAPP(hAPP(c_COMBB(tc_fun(D,A),tc_fun(tc_fun(D,tc_HOL_Obool),A),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,A)),F)),hAPP(hAPP(c_COMBB(tc_fun(D,tc_HOL_Obool),tc_fun(D,tc_HOL_Obool),B),c_Set_OCollect(D)),hAPP(hAPP(c_COMBB(tc_fun(D,tc_HOL_Obool),tc_fun(D,tc_HOL_Obool),B),hAPP(c_COMBS(D,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),D),c_fconj),hAPP(hAPP(c_COMBC(D,tc_fun(D,tc_HOL_Obool),tc_HOL_Obool),c_member(D)),E)))),V6)))),C) # label(fact_setsum__setsum__restrict) # label(axiom). [clausify(3204)].
% 32.49/32.44 5478 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBS(B,A,tc_fun(A,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),B),c_If(A)),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),D))),E)),c_Groups_Ozero__class_Ozero(A))),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(c_Set_OCollect(B),hAPP(hAPP(c_COMBS(B,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),B),c_fconj),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),C))),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),D)))) # label(fact_setsum__restrict__set_H) # label(axiom). [clausify(3207)].
% 32.49/32.44 5479 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,A),hAPP(hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),A,D),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool),D),c_Set_OCollect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool),D),hAPP(c_COMBS(B,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),B),c_fconj),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),C)))),hAPP(c_COMBC(B,D,tc_HOL_Obool),hAPP(hAPP(c_COMBB(D,tc_fun(D,tc_HOL_Obool),B),c_fequal),F)))))),hAPP(c_Set_Oimage(B,D,F),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C) # label(fact_setsum__image__gen) # label(axiom). [clausify(3208)].
% 32.49/32.44 5480 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,tc_HOL_Obool)),C),hAPP(c_Set_OCollect(B),E)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),F),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,tc_HOL_Obool)),C),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(B,tc_HOL_Obool)),hAPP(c_Set_OCollect(B),E))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBS(B,A,tc_fun(A,A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),B),c_If(A)),E)),D)),F)),C) # label(fact_setsum__cases) # label(axiom). [clausify(3210)].
% 32.49/32.44 5481 -class_Groups_Ocomm__monoid__add(A) | -c_Fun_Oinj__on(B,A,C,D) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,A),c_Fun_Oid(A)),hAPP(c_Set_Oimage(B,A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),D) # label(fact_setsum__reindex__id) # label(axiom). [clausify(3253)].
% 32.49/32.44 5482 -class_Groups_Ocomm__monoid__add(A) | -c_Fun_Oinj__on(B,C,D,E) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A),F),hAPP(c_Set_Oimage(B,C,D),E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_Fun_Ocomp(C,A,B,F),D)),E) # label(fact_setsum__reindex) # label(axiom). [clausify(3409)].
% 32.49/32.44 5483 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -c_Fun_Oinj__on(B,B,D,C) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_Fun_Ocomp(B,A,B,E),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),hAPP(c_Set_Oimage(B,B,D),C)) # label(fact_setsum_Oreindex) # label(axiom). [clausify(3412)].
% 32.49/32.44 5484 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),f344(D,E,F,C,B,A)),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,A),E),hAPP(c_Set_Oimage(B,D,F),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_Fun_Ocomp(D,A,B,E),F)),C) # label(fact_setsum__reindex__nonzero) # label(axiom). [clausify(3441)].
% 32.49/32.44 5485 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hBOOL(hAPP(hAPP(c_member(B),f345(D,E,F,C,B,A)),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,A),E),hAPP(c_Set_Oimage(B,D,F),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_Fun_Ocomp(D,A,B,E),F)),C) # label(fact_setsum__reindex__nonzero) # label(axiom). [clausify(3441)].
% 32.49/32.44 5486 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | f345(D,E,F,C,B,A) != f344(D,E,F,C,B,A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,A),E),hAPP(c_Set_Oimage(B,D,F),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_Fun_Ocomp(D,A,B,E),F)),C) # label(fact_setsum__reindex__nonzero) # label(axiom). [clausify(3441)].
% 32.49/32.44 5487 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | hAPP(D,f345(E,F,D,C,B,A)) = hAPP(D,f344(E,F,D,C,B,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,A),F),hAPP(c_Set_Oimage(B,E,D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_Fun_Ocomp(E,A,B,F),D)),C) # label(fact_setsum__reindex__nonzero) # label(axiom). [clausify(3441)].
% 32.49/32.44 5488 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(D,hAPP(E,f344(F,D,E,C,B,A))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(F,A),D),hAPP(c_Set_Oimage(B,F,E),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_Fun_Ocomp(F,A,B,D),E)),C) # label(fact_setsum__reindex__nonzero) # label(axiom). [clausify(3441)].
% 32.49/32.44 5489 -class_Groups_Ocomm__monoid__add(A) | -c_Fun_Oinj__on(B,C,D,E) | hAPP(c_Set_Oimage(B,C,D),E) != F | hBOOL(hAPP(hAPP(c_member(B),f357(V6,V7,F,E,D,C,B,A)),E)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A),V6),F) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),V7),E) # label(fact_setsum__reindex__cong) # label(axiom). [clausify(3468)].
% 32.49/32.44 5490 -class_Groups_Ocomm__monoid__add(A) | -c_Fun_Oinj__on(B,C,D,E) | hAPP(c_Set_Oimage(B,C,D),E) != F | hAPP(V6,hAPP(D,f357(V6,V7,F,E,D,C,B,A))) != hAPP(V7,f357(V6,V7,F,E,D,C,B,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A),V6),F) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),V7),E) # label(fact_setsum__reindex__cong) # label(axiom). [clausify(3468)].
% 32.49/32.44 5491 -class_Groups_Ocomm__monoid__add(A) | -class_Orderings_Oord(B) | C != D | E != F | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(B),C),f358(V6,V7,F,E,C,D,B,A))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),V7),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,D),E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,C),F)) # label(fact_setsum__ivl__cong) # label(axiom). [clausify(3475)].
% 32.49/32.44 5492 -class_Groups_Ocomm__monoid__add(A) | -class_Orderings_Oord(B) | C != D | E != F | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(B),f358(V6,V7,F,E,C,D,B,A)),F)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),V7),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,D),E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,C),F)) # label(fact_setsum__ivl__cong) # label(axiom). [clausify(3475)].
% 32.49/32.44 5493 -class_Groups_Ocomm__monoid__add(A) | -class_Orderings_Oord(B) | C != D | E != F | hAPP(V6,f358(V7,V6,F,E,C,D,B,A)) != hAPP(V7,f358(V7,V6,F,E,C,D,B,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,D),E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),V7),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,C),F)) # label(fact_setsum__ivl__cong) # label(axiom). [clausify(3475)].
% 32.49/32.44 5494 -class_Groups_Ocomm__monoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(c_List_Onth(A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B))) # label(fact_listsum__setsum__nth) # label(axiom). [clausify(3755)].
% 32.49/32.44 5495 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_List_Odistinct(A),B)) | hAPP(c_List_Omonoid__add__class_Olistsum(A),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,A),c_COMBI(A)),hAPP(c_List_Oset(A),B)) # label(fact_distinct__listsum__conv__Setsum) # label(axiom). [clausify(3801)].
% 32.49/32.44 5496 -class_Groups_Ocomm__monoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Oplus__class_Oplus(A)),C)),D)),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),C),E))),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),D),E))) # label(fact_listsum__addf) # label(axiom). [clausify(4068)].
% 32.49/32.44 5497 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_List_Odistinct(B),C)) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),hAPP(c_List_Oset(B),C)) # label(fact_listsum__distinct__conv__setsum__set) # label(axiom). [clausify(4097)].
% 32.49/32.44 5498 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_member(B),C),hAPP(c_List_Oset(B),D))) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),E),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(E,C)),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),E),c_List_Oremove1(B,C,D)))) # label(fact_listsum__map__remove1) # label(axiom). [clausify(4099)].
% 32.49/32.44 5499 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Nitpick_Osetsum_H(B,A,D,C) = hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),D),c_Hilbert__Choice_OEps(tc_List_Olist(B),hAPP(hAPP(c_COMBS(tc_List_Olist(B),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(B)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(B),tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_fun(tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(B)),c_fequal),c_List_Oset(B))),C))),c_List_Odistinct(B))))) # label(fact_Nitpick_Osetsum_H__def) # label(axiom). [clausify(4100)].
% 32.49/32.44 5500 -class_Groups_Ocomm__monoid__add(A) | hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Nitpick_Osetsum_H(B,A,D,C) = c_Groups_Ozero__class_Ozero(A) # label(fact_Nitpick_Osetsum_H__def) # label(axiom). [clausify(4100)].
% 32.49/32.44 5501 -class_Groups_Ocomm__monoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(tc_Int_Oint,A),B),c_List_Oupto(C,D))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,A),B),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(C,D))) # label(fact_interv__listsum__conv__setsum__set__int) # label(axiom). [clausify(4116)].
% 32.49/32.44 5502 -class_Groups_Ocomm__monoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(tc_Int_Oint,A),B),c_List_Oupto(C,D))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,A),B),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(C,D))) # label(fact_setsum__set__upto__conv__listsum__int) # label(axiom). [clausify(4117)].
% 32.49/32.44 5503 -class_Groups_Ocomm__monoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,A),B),c_List_Oupt(C,D))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(C,D))) # label(fact_interv__listsum__conv__setsum__set__nat) # label(axiom). [clausify(4320)].
% 32.49/32.44 5504 -class_Groups_Ocomm__monoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,A),B),c_List_Oupt(C,D))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),B),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(C,D))) # label(fact_setsum__set__upt__conv__listsum__nat) # label(axiom). [clausify(4321)].
% 32.49/32.44 5505 -class_Groups_Ocomm__monoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(c_List_Orev(A),B)) = hAPP(c_List_Omonoid__add__class_Olistsum(A),B) # label(fact_listsum__rev) # label(axiom). [clausify(4378)].
% 32.49/32.44 5506 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f507(D,C,B,A)),C)) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f508(D,C,B,A)),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.44 5507 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f507(D,C,B,A)),C)) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f509(D,C,B,A)),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.44 5508 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f507(D,C,B,A)),C)) | f509(D,C,B,A) != f508(D,C,B,A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.44 5509 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f507(D,C,B,A)),C)) | hBOOL(hAPP(hAPP(c_member(B),f510(D,C,B,A)),f508(D,C,B,A))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.44 5510 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f507(D,C,B,A)),C)) | hBOOL(hAPP(hAPP(c_member(B),f510(D,C,B,A)),f509(D,C,B,A))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.44 5511 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f507(D,C,B,A)),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(D,f510(D,C,B,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.44 5512 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),f507(D,C,B,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f508(D,C,B,A)),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.45 5513 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),f507(D,C,B,A))) | hBOOL(hAPP(hAPP(c_member(tc_fun(B,tc_HOL_Obool)),f509(D,C,B,A)),C)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.45 5514 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),f507(D,C,B,A))) | f509(D,C,B,A) != f508(D,C,B,A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.45 5515 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),f507(D,C,B,A))) | hBOOL(hAPP(hAPP(c_member(B),f510(D,C,B,A)),f508(D,C,B,A))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.45 5516 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),f507(D,C,B,A))) | hBOOL(hAPP(hAPP(c_member(B),f510(D,C,B,A)),f509(D,C,B,A))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.45 5517 -class_Groups_Ocomm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(B,tc_HOL_Obool)),C)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),f507(D,C,B,A))) | c_Groups_Ozero__class_Ozero(A) != hAPP(D,f510(D,C,B,A)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(B,tc_HOL_Obool),A),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D)),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),c_Complete__Lattice_OSup__class_OSup(tc_fun(B,tc_HOL_Obool),C)) # label(fact_setsum__UNION__zero) # label(axiom). [clausify(4593)].
% 32.49/32.45 Derived: -class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_member(A),f35(C,D,B,A,tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),B))). [resolve(5412,a,5413,a)].
% 32.49/32.45 Derived: -class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(C,f35(D,C,B,A,tc_Int_Oint))),hAPP(D,f35(D,C,B,A,tc_Int_Oint)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B))). [resolve(5412,a,5414,a)].
% 32.49/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B). [resolve(5412,a,5415,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Set_Oinsert(A),C),B)). [resolve(5412,a,5417,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)). [resolve(5412,a,5419,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(C,D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),D),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),hAPP(hAPP(c_Set_Oinsert(A),D),B)). [resolve(5412,a,5420,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5412,a,5421,a)].
% 32.53/32.45 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(5412,a,5422,a)].
% 32.53/32.45 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(5412,a,5423,a)].
% 32.53/32.45 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))). [resolve(5412,a,5424,a)].
% 32.53/32.45 Derived: hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),B). [resolve(5412,a,5426,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint)),C),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B). [resolve(5412,a,5428,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_member(A),f87(D,C,B,A,tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5412,a,5431,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(D,f87(D,C,B,A,tc_Int_Oint)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5412,a,5432,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_member(A),f88(D,C,B,A,tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5412,a,5433,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(D,f88(D,C,B,A,tc_Int_Oint)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5412,a,5434,a)].
% 32.53/32.45 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f89(D,C,B,A,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B))). [resolve(5412,a,5435,a)].
% 32.53/32.45 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(D,f89(D,C,B,A,tc_Int_Oint)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B))). [resolve(5412,a,5436,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f94(D,C,B,A,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B). [resolve(5412,a,5437,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(D,f94(D,C,B,A,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B). [resolve(5412,a,5438,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f95(D,C,B,A,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B). [resolve(5412,a,5439,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(D,f95(D,C,B,A,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B). [resolve(5412,a,5440,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),C)),D)),B). [resolve(5412,a,5441,a)].
% 32.53/32.45 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(B,tc_Int_Oint),tc_fun(tc_fun(B,tc_HOL_Obool),tc_Int_Oint),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint)),hAPP(c_COMBC(B,A,tc_Int_Oint),C))),D)),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(A,tc_Int_Oint),tc_fun(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint)),C)),E)),D). [resolve(5412,a,5442,a)].
% 32.53/32.45 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_COMBK(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),B). [resolve(5412,a,5443,a)].
% 32.53/32.45 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),B)),D)),C). [resolve(5412,a,5444,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_If(tc_Int_Oint)),hAPP(c_fequal,C))),D)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),B) = hAPP(D,C). [resolve(5412,a,5445,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_If(tc_Int_Oint)),hAPP(c_fequal,C))),D)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),B). [resolve(5412,a,5446,a)].
% 32.53/32.45 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_If(tc_Int_Oint)),hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),C))),D)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),B) = hAPP(D,C). [resolve(5412,a,5447,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_If(tc_Int_Oint)),hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),C))),D)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),B). [resolve(5412,a,5448,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_If(tc_Int_Oint)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C))),D)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5412,a,5449,a)].
% 32.53/32.46 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B))),hAPP(A,B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,B))). [resolve(5412,a,5450,a)].
% 32.53/32.46 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Nat_Onat),A),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),hAPP(c_Nat_OSuc,C))). [resolve(5412,a,5451,a)].
% 32.53/32.46 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Nat_Onat),A),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),B))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D),B))). [resolve(5412,a,5452,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)). [resolve(5412,a,5453,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))). [resolve(5412,a,5454,a)].
% 32.53/32.46 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,A))),hAPP(C,hAPP(c_Nat_OSuc,A))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))). [resolve(5412,a,5455,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))). [resolve(5412,a,5456,a)].
% 32.53/32.46 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),B))),hAPP(A,hAPP(c_Nat_OSuc,B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,B))). [resolve(5412,a,5457,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)). [resolve(5412,a,5458,a)].
% 32.53/32.46 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Nat_Onat),A),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)),hAPP(c_Nat_OSuc,C))). [resolve(5412,a,5459,a)].
% 32.53/32.46 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Nat_Onat),A),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),B))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D),B))). [resolve(5412,a,5460,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),C)). [resolve(5412,a,5461,a)].
% 32.53/32.46 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B)). [resolve(5412,a,5462,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)). [resolve(5412,a,5463,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A))). [resolve(5412,a,5464,a)].
% 32.53/32.46 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),A))),hAPP(C,A)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A))). [resolve(5412,a,5465,a)].
% 32.53/32.46 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),A),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,tc_Int_Oint),A),B). [resolve(5412,a,5466,a)].
% 32.53/32.46 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),A),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),B). [resolve(5412,a,5467,a)].
% 32.53/32.46 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | -c_Nat__Transfer_Onat__set(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Int_Oint),B),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),B),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),A)). [resolve(5412,a,5468,a)].
% 32.53/32.46 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | -c_Nat__Transfer_Onat__set(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),B),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),B),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),A)). [resolve(5412,a,5469,a)].
% 32.53/32.46 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | A != B | -c_Nat__Transfer_Onat__set(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),f285(C,D,A,B,tc_Int_Oint))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Int_Oint),D),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Int_Oint),C),A). [resolve(5412,a,5470,a)].
% 32.53/32.46 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | A != B | -c_Nat__Transfer_Onat__set(A) | hAPP(C,f285(D,C,A,B,tc_Int_Oint)) != hAPP(D,f285(D,C,A,B,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Int_Oint),C),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Int_Oint),D),A). [resolve(5412,a,5471,a)].
% 32.53/32.46 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | A != B | -c_Nat__Transfer_Onat__set(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),f286(C,D,A,B,tc_Int_Oint))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),D),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),C),A). [resolve(5412,a,5472,a)].
% 32.53/32.46 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | A != B | -c_Nat__Transfer_Onat__set(A) | hAPP(C,f286(D,C,A,B,tc_Int_Oint)) != hAPP(D,f286(D,C,A,B,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),C),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),D),A). [resolve(5412,a,5473,a)].
% 32.53/32.46 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,B),tc_Int_Oint),hAPP(c_Product__Type_Oprod_Oprod__case(A,B,tc_Int_Oint),C)),hAPP(hAPP(c_Product__Type_OSigma(A,B),D),hAPP(c_COMBK(tc_fun(B,tc_HOL_Obool),A),E))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(B,tc_Int_Oint),tc_fun(tc_fun(B,tc_HOL_Obool),tc_Int_Oint),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint)),C)),E)),D). [resolve(5412,a,5474,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f297(C,D,E,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,E),tc_Int_Oint),hAPP(c_Product__Type_Oprod_Oprod__case(A,E,tc_Int_Oint),C)),hAPP(hAPP(c_Product__Type_OSigma(A,E),B),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_fun(E,tc_HOL_Obool),tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(E,tc_Int_Oint),tc_fun(tc_fun(E,tc_HOL_Obool),tc_Int_Oint),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,tc_Int_Oint)),C)),D)),B). [resolve(5412,a,5475,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(C),hAPP(D,f297(E,D,C,B,A,tc_Int_Oint)))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,C),tc_Int_Oint),hAPP(c_Product__Type_Oprod_Oprod__case(A,C,tc_Int_Oint),E)),hAPP(hAPP(c_Product__Type_OSigma(A,C),B),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_fun(C,tc_HOL_Obool),tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(C,tc_Int_Oint),tc_fun(tc_fun(C,tc_HOL_Obool),tc_Int_Oint),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Int_Oint)),E)),D)),B). [resolve(5412,a,5476,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(C),D)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Int_Oint),hAPP(hAPP(c_COMBS(C,tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(A,tc_Int_Oint),tc_fun(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),C),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint)),hAPP(c_COMBC(A,C,tc_Int_Oint),E))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),c_Set_OCollect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B)))),hAPP(c_COMBC(A,C,tc_HOL_Obool),F))))),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_fun(C,tc_HOL_Obool),tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(C,tc_Int_Oint),tc_fun(tc_fun(C,tc_HOL_Obool),tc_Int_Oint),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Int_Oint)),E)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool),A),c_Set_OCollect(C)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool),A),hAPP(c_COMBS(C,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),C),c_fconj),hAPP(hAPP(c_COMBC(C,tc_fun(C,tc_HOL_Obool),tc_HOL_Obool),c_member(C)),D)))),F)))),B). [resolve(5412,a,5477,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_If(tc_Int_Oint)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C))),D)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C)))). [resolve(5412,a,5478,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_Int_Oint,C),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),c_Set_OCollect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B)))),hAPP(c_COMBC(A,C,tc_HOL_Obool),hAPP(hAPP(c_COMBB(C,tc_fun(C,tc_HOL_Obool),A),c_fequal),E)))))),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B). [resolve(5412,a,5479,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),hAPP(c_Set_OCollect(A),D)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),E),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(A),D))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),A),c_If(tc_Int_Oint)),D)),C)),E)),B). [resolve(5412,a,5480,a)].
% 32.53/32.46 Derived: -c_Fun_Oinj__on(A,tc_Int_Oint,B,C) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),c_Fun_Oid(tc_Int_Oint)),hAPP(c_Set_Oimage(A,tc_Int_Oint,B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),C). [resolve(5412,a,5481,a)].
% 32.53/32.46 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint),E),hAPP(c_Set_Oimage(A,B,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_Fun_Ocomp(B,tc_Int_Oint,A,E),C)),D). [resolve(5412,a,5482,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -c_Fun_Oinj__on(A,A,C,B) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_Fun_Ocomp(A,tc_Int_Oint,A,D),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),hAPP(c_Set_Oimage(A,A,C),B)). [resolve(5412,a,5483,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f344(C,D,E,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Int_Oint),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_Fun_Ocomp(C,tc_Int_Oint,A,D),E)),B). [resolve(5412,a,5484,a)].
% 32.53/32.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f345(C,D,E,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Int_Oint),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_Fun_Ocomp(C,tc_Int_Oint,A,D),E)),B). [resolve(5412,a,5485,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | f345(C,D,E,B,A,tc_Int_Oint) != f344(C,D,E,B,A,tc_Int_Oint) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Int_Oint),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_Fun_Ocomp(C,tc_Int_Oint,A,D),E)),B). [resolve(5412,a,5486,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(C,f345(D,E,C,B,A,tc_Int_Oint)) = hAPP(C,f344(D,E,C,B,A,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Int_Oint),E),hAPP(c_Set_Oimage(A,D,C),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_Fun_Ocomp(D,tc_Int_Oint,A,E),C)),B). [resolve(5412,a,5487,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(C,hAPP(D,f344(E,C,D,B,A,tc_Int_Oint))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,tc_Int_Oint),C),hAPP(c_Set_Oimage(A,E,D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_Fun_Ocomp(E,tc_Int_Oint,A,C),D)),B). [resolve(5412,a,5488,a)].
% 32.53/32.47 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(c_Set_Oimage(A,B,C),D) != E | hBOOL(hAPP(hAPP(c_member(A),f357(F,V6,E,D,C,B,A,tc_Int_Oint)),D)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint),F),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),V6),D). [resolve(5412,a,5489,a)].
% 32.53/32.47 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(c_Set_Oimage(A,B,C),D) != E | hAPP(F,hAPP(C,f357(F,V6,E,D,C,B,A,tc_Int_Oint))) != hAPP(V6,f357(F,V6,E,D,C,B,A,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint),F),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),V6),D). [resolve(5412,a,5490,a)].
% 32.53/32.47 Derived: -class_Orderings_Oord(A) | B != C | D != E | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),f358(F,V6,E,D,B,C,A,tc_Int_Oint))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5412,a,5491,a)].
% 32.53/32.47 Derived: -class_Orderings_Oord(A) | B != C | D != E | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),f358(F,V6,E,D,B,C,A,tc_Int_Oint)),E)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5412,a,5492,a)].
% 32.53/32.47 Derived: -class_Orderings_Oord(A) | B != C | D != E | hAPP(F,f358(V6,F,E,D,B,C,A,tc_Int_Oint)) != hAPP(V6,f358(V6,F,E,D,B,C,A,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5412,a,5493,a)].
% 32.53/32.47 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(c_List_Onth(tc_Int_Oint),A)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Int_Oint)),A))). [resolve(5412,a,5494,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),A)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),c_COMBI(tc_Int_Oint)),hAPP(c_List_Oset(tc_Int_Oint),A)). [resolve(5412,a,5495,a)].
% 32.53/32.47 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),hAPP(hAPP(c_COMBS(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),B)),C)),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),C),D))). [resolve(5412,a,5496,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_List_Odistinct(A),B)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),C),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),hAPP(c_List_Oset(A),B)). [resolve(5412,a,5497,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),D),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(D,B)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),D),c_List_Oremove1(A,B,C)))). [resolve(5412,a,5498,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Nitpick_Osetsum_H(A,tc_Int_Oint,C,B) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),C),c_Hilbert__Choice_OEps(tc_List_Olist(A),hAPP(hAPP(c_COMBS(tc_List_Olist(A),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(A)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(A),tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(A)),c_fequal),c_List_Oset(A))),B))),c_List_Odistinct(A))))). [resolve(5412,a,5499,a)].
% 32.53/32.47 Derived: hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Nitpick_Osetsum_H(A,tc_Int_Oint,C,B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(5412,a,5500,a)].
% 32.53/32.47 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Int_Oint),A),c_List_Oupto(B,C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),A),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(B,C))). [resolve(5412,a,5501,a)].
% 32.53/32.47 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),A),c_List_Oupt(B,C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),A),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(B,C))). [resolve(5412,a,5503,a)].
% 32.53/32.47 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(c_List_Orev(tc_Int_Oint),A)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),A). [resolve(5412,a,5505,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f508(C,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5506,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f509(C,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5507,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Int_Oint)),B)) | f509(C,B,A,tc_Int_Oint) != f508(C,B,A,tc_Int_Oint) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5508,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Int_Oint)),f508(C,B,A,tc_Int_Oint))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5509,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Int_Oint)),f509(C,B,A,tc_Int_Oint))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5510,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Int_Oint)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(C,f510(C,B,A,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5511,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f508(C,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5512,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f509(C,B,A,tc_Int_Oint)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5513,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Int_Oint))) | f509(C,B,A,tc_Int_Oint) != f508(C,B,A,tc_Int_Oint) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5514,a)].
% 32.53/32.47 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Int_Oint)),f508(C,B,A,tc_Int_Oint))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5515,a)].
% 32.53/32.49 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Int_Oint)),f509(C,B,A,tc_Int_Oint))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5516,a)].
% 32.53/32.49 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(C,f510(C,B,A,tc_Int_Oint)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5412,a,5517,a)].
% 32.53/32.49 5518 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 32.53/32.49 Derived: -class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_member(A),f35(C,D,B,A,tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),B))). [resolve(5518,a,5413,a)].
% 32.53/32.49 Derived: -class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(C,f35(D,C,B,A,tc_Nat_Onat))),hAPP(D,f35(D,C,B,A,tc_Nat_Onat)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B))). [resolve(5518,a,5414,a)].
% 32.53/32.49 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B). [resolve(5518,a,5415,a)].
% 32.53/32.49 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Set_Oinsert(A),C),B)). [resolve(5518,a,5417,a)].
% 32.53/32.49 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)). [resolve(5518,a,5419,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(C,D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),D),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),hAPP(hAPP(c_Set_Oinsert(A),D),B)). [resolve(5518,a,5420,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5518,a,5421,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A) = A. [resolve(5518,a,5422,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(5518,a,5423,a)].
% 32.53/32.50 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))). [resolve(5518,a,5424,a)].
% 32.53/32.50 Derived: hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),B). [resolve(5518,a,5426,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B). [resolve(5518,a,5428,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_member(A),f87(D,C,B,A,tc_Nat_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5518,a,5431,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(D,f87(D,C,B,A,tc_Nat_Onat)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5518,a,5432,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_member(A),f88(D,C,B,A,tc_Nat_Onat)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5518,a,5433,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(D,f88(D,C,B,A,tc_Nat_Onat)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5518,a,5434,a)].
% 32.53/32.50 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f89(D,C,B,A,tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B))). [resolve(5518,a,5435,a)].
% 32.53/32.50 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(D,f89(D,C,B,A,tc_Nat_Onat)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B))). [resolve(5518,a,5436,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f94(D,C,B,A,tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B). [resolve(5518,a,5437,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(D,f94(D,C,B,A,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B). [resolve(5518,a,5438,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f95(D,C,B,A,tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B). [resolve(5518,a,5439,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(D,f95(D,C,B,A,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B). [resolve(5518,a,5440,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),C)),D)),B). [resolve(5518,a,5441,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(B,tc_Nat_Onat),tc_fun(tc_fun(B,tc_HOL_Obool),tc_Nat_Onat),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat)),hAPP(c_COMBC(B,A,tc_Nat_Onat),C))),D)),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_Nat_Onat),tc_fun(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat)),C)),E)),D). [resolve(5518,a,5442,a)].
% 32.53/32.50 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B). [resolve(5518,a,5443,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),B),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),B)),D)),C). [resolve(5518,a,5444,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),A),c_If(tc_Nat_Onat)),hAPP(c_fequal,C))),D)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B) = hAPP(D,C). [resolve(5518,a,5445,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),A),c_If(tc_Nat_Onat)),hAPP(c_fequal,C))),D)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B). [resolve(5518,a,5446,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),A),c_If(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),C))),D)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B) = hAPP(D,C). [resolve(5518,a,5447,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),A),c_If(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),C))),D)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B). [resolve(5518,a,5448,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),A),c_If(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C))),D)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5518,a,5449,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B))),hAPP(A,B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,B))). [resolve(5518,a,5450,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),A),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),hAPP(c_Nat_OSuc,C))). [resolve(5518,a,5451,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),A),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),B))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D),B))). [resolve(5518,a,5452,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)). [resolve(5518,a,5453,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))). [resolve(5518,a,5454,a)].
% 32.53/32.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,A))),hAPP(C,hAPP(c_Nat_OSuc,A))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))). [resolve(5518,a,5455,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))). [resolve(5518,a,5456,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),B))),hAPP(A,hAPP(c_Nat_OSuc,B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,B))). [resolve(5518,a,5457,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)). [resolve(5518,a,5458,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),A),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)),hAPP(c_Nat_OSuc,C))). [resolve(5518,a,5459,a)].
% 32.53/32.50 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),A),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),B))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D),B))). [resolve(5518,a,5460,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),C)). [resolve(5518,a,5461,a)].
% 32.53/32.50 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B)). [resolve(5518,a,5462,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)). [resolve(5518,a,5463,a)].
% 32.53/32.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A))). [resolve(5518,a,5464,a)].
% 32.53/32.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),A))),hAPP(C,A)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A))). [resolve(5518,a,5465,a)].
% 32.53/32.51 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),A),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,tc_Nat_Onat),A),B). [resolve(5518,a,5466,a)].
% 32.53/32.51 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),A),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),B). [resolve(5518,a,5467,a)].
% 32.53/32.51 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | -c_Nat__Transfer_Onat__set(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Nat_Onat),B),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),B),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),A)). [resolve(5518,a,5468,a)].
% 32.53/32.51 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | -c_Nat__Transfer_Onat__set(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Nat_Onat),B),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),B),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),A)). [resolve(5518,a,5469,a)].
% 32.53/32.51 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | A != B | -c_Nat__Transfer_Onat__set(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),f285(C,D,A,B,tc_Nat_Onat))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Nat_Onat),D),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Nat_Onat),C),A). [resolve(5518,a,5470,a)].
% 32.53/32.51 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | A != B | -c_Nat__Transfer_Onat__set(A) | hAPP(C,f285(D,C,A,B,tc_Nat_Onat)) != hAPP(D,f285(D,C,A,B,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Nat_Onat),C),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Nat_Onat),D),A). [resolve(5518,a,5471,a)].
% 32.53/32.51 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | A != B | -c_Nat__Transfer_Onat__set(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),f286(C,D,A,B,tc_Nat_Onat))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Nat_Onat),D),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Nat_Onat),C),A). [resolve(5518,a,5472,a)].
% 32.53/32.51 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | A != B | -c_Nat__Transfer_Onat__set(A) | hAPP(C,f286(D,C,A,B,tc_Nat_Onat)) != hAPP(D,f286(D,C,A,B,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Nat_Onat),C),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Nat_Onat),D),A). [resolve(5518,a,5473,a)].
% 32.53/32.51 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,B),tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(A,B,tc_Nat_Onat),C)),hAPP(hAPP(c_Product__Type_OSigma(A,B),D),hAPP(c_COMBK(tc_fun(B,tc_HOL_Obool),A),E))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(B,tc_Nat_Onat),tc_fun(tc_fun(B,tc_HOL_Obool),tc_Nat_Onat),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat)),C)),E)),D). [resolve(5518,a,5474,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f297(C,D,E,B,A,tc_Nat_Onat)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,E),tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(A,E,tc_Nat_Onat),C)),hAPP(hAPP(c_Product__Type_OSigma(A,E),B),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_fun(E,tc_HOL_Obool),tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(E,tc_Nat_Onat),tc_fun(tc_fun(E,tc_HOL_Obool),tc_Nat_Onat),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,tc_Nat_Onat)),C)),D)),B). [resolve(5518,a,5475,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(C),hAPP(D,f297(E,D,C,B,A,tc_Nat_Onat)))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,C),tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(A,C,tc_Nat_Onat),E)),hAPP(hAPP(c_Product__Type_OSigma(A,C),B),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_fun(C,tc_HOL_Obool),tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(C,tc_Nat_Onat),tc_fun(tc_fun(C,tc_HOL_Obool),tc_Nat_Onat),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Nat_Onat)),E)),D)),B). [resolve(5518,a,5476,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(C),D)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Nat_Onat),hAPP(hAPP(c_COMBS(C,tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_Nat_Onat),tc_fun(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),C),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat)),hAPP(c_COMBC(A,C,tc_Nat_Onat),E))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),c_Set_OCollect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B)))),hAPP(c_COMBC(A,C,tc_HOL_Obool),F))))),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_fun(C,tc_HOL_Obool),tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(C,tc_Nat_Onat),tc_fun(tc_fun(C,tc_HOL_Obool),tc_Nat_Onat),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Nat_Onat)),E)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool),A),c_Set_OCollect(C)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool),A),hAPP(c_COMBS(C,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),C),c_fconj),hAPP(hAPP(c_COMBC(C,tc_fun(C,tc_HOL_Obool),tc_HOL_Obool),c_member(C)),D)))),F)))),B). [resolve(5518,a,5477,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),A),c_If(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C))),D)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C)))). [resolve(5518,a,5478,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat,C),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),c_Set_OCollect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B)))),hAPP(c_COMBC(A,C,tc_HOL_Obool),hAPP(hAPP(c_COMBB(C,tc_fun(C,tc_HOL_Obool),A),c_fequal),E)))))),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B). [resolve(5518,a,5479,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),hAPP(c_Set_OCollect(A),D)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),E),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(A),D))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),A),c_If(tc_Nat_Onat)),D)),C)),E)),B). [resolve(5518,a,5480,a)].
% 32.53/32.51 Derived: -c_Fun_Oinj__on(A,tc_Nat_Onat,B,C) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),c_Fun_Oid(tc_Nat_Onat)),hAPP(c_Set_Oimage(A,tc_Nat_Onat,B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),B),C). [resolve(5518,a,5481,a)].
% 32.53/32.51 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat),E),hAPP(c_Set_Oimage(A,B,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_Fun_Ocomp(B,tc_Nat_Onat,A,E),C)),D). [resolve(5518,a,5482,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -c_Fun_Oinj__on(A,A,C,B) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_Fun_Ocomp(A,tc_Nat_Onat,A,D),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),hAPP(c_Set_Oimage(A,A,C),B)). [resolve(5518,a,5483,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f344(C,D,E,B,A,tc_Nat_Onat)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Nat_Onat),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_Fun_Ocomp(C,tc_Nat_Onat,A,D),E)),B). [resolve(5518,a,5484,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f345(C,D,E,B,A,tc_Nat_Onat)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Nat_Onat),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_Fun_Ocomp(C,tc_Nat_Onat,A,D),E)),B). [resolve(5518,a,5485,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | f345(C,D,E,B,A,tc_Nat_Onat) != f344(C,D,E,B,A,tc_Nat_Onat) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Nat_Onat),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_Fun_Ocomp(C,tc_Nat_Onat,A,D),E)),B). [resolve(5518,a,5486,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(C,f345(D,E,C,B,A,tc_Nat_Onat)) = hAPP(C,f344(D,E,C,B,A,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Nat_Onat),E),hAPP(c_Set_Oimage(A,D,C),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_Fun_Ocomp(D,tc_Nat_Onat,A,E),C)),B). [resolve(5518,a,5487,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(C,hAPP(D,f344(E,C,D,B,A,tc_Nat_Onat))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,tc_Nat_Onat),C),hAPP(c_Set_Oimage(A,E,D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_Fun_Ocomp(E,tc_Nat_Onat,A,C),D)),B). [resolve(5518,a,5488,a)].
% 32.53/32.51 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(c_Set_Oimage(A,B,C),D) != E | hBOOL(hAPP(hAPP(c_member(A),f357(F,V6,E,D,C,B,A,tc_Nat_Onat)),D)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat),F),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),V6),D). [resolve(5518,a,5489,a)].
% 32.53/32.51 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(c_Set_Oimage(A,B,C),D) != E | hAPP(F,hAPP(C,f357(F,V6,E,D,C,B,A,tc_Nat_Onat))) != hAPP(V6,f357(F,V6,E,D,C,B,A,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat),F),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),V6),D). [resolve(5518,a,5490,a)].
% 32.53/32.51 Derived: -class_Orderings_Oord(A) | B != C | D != E | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),f358(F,V6,E,D,B,C,A,tc_Nat_Onat))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5518,a,5491,a)].
% 32.53/32.51 Derived: -class_Orderings_Oord(A) | B != C | D != E | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),f358(F,V6,E,D,B,C,A,tc_Nat_Onat)),E)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5518,a,5492,a)].
% 32.53/32.51 Derived: -class_Orderings_Oord(A) | B != C | D != E | hAPP(F,f358(V6,F,E,D,B,C,A,tc_Nat_Onat)) != hAPP(V6,f358(V6,F,E,D,B,C,A,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5518,a,5493,a)].
% 32.53/32.51 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_List_Onth(tc_Nat_Onat),A)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),A))). [resolve(5518,a,5494,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),A)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),c_COMBI(tc_Nat_Onat)),hAPP(c_List_Oset(tc_Nat_Onat),A)). [resolve(5518,a,5495,a)].
% 32.53/32.51 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),hAPP(hAPP(c_COMBS(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),B)),C)),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),D))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),C),D))). [resolve(5518,a,5496,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_List_Odistinct(A),B)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),hAPP(c_List_Oset(A),B)). [resolve(5518,a,5497,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),D),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(D,B)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),D),c_List_Oremove1(A,B,C)))). [resolve(5518,a,5498,a)].
% 32.53/32.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Nitpick_Osetsum_H(A,tc_Nat_Onat,C,B) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),C),c_Hilbert__Choice_OEps(tc_List_Olist(A),hAPP(hAPP(c_COMBS(tc_List_Olist(A),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(A)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(A),tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(A)),c_fequal),c_List_Oset(A))),B))),c_List_Odistinct(A))))). [resolve(5518,a,5499,a)].
% 32.53/32.52 Derived: hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Nitpick_Osetsum_H(A,tc_Nat_Onat,C,B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(5518,a,5500,a)].
% 32.53/32.52 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),A),c_List_Oupto(B,C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Nat_Onat),A),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(B,C))). [resolve(5518,a,5501,a)].
% 32.53/32.52 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),A),c_List_Oupt(B,C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),A),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(B,C))). [resolve(5518,a,5503,a)].
% 32.53/32.52 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(c_List_Orev(tc_Nat_Onat),A)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),A). [resolve(5518,a,5505,a)].
% 32.53/32.52 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f508(C,B,A,tc_Nat_Onat)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5506,a)].
% 32.53/32.52 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f509(C,B,A,tc_Nat_Onat)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5507,a)].
% 32.53/32.52 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Nat_Onat)),B)) | f509(C,B,A,tc_Nat_Onat) != f508(C,B,A,tc_Nat_Onat) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5508,a)].
% 32.53/32.52 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Nat_Onat)),f508(C,B,A,tc_Nat_Onat))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5509,a)].
% 32.53/32.52 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Nat_Onat)),f509(C,B,A,tc_Nat_Onat))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5510,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(C,f510(C,B,A,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5511,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f508(C,B,A,tc_Nat_Onat)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5512,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f509(C,B,A,tc_Nat_Onat)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5513,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Nat_Onat))) | f509(C,B,A,tc_Nat_Onat) != f508(C,B,A,tc_Nat_Onat) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5514,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Nat_Onat)),f508(C,B,A,tc_Nat_Onat))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5515,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Nat_Onat)),f509(C,B,A,tc_Nat_Onat))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5516,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Nat_Onat))) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(C,f510(C,B,A,tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5518,a,5517,a)].
% 32.62/32.54 5519 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) # label(axiom). [assumption].
% 32.62/32.54 Derived: -class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | hBOOL(hAPP(hAPP(c_member(A),f35(C,D,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(5519,a,5413,a)].
% 32.62/32.54 Derived: -class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(C,f35(D,C,B,A,tc_Code__Numeral_Ocode__numeral))),hAPP(D,f35(D,C,B,A,tc_Code__Numeral_Ocode__numeral)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B))). [resolve(5519,a,5414,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B). [resolve(5519,a,5415,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Set_Oinsert(A),C),B)). [resolve(5519,a,5417,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)). [resolve(5519,a,5419,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(C,D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),hAPP(hAPP(c_Set_Oinsert(A),D),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),hAPP(hAPP(c_Set_Oinsert(A),D),B)). [resolve(5519,a,5420,a)].
% 32.62/32.54 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5519,a,5421,a)].
% 32.62/32.55 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A) = A. [resolve(5519,a,5422,a)].
% 32.62/32.55 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(5519,a,5423,a)].
% 32.62/32.55 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))). [resolve(5519,a,5424,a)].
% 32.62/32.55 Derived: hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),B). [resolve(5519,a,5426,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),B) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral)),C),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B). [resolve(5519,a,5428,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_member(A),f87(D,C,B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5519,a,5431,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(D,f87(D,C,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5519,a,5432,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | hBOOL(hAPP(hAPP(c_member(A),f88(D,C,B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5519,a,5433,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),C)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(D,f88(D,C,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5519,a,5434,a)].
% 32.62/32.55 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f89(D,C,B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B))). [resolve(5519,a,5435,a)].
% 32.62/32.55 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(D,f89(D,C,B,A,tc_Code__Numeral_Ocode__numeral)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B))). [resolve(5519,a,5436,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f94(D,C,B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B). [resolve(5519,a,5437,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(D,f94(D,C,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B). [resolve(5519,a,5438,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f95(D,C,B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B). [resolve(5519,a,5439,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(D,f95(D,C,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B). [resolve(5519,a,5440,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),B)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral)),C)),D)),B). [resolve(5519,a,5441,a)].
% 32.62/32.55 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(B,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral)),hAPP(c_COMBC(B,A,tc_Code__Numeral_Ocode__numeral),C))),D)),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(A,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral)),C)),E)),D). [resolve(5519,a,5442,a)].
% 32.62/32.55 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBK(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),B). [resolve(5519,a,5443,a)].
% 32.62/32.55 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),B),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral)),B)),D)),C). [resolve(5519,a,5444,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),A),c_If(tc_Code__Numeral_Ocode__numeral)),hAPP(c_fequal,C))),D)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),B) = hAPP(D,C). [resolve(5519,a,5445,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),A),c_If(tc_Code__Numeral_Ocode__numeral)),hAPP(c_fequal,C))),D)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),B). [resolve(5519,a,5446,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),A),c_If(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),C))),D)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),B) = hAPP(D,C). [resolve(5519,a,5447,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),A),c_If(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),C))),D)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),B). [resolve(5519,a,5448,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),A),c_If(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C))),D)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),C)). [resolve(5519,a,5449,a)].
% 32.62/32.55 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B))),hAPP(A,B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,B))). [resolve(5519,a,5450,a)].
% 32.62/32.55 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat),A),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),hAPP(c_Nat_OSuc,C))). [resolve(5519,a,5451,a)].
% 32.62/32.55 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat),A),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),B))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D),B))). [resolve(5519,a,5452,a)].
% 32.62/32.55 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)). [resolve(5519,a,5453,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))). [resolve(5519,a,5454,a)].
% 32.62/32.56 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,A))),hAPP(C,hAPP(c_Nat_OSuc,A))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))). [resolve(5519,a,5455,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))). [resolve(5519,a,5456,a)].
% 32.62/32.56 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),B))),hAPP(A,hAPP(c_Nat_OSuc,B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,B))). [resolve(5519,a,5457,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,A,B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)). [resolve(5519,a,5458,a)].
% 32.62/32.56 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat),A),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)),hAPP(c_Nat_OSuc,C))). [resolve(5519,a,5459,a)].
% 32.62/32.56 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat),A),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),B))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),D),B))). [resolve(5519,a,5460,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),D),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),C)). [resolve(5519,a,5461,a)].
% 32.62/32.56 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B)). [resolve(5519,a,5462,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(C,A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A),B)). [resolve(5519,a,5463,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A))). [resolve(5519,a,5464,a)].
% 32.62/32.56 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),A))),hAPP(C,A)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A))). [resolve(5519,a,5465,a)].
% 32.62/32.56 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint),A),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),B). [resolve(5519,a,5466,a)].
% 32.62/32.56 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint),A),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),B). [resolve(5519,a,5467,a)].
% 32.62/32.56 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | -c_Nat__Transfer_Onat__set(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),B),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat),B),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),A)). [resolve(5519,a,5468,a)].
% 32.62/32.56 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | -c_Nat__Transfer_Onat__set(A) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),B),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat),B),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),A)). [resolve(5519,a,5469,a)].
% 32.62/32.56 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | A != B | -c_Nat__Transfer_Onat__set(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),f285(C,D,A,B,tc_Code__Numeral_Ocode__numeral))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),D),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),C),A). [resolve(5519,a,5470,a)].
% 32.62/32.56 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | A != B | -c_Nat__Transfer_Onat__set(A) | hAPP(C,f285(D,C,A,B,tc_Code__Numeral_Ocode__numeral)) != hAPP(D,f285(D,C,A,B,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),C),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),D),A). [resolve(5519,a,5471,a)].
% 32.62/32.56 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | A != B | -c_Nat__Transfer_Onat__set(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),f286(C,D,A,B,tc_Code__Numeral_Ocode__numeral))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),D),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),C),A). [resolve(5519,a,5472,a)].
% 32.62/32.56 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | A != B | -c_Nat__Transfer_Onat__set(A) | hAPP(C,f286(D,C,A,B,tc_Code__Numeral_Ocode__numeral)) != hAPP(D,f286(D,C,A,B,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),C),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),D),A). [resolve(5519,a,5473,a)].
% 32.62/32.56 Derived: hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,B),tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Oprod_Oprod__case(A,B,tc_Code__Numeral_Ocode__numeral),C)),hAPP(hAPP(c_Product__Type_OSigma(A,B),D),hAPP(c_COMBK(tc_fun(B,tc_HOL_Obool),A),E))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(B,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral)),C)),E)),D). [resolve(5519,a,5474,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f297(C,D,E,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,E),tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Oprod_Oprod__case(A,E,tc_Code__Numeral_Ocode__numeral),C)),hAPP(hAPP(c_Product__Type_OSigma(A,E),B),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_fun(E,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(E,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(E,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,tc_Code__Numeral_Ocode__numeral)),C)),D)),B). [resolve(5519,a,5475,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(C),hAPP(D,f297(E,D,C,B,A,tc_Code__Numeral_Ocode__numeral)))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(A,C),tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Oprod_Oprod__case(A,C,tc_Code__Numeral_Ocode__numeral),E)),hAPP(hAPP(c_Product__Type_OSigma(A,C),B),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_fun(C,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(C,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(C,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Code__Numeral_Ocode__numeral)),E)),D)),B). [resolve(5519,a,5476,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(C),D)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(C,tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(A,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),C),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_COMBC(A,C,tc_Code__Numeral_Ocode__numeral),E))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),c_Set_OCollect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B)))),hAPP(c_COMBC(A,C,tc_HOL_Obool),F))))),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_fun(C,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(C,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(C,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Code__Numeral_Ocode__numeral)),E)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool),A),c_Set_OCollect(C)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool),A),hAPP(c_COMBS(C,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),C),c_fconj),hAPP(hAPP(c_COMBC(C,tc_fun(C,tc_HOL_Obool),tc_HOL_Obool),c_member(C)),D)))),F)))),B). [resolve(5519,a,5477,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),A),c_If(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C))),D)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),C)))). [resolve(5519,a,5478,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral,C),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),c_Set_OCollect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool),C),hAPP(c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B)))),hAPP(c_COMBC(A,C,tc_HOL_Obool),hAPP(hAPP(c_COMBB(C,tc_fun(C,tc_HOL_Obool),A),c_fequal),E)))))),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B). [resolve(5519,a,5479,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),hAPP(c_Set_OCollect(A),D)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),E),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool)),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(A),D))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),A),c_If(tc_Code__Numeral_Ocode__numeral)),D)),C)),E)),B). [resolve(5519,a,5480,a)].
% 32.62/32.56 Derived: -c_Fun_Oinj__on(A,tc_Code__Numeral_Ocode__numeral,B,C) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),c_Fun_Oid(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Set_Oimage(A,tc_Code__Numeral_Ocode__numeral,B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),B),C). [resolve(5519,a,5481,a)].
% 32.62/32.56 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral),E),hAPP(c_Set_Oimage(A,B,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_Fun_Ocomp(B,tc_Code__Numeral_Ocode__numeral,A,E),C)),D). [resolve(5519,a,5482,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -c_Fun_Oinj__on(A,A,C,B) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_Fun_Ocomp(A,tc_Code__Numeral_Ocode__numeral,A,D),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),hAPP(c_Set_Oimage(A,A,C),B)). [resolve(5519,a,5483,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f344(C,D,E,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Code__Numeral_Ocode__numeral),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_Fun_Ocomp(C,tc_Code__Numeral_Ocode__numeral,A,D),E)),B). [resolve(5519,a,5484,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hBOOL(hAPP(hAPP(c_member(A),f345(C,D,E,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Code__Numeral_Ocode__numeral),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_Fun_Ocomp(C,tc_Code__Numeral_Ocode__numeral,A,D),E)),B). [resolve(5519,a,5485,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | f345(C,D,E,B,A,tc_Code__Numeral_Ocode__numeral) != f344(C,D,E,B,A,tc_Code__Numeral_Ocode__numeral) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,tc_Code__Numeral_Ocode__numeral),D),hAPP(c_Set_Oimage(A,C,E),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_Fun_Ocomp(C,tc_Code__Numeral_Ocode__numeral,A,D),E)),B). [resolve(5519,a,5486,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | hAPP(C,f345(D,E,C,B,A,tc_Code__Numeral_Ocode__numeral)) = hAPP(C,f344(D,E,C,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Code__Numeral_Ocode__numeral),E),hAPP(c_Set_Oimage(A,D,C),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_Fun_Ocomp(D,tc_Code__Numeral_Ocode__numeral,A,E),C)),B). [resolve(5519,a,5487,a)].
% 32.62/32.56 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(C,hAPP(D,f344(E,C,D,B,A,tc_Code__Numeral_Ocode__numeral))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,tc_Code__Numeral_Ocode__numeral),C),hAPP(c_Set_Oimage(A,E,D),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_Fun_Ocomp(E,tc_Code__Numeral_Ocode__numeral,A,C),D)),B). [resolve(5519,a,5488,a)].
% 32.62/32.56 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(c_Set_Oimage(A,B,C),D) != E | hBOOL(hAPP(hAPP(c_member(A),f357(F,V6,E,D,C,B,A,tc_Code__Numeral_Ocode__numeral)),D)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral),F),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),V6),D). [resolve(5519,a,5489,a)].
% 32.62/32.56 Derived: -c_Fun_Oinj__on(A,B,C,D) | hAPP(c_Set_Oimage(A,B,C),D) != E | hAPP(F,hAPP(C,f357(F,V6,E,D,C,B,A,tc_Code__Numeral_Ocode__numeral))) != hAPP(V6,f357(F,V6,E,D,C,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral),F),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),V6),D). [resolve(5519,a,5490,a)].
% 32.62/32.56 Derived: -class_Orderings_Oord(A) | B != C | D != E | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),f358(F,V6,E,D,B,C,A,tc_Code__Numeral_Ocode__numeral))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5519,a,5491,a)].
% 32.62/32.56 Derived: -class_Orderings_Oord(A) | B != C | D != E | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),f358(F,V6,E,D,B,C,A,tc_Code__Numeral_Ocode__numeral)),E)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5519,a,5492,a)].
% 32.62/32.56 Derived: -class_Orderings_Oord(A) | B != C | D != E | hAPP(F,f358(V6,F,E,D,B,C,A,tc_Code__Numeral_Ocode__numeral)) != hAPP(V6,f358(V6,F,E,D,B,C,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),F),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),V6),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,B),E)). [resolve(5519,a,5493,a)].
% 32.62/32.57 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Code__Numeral_Ocode__numeral)),A))). [resolve(5519,a,5494,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_List_Odistinct(tc_Code__Numeral_Ocode__numeral),A)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),c_COMBI(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(tc_Code__Numeral_Ocode__numeral),A)). [resolve(5519,a,5495,a)].
% 32.62/32.57 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBS(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral)),B)),C)),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),D))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),C),D))). [resolve(5519,a,5496,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_List_Odistinct(A),B)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),C),B)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),hAPP(c_List_Oset(A),B)). [resolve(5519,a,5497,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(hAPP(c_member(A),B),hAPP(c_List_Oset(A),C))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),D),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(D,B)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),D),c_List_Oremove1(A,B,C)))). [resolve(5519,a,5498,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Nitpick_Osetsum_H(A,tc_Code__Numeral_Ocode__numeral,C,B) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),C),c_Hilbert__Choice_OEps(tc_List_Olist(A),hAPP(hAPP(c_COMBS(tc_List_Olist(A),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(A)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(A),tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(A)),c_fequal),c_List_Oset(A))),B))),c_List_Odistinct(A))))). [resolve(5519,a,5499,a)].
% 32.62/32.57 Derived: hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Nitpick_Osetsum_H(A,tc_Code__Numeral_Ocode__numeral,C,B) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(5519,a,5500,a)].
% 32.62/32.57 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),A),c_List_Oupto(B,C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(B,C))). [resolve(5519,a,5501,a)].
% 32.62/32.57 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),c_List_Oupt(B,C))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(B,C))). [resolve(5519,a,5503,a)].
% 32.62/32.57 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Orev(tc_Code__Numeral_Ocode__numeral),A)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),A). [resolve(5519,a,5505,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f508(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5506,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f509(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5507,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | f509(C,B,A,tc_Code__Numeral_Ocode__numeral) != f508(C,B,A,tc_Code__Numeral_Ocode__numeral) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5508,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Code__Numeral_Ocode__numeral)),f508(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5509,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Code__Numeral_Ocode__numeral)),f509(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5510,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f507(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(C,f510(C,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5511,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f508(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5512,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_member(tc_fun(A,tc_HOL_Obool)),f509(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5513,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Code__Numeral_Ocode__numeral))) | f509(C,B,A,tc_Code__Numeral_Ocode__numeral) != f508(C,B,A,tc_Code__Numeral_Ocode__numeral) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5514,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Code__Numeral_Ocode__numeral)),f508(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5515,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_member(A),f510(C,B,A,tc_Code__Numeral_Ocode__numeral)),f509(C,B,A,tc_Code__Numeral_Ocode__numeral))) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5516,a)].
% 32.62/32.57 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(A,tc_HOL_Obool)),B)) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),f507(C,B,A,tc_Code__Numeral_Ocode__numeral))) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(C,f510(C,B,A,tc_Code__Numeral_Ocode__numeral)) | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C)),B) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B)). [resolve(5519,a,5517,a)].
% 34.71/34.67 5520 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 34.71/34.67 5521 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D # label(fact_add__right__imp__eq) # label(axiom). [clausify(424)].
% 34.71/34.67 5522 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__left__imp__eq) # label(axiom). [clausify(426)].
% 34.71/34.67 5523 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B = D # label(fact_add__right__cancel) # label(axiom). [clausify(427)].
% 34.71/34.67 5524 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C) | B != D # label(fact_add__right__cancel) # label(axiom). [clausify(427)].
% 34.71/34.67 5525 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__left__cancel) # label(axiom). [clausify(428)].
% 34.71/34.67 5526 -class_Groups_Ocancel__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C != D # label(fact_add__left__cancel) # label(axiom). [clausify(428)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B) | A = C. [resolve(5520,a,5521,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(5520,a,5522,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B) | A != C. [resolve(5520,a,5524,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C) | B != C. [resolve(5520,a,5526,a)].
% 34.71/34.67 5527 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B) | A = C. [resolve(5527,a,5521,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C) | B = C. [resolve(5527,a,5522,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B) | A != C. [resolve(5527,a,5524,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C) | B != C. [resolve(5527,a,5526,a)].
% 34.71/34.67 5528 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) # label(axiom). [assumption].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B) | A = C. [resolve(5528,a,5521,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C) | B = C. [resolve(5528,a,5522,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B) | A != C. [resolve(5528,a,5524,a)].
% 34.71/34.67 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C) | B != C. [resolve(5528,a,5526,a)].
% 40.91/40.87 5529 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 40.91/40.87 5530 -class_Groups_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) | C = D # label(fact_add__imp__eq) # label(axiom). [clausify(425)].
% 40.91/40.87 5531 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 40.91/40.87 5532 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 40.91/40.87 5533 class_Groups_Oab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 40.91/40.87 5534 -class_Groups_Oab__semigroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom). [clausify(429)].
% 40.91/40.87 5535 -class_Groups_Oab__semigroup__add(A) | c_List_Ofoldr(A,A,c_Groups_Oplus__class_Oplus(A),B,C) = hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),C),B) # label(fact_foldr__conv__foldl) # label(axiom). [clausify(4286)].
% 40.91/40.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(5533,a,5534,a)].
% 40.91/40.87 Derived: c_List_Ofoldr(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),A,B) = hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(5533,a,5535,a)].
% 40.91/40.87 5536 class_Groups_Oab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 40.91/40.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(5536,a,5534,a)].
% 40.91/40.87 Derived: c_List_Ofoldr(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A,B) = hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),A). [resolve(5536,a,5535,a)].
% 40.91/40.87 5537 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) # label(axiom). [assumption].
% 40.91/40.87 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5537,a,5534,a)].
% 40.91/40.87 Derived: c_List_Ofoldr(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A,B) = hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),A). [resolve(5537,a,5535,a)].
% 40.91/40.87 5538 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 40.91/40.87 5539 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_add__le__cancel__right) # label(axiom). [clausify(430)].
% 40.91/40.87 5540 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_add__le__cancel__right) # label(axiom). [clausify(430)].
% 40.91/40.87 5541 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_add__le__cancel__left) # label(axiom). [clausify(431)].
% 40.91/40.87 5542 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_add__le__cancel__left) # label(axiom). [clausify(431)].
% 40.91/40.87 5543 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_add__le__imp__le__right) # label(axiom). [clausify(435)].
% 40.91/40.87 5544 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_add__le__imp__le__left) # label(axiom). [clausify(436)].
% 40.91/40.87 5545 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__imp__less__left) # label(axiom). [clausify(437)].
% 40.91/40.87 5546 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__imp__less__right) # label(axiom). [clausify(438)].
% 40.91/40.87 5547 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__cancel__left) # label(axiom). [clausify(442)].
% 40.91/40.87 5548 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_add__less__cancel__left) # label(axiom). [clausify(442)].
% 40.91/40.87 5549 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__cancel__right) # label(axiom). [clausify(443)].
% 40.91/40.87 5550 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_add__less__cancel__right) # label(axiom). [clausify(443)].
% 40.91/40.87 5551 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),D)),C) # label(fact_min__add__distrib__left) # label(axiom). [clausify(636)].
% 40.91/40.87 5552 -class_Groups_Oordered__ab__semigroup__add__imp__le(A) | hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)),C) # label(fact_max__add__distrib__left) # label(axiom). [clausify(2478)].
% 40.97/40.89 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(5538,a,5539,a)].
% 40.97/40.89 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(5538,a,5540,a)].
% 40.97/40.89 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)). [resolve(5538,a,5541,a)].
% 40.97/40.89 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)). [resolve(5538,a,5542,a)].
% 40.97/40.89 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(5538,a,5545,a)].
% 40.97/40.89 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(5538,a,5546,a)].
% 40.97/40.89 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(5538,a,5548,a)].
% 40.97/40.89 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(5538,a,5550,a)].
% 40.97/40.89 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),C)),B). [resolve(5538,a,5551,a)].
% 40.97/40.89 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),C)),B). [resolve(5538,a,5552,a)].
% 40.97/40.89 5553 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 40.97/40.89 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5553,a,5539,a)].
% 40.97/40.89 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5553,a,5540,a)].
% 40.97/40.89 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5553,a,5541,a)].
% 40.97/40.91 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5553,a,5542,a)].
% 40.97/40.91 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5553,a,5545,a)].
% 40.97/40.91 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5553,a,5546,a)].
% 40.97/40.91 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5553,a,5548,a)].
% 40.97/40.91 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5553,a,5550,a)].
% 40.97/40.91 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),A),C)),B). [resolve(5553,a,5551,a)].
% 40.97/40.91 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),A),C)),B). [resolve(5553,a,5552,a)].
% 40.97/40.91 5554 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 40.97/40.91 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5554,a,5539,a)].
% 40.97/40.91 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5554,a,5540,a)].
% 40.97/40.91 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5554,a,5541,a)].
% 40.97/40.91 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5554,a,5542,a)].
% 40.97/40.91 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5554,a,5545,a)].
% 43.03/42.96 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5554,a,5546,a)].
% 43.03/42.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5554,a,5548,a)].
% 43.03/42.96 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5554,a,5550,a)].
% 43.03/42.96 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(5554,a,5551,a)].
% 43.03/42.96 Derived: hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(5554,a,5552,a)].
% 43.03/42.96 5555 class_Groups_Ogroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Ogroup__add) # label(axiom). [assumption].
% 43.03/42.96 5556 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),C) = B # label(fact_diff__add__cancel) # label(axiom). [clausify(445)].
% 43.03/42.96 5557 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),C) = B # label(fact_add__diff__cancel) # label(axiom). [clausify(446)].
% 43.03/42.96 5558 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) | C = B # label(fact_right__minus__eq) # label(axiom). [clausify(869)].
% 43.03/42.96 5559 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) | C != B # label(fact_right__minus__eq) # label(axiom). [clausify(869)].
% 43.03/42.96 5560 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),B) # label(fact_diff__self) # label(axiom). [clausify(871)].
% 43.03/42.96 5561 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_diff__0__right) # label(axiom). [clausify(872)].
% 43.03/42.96 5562 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) = B # label(fact_minus__minus) # label(axiom). [clausify(1483)].
% 43.03/42.96 5563 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) = B # label(fact_equation__minus__iff) # label(axiom). [clausify(1484)].
% 43.03/42.96 5564 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) != B # label(fact_equation__minus__iff) # label(axiom). [clausify(1484)].
% 43.03/42.96 5565 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) = B # label(fact_minus__equation__iff) # label(axiom). [clausify(1485)].
% 43.03/42.96 5566 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C | hAPP(c_Groups_Ouminus__class_Ouminus(A),C) != B # label(fact_minus__equation__iff) # label(axiom). [clausify(1485)].
% 43.03/42.96 5567 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != hAPP(c_Groups_Ouminus__class_Ouminus(A),C) | B = C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(1486)].
% 43.03/42.96 5568 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),C) | B != C # label(fact_neg__equal__iff__equal) # label(axiom). [clausify(1486)].
% 43.03/42.96 5569 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_minus__zero) # label(axiom). [clausify(1506)].
% 43.03/42.96 5570 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(1507)].
% 43.03/42.96 5571 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__0__equal__iff__equal) # label(axiom). [clausify(1507)].
% 43.03/42.96 5572 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(1509)].
% 43.03/42.96 5573 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Ouminus__class_Ouminus(A),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__0__iff__equal) # label(axiom). [clausify(1509)].
% 43.03/42.96 5574 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) # label(fact_minus__add) # label(axiom). [clausify(1515)].
% 43.03/42.96 5575 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) = C # label(fact_add__minus__cancel) # label(axiom). [clausify(1516)].
% 43.03/42.96 5576 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)) = C # label(fact_minus__add__cancel) # label(axiom). [clausify(1517)].
% 43.03/42.96 5577 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) # label(fact_right__minus) # label(axiom). [clausify(1565)].
% 43.03/42.96 5578 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B) # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(1566)].
% 43.03/42.96 5579 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B) # label(fact_eq__neg__iff__add__eq__0) # label(axiom). [clausify(1566)].
% 43.03/42.96 5580 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B) # label(fact_left__minus) # label(axiom). [clausify(1567)].
% 43.03/42.96 5581 -class_Groups_Ogroup__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C # label(fact_minus__unique) # label(axiom). [clausify(1569)].
% 43.03/42.96 5582 -class_Groups_Ogroup__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_diff__0) # label(axiom). [clausify(1570)].
% 43.03/42.96 5583 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) # label(fact_diff__def) # label(axiom). [clausify(1572)].
% 47.25/47.17 5584 -class_Groups_Ogroup__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_diff__minus__eq__add) # label(axiom). [clausify(1574)].
% 47.25/47.17 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),B) = A. [resolve(5555,a,5556,a)].
% 47.25/47.17 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),B) = A. [resolve(5555,a,5557,a)].
% 47.25/47.17 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),A). [resolve(5555,a,5560,a)].
% 47.25/47.17 Derived: hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(5555,a,5561,a)].
% 47.25/47.17 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)) = A. [resolve(5555,a,5562,a)].
% 47.25/47.17 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != B | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B) = A. [resolve(5555,a,5563,a)].
% 47.25/47.17 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B) | A = B. [resolve(5555,a,5567,a)].
% 47.25/47.17 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B) | A != B. [resolve(5555,a,5568,a)].
% 47.25/47.17 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(5555,a,5569,a)].
% 47.25/47.17 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5555,a,5570,a)].
% 47.25/47.17 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(5555,a,5571,a)].
% 47.25/47.17 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(5555,a,5574,a)].
% 47.25/47.17 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) = B. [resolve(5555,a,5575,a)].
% 47.25/47.17 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)) = B. [resolve(5555,a,5576,a)].
% 47.25/47.17 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(5555,a,5577,a)].
% 47.25/47.17 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(5555,a,5578,a)].
% 47.25/47.17 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = B | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(5555,a,5579,a)].
% 47.25/47.17 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = B. [resolve(5555,a,5581,a)].
% 47.25/47.17 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(5555,a,5582,a)].
% 47.25/47.17 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(5555,a,5584,a)].
% 47.25/47.17 5585 class_Rings_Oordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring) # label(axiom). [assumption].
% 47.25/47.17 5586 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_less__add__iff2) # label(axiom). [clausify(472)].
% 47.25/47.17 5587 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_less__add__iff2) # label(axiom). [clausify(472)].
% 47.25/47.17 5588 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(473)].
% 47.25/47.17 5589 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_less__add__iff1) # label(axiom). [clausify(473)].
% 47.25/47.17 5590 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_le__add__iff2) # label(axiom). [clausify(474)].
% 47.25/47.17 5591 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F))) # label(fact_le__add__iff2) # label(axiom). [clausify(474)].
% 47.25/47.17 5592 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(475)].
% 47.25/47.17 5593 -class_Rings_Oordered__ring(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)),F)) # label(fact_le__add__iff1) # label(axiom). [clausify(475)].
% 47.25/47.17 5594 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_mult__nonpos__nonpos) # label(axiom). [clausify(928)].
% 47.25/47.17 5595 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) # label(fact_mult__right__mono__neg) # label(axiom). [clausify(932)].
% 47.25/47.17 5596 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))) # label(fact_mult__left__mono__neg) # label(axiom). [clausify(933)].
% 47.25/47.17 5597 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_split__mult__pos__le) # label(axiom). [clausify(936)].
% 47.25/47.17 5598 -class_Rings_Oordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_split__mult__pos__le) # label(axiom). [clausify(936)].
% 47.25/47.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(5585,a,5586,a)].
% 47.25/47.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(5585,a,5587,a)].
% 47.25/47.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(5585,a,5588,a)].
% 47.25/47.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(5585,a,5589,a)].
% 47.25/47.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(5585,a,5590,a)].
% 47.25/47.18 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E))). [resolve(5585,a,5591,a)].
% 47.25/47.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(5585,a,5592,a)].
% 47.25/47.18 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)),E)). [resolve(5585,a,5593,a)].
% 47.25/47.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(5585,a,5594,a)].
% 47.25/47.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(5585,a,5595,a)].
% 47.25/47.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(5585,a,5596,a)].
% 47.25/47.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(5585,a,5597,a)].
% 49.40/49.32 5599 class_Rings_Ocomm__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 49.40/49.32 5600 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(480)].
% 49.40/49.32 5601 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(482)].
% 49.40/49.32 5602 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(483)].
% 49.40/49.32 5603 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(484)].
% 49.40/49.32 5604 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(485)].
% 49.40/49.32 5605 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(486)].
% 49.40/49.32 5606 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(487)].
% 49.40/49.32 5607 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(488)].
% 49.40/49.32 5608 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),E)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(489)].
% 49.40/49.32 5609 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(490)].
% 49.40/49.32 5610 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(491)].
% 49.40/49.32 5611 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(492)].
% 49.40/49.32 5612 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(493)].
% 49.40/49.32 5613 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(494)].
% 49.40/49.32 5614 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(495)].
% 49.40/49.32 5615 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(498)].
% 49.40/49.32 5616 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(499)].
% 49.40/49.32 5617 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(689)].
% 49.40/49.32 5618 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(690)].
% 49.40/49.32 5619 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A))),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(703)].
% 49.40/49.32 5620 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),c_Groups_Oone__class_Oone(A))),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(704)].
% 49.40/49.32 5621 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),C) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(705)].
% 49.40/49.32 5622 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(855)].
% 49.40/49.32 5623 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(856)].
% 49.40/49.32 5624 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(865)].
% 49.40/49.32 5625 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(867)].
% 49.40/49.32 5626 -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Ono__zero__divisors(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),D),C) | hBOOL(hAPP(hAPP(c_member(B),f74(D,C,B,A)),C)) # label(fact_setprod__zero__iff) # label(axiom). [clausify(972)].
% 49.40/49.32 5627 -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Ono__zero__divisors(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),D),C) | c_Groups_Ozero__class_Ozero(A) = hAPP(D,f74(D,C,B,A)) # label(fact_setprod__zero__iff) # label(axiom). [clausify(972)].
% 49.40/49.32 5628 -class_Rings_Ocomm__semiring__1(A) | -class_Rings_Ono__zero__divisors(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),D),C) | -hBOOL(hAPP(hAPP(c_member(B),E),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(D,E) # label(fact_setprod__zero__iff) # label(axiom). [clausify(972)].
% 49.40/49.32 5629 -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(E,D) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),E),C) # label(fact_setprod__zero) # label(axiom). [clausify(973)].
% 49.40/49.32 5630 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom). [clausify(1831)].
% 49.40/49.32 5631 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(1838)].
% 49.40/49.32 5632 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(1840)].
% 49.40/49.32 5633 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom). [clausify(1847)].
% 49.40/49.32 5634 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom). [clausify(1848)].
% 49.40/49.32 5635 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom). [clausify(1849)].
% 49.40/49.33 5636 -class_Rings_Ocomm__semiring__1(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom). [clausify(1850)].
% 49.40/49.33 5637 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(1851)].
% 49.40/49.33 5638 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom). [clausify(1890)].
% 49.40/49.33 5639 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom). [clausify(1906)].
% 49.40/49.33 5640 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom). [clausify(1917)].
% 49.40/49.33 5641 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),D)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),hAPP(hAPP(c_COMBB(A,A,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(A),C)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(A)),c_Nat_Osemiring__1__class_Oof__nat(A))),D))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),B))) # label(fact_arith__series__general) # label(axiom). [clausify(2450)].
% 49.40/49.33 5642 -class_Rings_Ocomm__semiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),c_Groups_Oone__class_Oone(A))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A),c_Nat_Osemiring__1__class_Oof__nat(A)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),B))) # label(fact_gauss__sum) # label(axiom). [clausify(2559)].
% 49.40/49.33 5643 -class_Rings_Ocomm__semiring__1(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_dvd__0__right) # label(axiom). [clausify(4799)].
% 49.40/49.33 5644 -class_Rings_Ocomm__semiring__1(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_dvd__triv__left) # label(axiom). [clausify(4816)].
% 49.40/49.33 5645 -class_Rings_Ocomm__semiring__1(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B))) # label(fact_dvd__triv__right) # label(axiom). [clausify(4817)].
% 49.40/49.33 5646 -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) # label(fact_dvd__mult2) # label(axiom). [clausify(4818)].
% 49.40/49.33 5647 -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_dvd__mult) # label(axiom). [clausify(4819)].
% 49.40/49.33 5648 -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),D),E)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__dvd__mono) # label(axiom). [clausify(4820)].
% 49.40/49.33 5649 -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) # label(fact_dvd__mult__left) # label(axiom). [clausify(4822)].
% 49.40/49.33 5650 -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)) # label(fact_dvd__mult__right) # label(axiom). [clausify(4823)].
% 49.40/49.33 5651 -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_member(B),D),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(E,D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),E),C))) # label(fact_dvd__setprod) # label(axiom). [clausify(4825)].
% 49.40/49.33 5652 -class_Rings_Ocomm__semiring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) # label(fact_dvd__trans) # label(axiom). [clausify(4851)].
% 49.40/49.33 5653 -class_Rings_Ocomm__semiring__1(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),B)) # label(fact_dvd__refl) # label(axiom). [clausify(4852)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(5599,a,5600,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(5599,a,5601,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(5599,a,5602,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(5599,a,5605,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(5599,a,5606,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(5599,a,5607,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),D)). [resolve(5599,a,5608,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),B). [resolve(5599,a,5610,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(5599,a,5613,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A). [resolve(5599,a,5614,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(5599,a,5615,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(5599,a,5617,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(5599,a,5618,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),A). [resolve(5599,a,5619,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))),A). [resolve(5599,a,5620,a)].
% 49.40/49.33 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),B). [resolve(5599,a,5621,a)].
% 49.40/49.33 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(5599,a,5624,a)].
% 49.40/49.33 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(5599,a,5625,a)].
% 49.40/49.33 Derived: -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),C),B) | hBOOL(hAPP(hAPP(c_member(A),f74(C,B,A,tc_Int_Oint)),B)). [resolve(5599,a,5626,a)].
% 49.40/49.33 Derived: -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),C),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(C,f74(C,B,A,tc_Int_Oint)). [resolve(5599,a,5627,a)].
% 49.40/49.33 Derived: -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),C),B) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(C,D). [resolve(5599,a,5628,a)].
% 49.40/49.33 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(D,C) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),D),B). [resolve(5599,a,5629,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)). [resolve(5599,a,5630,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(5599,a,5631,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(5599,a,5632,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(5599,a,5633,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A). [resolve(5599,a,5635,a)].
% 49.40/49.34 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(5599,a,5636,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)). [resolve(5599,a,5637,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A). [resolve(5599,a,5638,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(5599,a,5639,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(5599,a,5640,a)].
% 49.40/49.34 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),C))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A))). [resolve(5599,a,5641,a)].
% 49.43/49.35 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A))). [resolve(5599,a,5642,a)].
% 49.43/49.35 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5599,a,5643,a)].
% 49.43/49.35 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(5599,a,5644,a)].
% 49.43/49.35 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(5599,a,5645,a)].
% 49.43/49.35 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(5599,a,5646,a)].
% 49.43/49.35 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(5599,a,5647,a)].
% 49.43/49.35 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),C),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(5599,a,5648,a)].
% 49.43/49.35 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)). [resolve(5599,a,5649,a)].
% 49.43/49.35 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),C)). [resolve(5599,a,5650,a)].
% 49.43/49.35 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),D),B))). [resolve(5599,a,5651,a)].
% 49.43/49.35 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)). [resolve(5599,a,5652,a)].
% 49.43/49.35 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),A)). [resolve(5599,a,5653,a)].
% 49.43/49.35 5654 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 49.43/49.35 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(5654,a,5600,a)].
% 49.43/49.35 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D)). [resolve(5654,a,5601,a)].
% 49.43/49.35 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),B). [resolve(5654,a,5602,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)). [resolve(5654,a,5605,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),A). [resolve(5654,a,5606,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)). [resolve(5654,a,5607,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),D)). [resolve(5654,a,5608,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),B). [resolve(5654,a,5610,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)). [resolve(5654,a,5613,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A). [resolve(5654,a,5614,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),B). [resolve(5654,a,5615,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(5654,a,5617,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) = A. [resolve(5654,a,5618,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),A). [resolve(5654,a,5619,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))),A). [resolve(5654,a,5620,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat))),B). [resolve(5654,a,5621,a)].
% 49.43/49.36 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(5654,a,5624,a)].
% 49.43/49.36 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(5654,a,5625,a)].
% 49.43/49.36 Derived: -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),C),B) | hBOOL(hAPP(hAPP(c_member(A),f74(C,B,A,tc_Nat_Onat)),B)). [resolve(5654,a,5626,a)].
% 49.43/49.36 Derived: -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),C),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(C,f74(C,B,A,tc_Nat_Onat)). [resolve(5654,a,5627,a)].
% 49.43/49.36 Derived: -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),C),B) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(C,D). [resolve(5654,a,5628,a)].
% 49.43/49.36 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(D,C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),D),B). [resolve(5654,a,5629,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)). [resolve(5654,a,5630,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(5654,a,5631,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(5654,a,5632,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(5654,a,5633,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),A). [resolve(5654,a,5635,a)].
% 49.43/49.36 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(5654,a,5636,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)). [resolve(5654,a,5637,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),A). [resolve(5654,a,5638,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)). [resolve(5654,a,5639,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(5654,a,5640,a)].
% 49.43/49.36 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat))),C))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A))). [resolve(5654,a,5641,a)].
% 49.43/49.38 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A))). [resolve(5654,a,5642,a)].
% 49.43/49.38 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5654,a,5643,a)].
% 49.43/49.38 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))). [resolve(5654,a,5644,a)].
% 49.43/49.38 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A))). [resolve(5654,a,5645,a)].
% 49.43/49.38 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))). [resolve(5654,a,5646,a)].
% 49.43/49.38 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))). [resolve(5654,a,5647,a)].
% 49.43/49.38 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),C),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(5654,a,5648,a)].
% 49.43/49.38 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)). [resolve(5654,a,5649,a)].
% 49.43/49.38 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),C)). [resolve(5654,a,5650,a)].
% 49.43/49.38 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),D),B))). [resolve(5654,a,5651,a)].
% 49.43/49.38 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)). [resolve(5654,a,5652,a)].
% 49.43/49.38 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),A)). [resolve(5654,a,5653,a)].
% 49.43/49.38 5655 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) # label(axiom). [assumption].
% 49.43/49.38 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5655,a,5600,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),D)). [resolve(5655,a,5601,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(5655,a,5602,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5655,a,5605,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),A). [resolve(5655,a,5606,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D)). [resolve(5655,a,5607,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),D)). [resolve(5655,a,5608,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(5655,a,5610,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5655,a,5613,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A). [resolve(5655,a,5614,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C)),B). [resolve(5655,a,5615,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(5655,a,5617,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A) = A. [resolve(5655,a,5618,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),A). [resolve(5655,a,5619,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),A). [resolve(5655,a,5620,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),B). [resolve(5655,a,5621,a)].
% 49.43/49.39 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(5655,a,5624,a)].
% 49.43/49.39 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A). [resolve(5655,a,5625,a)].
% 49.43/49.39 Derived: -class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Code__Numeral_Ocode__numeral),C),B) | hBOOL(hAPP(hAPP(c_member(A),f74(C,B,A,tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5655,a,5626,a)].
% 49.43/49.39 Derived: -class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Code__Numeral_Ocode__numeral),C),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(C,f74(C,B,A,tc_Code__Numeral_Ocode__numeral)). [resolve(5655,a,5627,a)].
% 49.43/49.39 Derived: -class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Code__Numeral_Ocode__numeral),C),B) | -hBOOL(hAPP(hAPP(c_member(A),D),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(C,D). [resolve(5655,a,5628,a)].
% 49.43/49.39 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(D,C) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Code__Numeral_Ocode__numeral),D),B). [resolve(5655,a,5629,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5655,a,5630,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)). [resolve(5655,a,5631,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(5655,a,5632,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5655,a,5633,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),A). [resolve(5655,a,5635,a)].
% 49.43/49.39 Derived: c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(5655,a,5636,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5655,a,5637,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),A). [resolve(5655,a,5638,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5655,a,5639,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5655,a,5640,a)].
% 49.43/49.39 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))),C))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),A))). [resolve(5655,a,5641,a)].
% 49.43/49.40 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral),c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A))). [resolve(5655,a,5642,a)].
% 49.43/49.40 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5655,a,5643,a)].
% 49.43/49.40 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5655,a,5644,a)].
% 49.43/49.40 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A))). [resolve(5655,a,5645,a)].
% 49.43/49.40 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(5655,a,5646,a)].
% 49.43/49.40 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(5655,a,5647,a)].
% 49.43/49.40 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),C),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(5655,a,5648,a)].
% 49.43/49.40 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5655,a,5649,a)].
% 49.43/49.40 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5655,a,5650,a)].
% 49.43/49.40 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_member(A),C),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),hAPP(D,C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Code__Numeral_Ocode__numeral),D),B))). [resolve(5655,a,5651,a)].
% 49.43/49.40 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5655,a,5652,a)].
% 51.52/51.48 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),A)). [resolve(5655,a,5653,a)].
% 51.52/51.48 5656 class_Rings_Olinordered__idom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__idom) # label(axiom). [assumption].
% 51.52/51.48 5657 -class_Rings_Olinordered__idom(A) | B = C | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_linorder__neqE__linordered__idom) # label(axiom). [clausify(481)].
% 51.52/51.48 5658 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),B)) # label(fact_mult__right__le__one__le) # label(axiom). [clausify(1019)].
% 51.52/51.48 5659 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),B)) # label(fact_mult__left__le__one__le) # label(axiom). [clausify(1020)].
% 51.52/51.48 5660 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_even__less__0__iff) # label(axiom). [clausify(1046)].
% 51.52/51.48 5661 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_even__less__0__iff) # label(axiom). [clausify(1046)].
% 51.52/51.48 5662 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),B)),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_Ints__odd__less__0) # label(axiom). [clausify(1057)].
% 51.52/51.48 5663 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),B)),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_Ints__odd__less__0) # label(axiom). [clausify(1057)].
% 51.52/51.48 5664 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) # label(fact_le__number__of) # label(axiom). [clausify(1159)].
% 51.52/51.48 5665 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) # label(fact_le__number__of) # label(axiom). [clausify(1159)].
% 51.52/51.48 5666 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) # label(fact_less__number__of) # label(axiom). [clausify(1160)].
% 51.52/51.48 5667 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) # label(fact_less__number__of) # label(axiom). [clausify(1160)].
% 51.52/51.48 5668 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Int_OPls)) # label(fact_le__special_I3_J) # label(axiom). [clausify(1330)].
% 51.52/51.48 5669 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Int_OPls)) # label(fact_le__special_I3_J) # label(axiom). [clausify(1330)].
% 51.52/51.48 5670 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),B)) # label(fact_le__special_I1_J) # label(axiom). [clausify(1331)].
% 51.52/51.48 5671 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),B)) # label(fact_le__special_I1_J) # label(axiom). [clausify(1331)].
% 51.52/51.48 5672 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),B)) # label(fact_less__special_I1_J) # label(axiom). [clausify(1332)].
% 51.52/51.48 5673 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),B)) # label(fact_less__special_I1_J) # label(axiom). [clausify(1332)].
% 51.52/51.48 5674 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Int_OPls)) # label(fact_less__special_I3_J) # label(axiom). [clausify(1333)].
% 51.52/51.48 5675 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Int_OPls)) # label(fact_less__special_I3_J) # label(axiom). [clausify(1333)].
% 51.52/51.48 5676 -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) # label(fact_abs__mult__self) # label(axiom). [clausify(1351)].
% 51.52/51.48 5677 -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__mult) # label(axiom). [clausify(1352)].
% 51.52/51.48 5678 -class_Rings_Olinordered__idom(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Groups_Oabs__class_Oabs(A),c_Groups_Oone__class_Oone(A)) # label(fact_abs__one) # label(axiom). [clausify(1354)].
% 51.52/51.48 5679 -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B) # label(fact_abs__of__nat) # label(axiom). [clausify(1355)].
% 51.52/51.48 5680 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Oabs__class_Oabs(A),D)),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_abs__mult__less) # label(axiom). [clausify(1365)].
% 51.52/51.48 5681 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),C)),B) # label(fact_abs__mult__pos) # label(axiom). [clausify(1371)].
% 51.52/51.48 5682 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Int_OBit1(c_Int_OPls))) # label(fact_le__special_I4_J) # label(axiom). [clausify(1456)].
% 51.52/51.48 5683 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Int_OBit1(c_Int_OPls))) # label(fact_le__special_I4_J) # label(axiom). [clausify(1456)].
% 51.52/51.48 5684 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Oone__class_Oone(A)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),B)) # label(fact_le__special_I2_J) # label(axiom). [clausify(1457)].
% 51.52/51.48 5685 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Oone__class_Oone(A)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),B)) # label(fact_le__special_I2_J) # label(axiom). [clausify(1457)].
% 51.52/51.48 5686 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),B)) # label(fact_less__special_I2_J) # label(axiom). [clausify(1458)].
% 51.52/51.48 5687 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(c_Int_Onumber__class_Onumber__of(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),B)) # label(fact_less__special_I2_J) # label(axiom). [clausify(1458)].
% 51.52/51.48 5688 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Int_OBit1(c_Int_OPls))) # label(fact_less__special_I4_J) # label(axiom). [clausify(1459)].
% 51.52/51.48 5689 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Int_OBit1(c_Int_OPls))) # label(fact_less__special_I4_J) # label(axiom). [clausify(1459)].
% 51.52/51.48 5690 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__minus__self__iff) # label(axiom). [clausify(1561)].
% 51.52/51.48 5691 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_less__minus__self__iff) # label(axiom). [clausify(1561)].
% 51.52/51.48 5692 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_abs__less__iff) # label(axiom). [clausify(1591)].
% 51.52/51.48 5693 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) # label(fact_abs__less__iff) # label(axiom). [clausify(1591)].
% 51.52/51.48 5694 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) # label(fact_abs__less__iff) # label(axiom). [clausify(1591)].
% 51.52/51.48 5695 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Int_Onumber__class_Onumber__of(A),c_Int_OMin)) # label(fact_abs__minus__one) # label(axiom). [clausify(1648)].
% 51.52/51.48 5696 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Ozero__class_Ozero(A))) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)) = hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)) # label(fact_abs__number__of) # label(axiom). [clausify(1663)].
% 51.52/51.48 5697 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),c_Groups_Ozero__class_Ozero(A))) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)) = hAPP(c_Int_Onumber__class_Onumber__of(A),B) # label(fact_abs__number__of) # label(axiom). [clausify(1663)].
% 51.52/51.48 5698 -class_Int_Onumber__ring(A) | -class_Rings_Olinordered__idom(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Int_Onumber__class_Onumber__of(A),c_Int_OMin)),B)) # label(fact_abs__power__minus__one) # label(axiom). [clausify(1877)].
% 51.52/51.48 5699 -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) # label(fact_abs__power2) # label(axiom). [clausify(1895)].
% 51.52/51.48 5700 -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) # label(fact_power2__abs) # label(axiom). [clausify(1896)].
% 51.52/51.48 5701 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) # label(fact_zero__le__power2) # label(axiom). [clausify(1899)].
% 51.52/51.48 5702 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(A))) # label(fact_power2__less__0) # label(axiom). [clausify(1900)].
% 51.52/51.48 5703 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__power2) # label(axiom). [clausify(1901)].
% 51.52/51.48 5704 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__power2) # label(axiom). [clausify(1901)].
% 51.52/51.48 5705 -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__power2__eq__zero__iff) # label(axiom). [clausify(1902)].
% 51.52/51.48 5706 -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__power2__eq__zero__iff) # label(axiom). [clausify(1902)].
% 51.52/51.48 5707 -class_Rings_Olinordered__idom(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__power2__eq__zero__iff) # label(axiom). [clausify(1902)].
% 51.52/51.48 5708 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__power2__le__zero__iff) # label(axiom). [clausify(1911)].
% 51.52/51.48 5709 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__power2__le__zero__iff) # label(axiom). [clausify(1911)].
% 51.52/51.48 5710 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__power2__le__zero__iff) # label(axiom). [clausify(1911)].
% 51.52/51.48 5711 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) # label(fact_sum__power2__ge__zero) # label(axiom). [clausify(1912)].
% 51.52/51.48 5712 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__power2__gt__zero__iff) # label(axiom). [clausify(1913)].
% 51.52/51.48 5713 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__power2__gt__zero__iff) # label(axiom). [clausify(1913)].
% 51.52/51.48 5714 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__power2__gt__zero__iff) # label(axiom). [clausify(1913)].
% 51.52/51.48 5715 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__sum__power2__lt__zero) # label(axiom). [clausify(1914)].
% 51.52/51.48 5716 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C)))) # label(fact_zero__le__even__power_H) # label(axiom). [clausify(1916)].
% 51.52/51.48 5717 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C))))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_odd__0__le__power__imp__0__le) # label(axiom). [clausify(1923)].
% 51.52/51.48 5718 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C)))),c_Groups_Ozero__class_Ozero(A))) # label(fact_odd__power__less__zero) # label(axiom). [clausify(1924)].
% 51.52/51.48 5719 -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C) # label(fact_power__abs) # label(axiom). [clausify(1943)].
% 51.52/51.48 5720 -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) = hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_abs__power__minus) # label(axiom). [clausify(1959)].
% 51.52/51.48 5721 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C))) # label(fact_zero__le__power__abs) # label(axiom). [clausify(1970)].
% 51.52/51.48 5722 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),hAPP(c_Int_Oring__1__class_Oof__int(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) # label(fact_of__int__le__iff) # label(axiom). [clausify(1994)].
% 51.52/51.48 5723 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),hAPP(c_Int_Oring__1__class_Oof__int(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) # label(fact_of__int__le__iff) # label(axiom). [clausify(1994)].
% 51.52/51.48 5724 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),hAPP(c_Int_Oring__1__class_Oof__int(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) # label(fact_of__int__less__iff) # label(axiom). [clausify(1995)].
% 51.52/51.48 5725 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),hAPP(c_Int_Oring__1__class_Oof__int(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) # label(fact_of__int__less__iff) # label(axiom). [clausify(1995)].
% 51.52/51.48 5726 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_of__int__le__0__iff) # label(axiom). [clausify(2016)].
% 51.52/51.48 5727 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_of__int__le__0__iff) # label(axiom). [clausify(2016)].
% 51.52/51.48 5728 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Oring__1__class_Oof__int(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) # label(fact_of__int__0__le__iff) # label(axiom). [clausify(2017)].
% 51.52/51.48 5729 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Oring__1__class_Oof__int(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) # label(fact_of__int__0__le__iff) # label(axiom). [clausify(2017)].
% 51.52/51.48 5730 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Oring__1__class_Oof__int(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) # label(fact_of__int__0__less__iff) # label(axiom). [clausify(2018)].
% 51.52/51.48 5731 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Oring__1__class_Oof__int(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) # label(fact_of__int__0__less__iff) # label(axiom). [clausify(2018)].
% 51.52/51.48 5732 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_of__int__less__0__iff) # label(axiom). [clausify(2019)].
% 51.52/51.48 5733 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_of__int__less__0__iff) # label(axiom). [clausify(2019)].
% 51.52/51.48 5734 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Osgn__class_Osgn(A,B)) = c_Groups_Osgn__class_Osgn(A,B) # label(fact_sgn__sgn) # label(axiom). [clausify(2027)].
% 51.52/51.48 5735 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) != c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sgn__0__0) # label(axiom). [clausify(2028)].
% 51.52/51.48 5736 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_sgn__0__0) # label(axiom). [clausify(2028)].
% 51.52/51.48 5737 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C)) # label(fact_sgn__times) # label(axiom). [clausify(2030)].
% 51.52/51.48 5738 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_sgn__less) # label(axiom). [clausify(2033)].
% 51.52/51.48 5739 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_sgn__less) # label(axiom). [clausify(2033)].
% 51.52/51.48 5740 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Groups_Osgn__class_Osgn(A,B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_sgn__greater) # label(axiom). [clausify(2034)].
% 51.52/51.48 5741 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Groups_Osgn__class_Osgn(A,B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_sgn__greater) # label(axiom). [clausify(2034)].
% 51.52/51.48 5742 -class_Rings_Olinordered__idom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Osgn__class_Osgn(A,B)),hAPP(c_Groups_Oabs__class_Oabs(A),B)) = B # label(fact_mult__sgn__abs) # label(axiom). [clausify(2036)].
% 51.52/51.48 5743 -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(A),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Osgn__class_Osgn(A,B)) # label(fact_abs__sgn) # label(axiom). [clausify(2037)].
% 51.52/51.48 5744 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) != c_Groups_Oone__class_Oone(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_sgn__1__pos) # label(axiom). [clausify(2039)].
% 51.52/51.48 5745 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Oone__class_Oone(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_sgn__1__pos) # label(axiom). [clausify(2039)].
% 51.52/51.48 5746 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__pos) # label(axiom). [clausify(2040)].
% 51.52/51.48 5747 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Osgn__class_Osgn(A,B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) # label(fact_sgn__neg) # label(axiom). [clausify(2043)].
% 51.52/51.48 5748 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) != hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_sgn__1__neg) # label(axiom). [clausify(2044)].
% 51.52/51.48 5749 -class_Rings_Olinordered__idom(A) | c_Groups_Osgn__class_Osgn(A,B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_sgn__1__neg) # label(axiom). [clausify(2044)].
% 51.52/51.48 5750 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(c_Groups_Oabs__class_Oabs(A),C))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_dvd__abs__iff) # label(axiom). [clausify(4848)].
% 51.52/51.48 5751 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(c_Groups_Oabs__class_Oabs(A),C))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_dvd__abs__iff) # label(axiom). [clausify(4848)].
% 51.52/51.48 5752 -class_Rings_Olinordered__idom(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_abs__dvd__iff) # label(axiom). [clausify(4849)].
% 51.52/51.48 5753 -class_Rings_Olinordered__idom(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_abs__dvd__iff) # label(axiom). [clausify(4849)].
% 51.52/51.48 5754 -class_Rings_Olinordered__idom(A) | hAPP(c_Groups_Oabs__class_Oabs(A),B) != hAPP(c_Groups_Oabs__class_Oabs(A),C) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_dvd__if__abs__eq) # label(axiom). [clausify(4850)].
% 51.52/51.48 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),A)). [resolve(5656,a,5658,a)].
% 51.52/51.48 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A)),A)). [resolve(5656,a,5659,a)].
% 51.52/51.48 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5660,a)].
% 51.52/51.48 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5661,a)].
% 51.52/51.48 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5662,a)].
% 51.52/51.48 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5663,a)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(5656,a,5664,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(5656,a,5665,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(5656,a,5666,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(5656,a,5667,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Int_OPls)). [resolve(5656,a,5668,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Int_OPls)). [resolve(5656,a,5669,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),A)). [resolve(5656,a,5670,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),A)). [resolve(5656,a,5671,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),A)). [resolve(5656,a,5672,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),A)). [resolve(5656,a,5673,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Int_OPls)). [resolve(5656,a,5674,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Int_OPls)). [resolve(5656,a,5675,b)].
% 51.52/51.49 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A). [resolve(5656,a,5676,a)].
% 51.52/51.49 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(5656,a,5677,a)].
% 51.52/51.49 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(5656,a,5678,a)].
% 51.52/51.49 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A). [resolve(5656,a,5679,a)].
% 51.52/51.49 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),C)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(5656,a,5680,a)].
% 51.52/51.49 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)),A). [resolve(5656,a,5681,a)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Int_OBit1(c_Int_OPls))). [resolve(5656,a,5682,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Int_OBit1(c_Int_OPls))). [resolve(5656,a,5683,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),A)). [resolve(5656,a,5684,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),A)). [resolve(5656,a,5685,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),A)). [resolve(5656,a,5686,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),A)). [resolve(5656,a,5687,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Int_OBit1(c_Int_OPls))). [resolve(5656,a,5688,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Int_OBit1(c_Int_OPls))). [resolve(5656,a,5689,b)].
% 51.52/51.49 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5690,a)].
% 51.52/51.49 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5691,a)].
% 51.52/51.49 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(5656,a,5692,a)].
% 51.52/51.49 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)). [resolve(5656,a,5693,a)].
% 51.52/51.49 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)). [resolve(5656,a,5694,a)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)). [resolve(5656,a,5695,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)). [resolve(5656,a,5696,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A). [resolve(5656,a,5697,b)].
% 51.52/51.49 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),A)). [resolve(5656,a,5698,b)].
% 51.52/51.49 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(5656,a,5699,a)].
% 51.52/51.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(5656,a,5700,a)].
% 51.52/51.49 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))). [resolve(5656,a,5701,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5702,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(5656,a,5703,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5656,a,5704,a)].
% 51.52/51.50 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5656,a,5705,a)].
% 51.52/51.50 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5656,a,5706,a)].
% 51.52/51.50 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5656,a,5707,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5656,a,5708,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5656,a,5709,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5656,a,5710,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))). [resolve(5656,a,5711,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5656,a,5712,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5656,a,5713,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5656,a,5714,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5715,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)))). [resolve(5656,a,5716,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5717,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5718,a)].
% 51.52/51.50 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B). [resolve(5656,a,5719,a)].
% 51.52/51.50 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(5656,a,5720,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B))). [resolve(5656,a,5721,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(5656,a,5722,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(5656,a,5723,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(5656,a,5724,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(5656,a,5725,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5726,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5727,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5728,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5729,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5730,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5731,a)].
% 51.52/51.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5732,a)].
% 51.52/51.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5733,a)].
% 51.52/51.51 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,A). [resolve(5656,a,5734,a)].
% 51.52/51.51 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5656,a,5735,a)].
% 51.52/51.51 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(5656,a,5736,a)].
% 51.52/51.51 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,B)). [resolve(5656,a,5737,a)].
% 51.52/51.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5738,a)].
% 51.52/51.51 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5739,a)].
% 51.52/51.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5740,a)].
% 51.52/51.51 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5741,a)].
% 51.52/51.51 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)) = A. [resolve(5656,a,5742,a)].
% 51.52/51.51 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)). [resolve(5656,a,5743,a)].
% 51.52/51.51 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) != c_Groups_Oone__class_Oone(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5744,a)].
% 51.52/51.51 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = c_Groups_Oone__class_Oone(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5656,a,5745,a)].
% 51.52/51.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(5656,a,5747,a)].
% 51.52/51.51 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5656,a,5748,a)].
% 51.52/51.51 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(5656,a,5750,a)].
% 51.52/51.51 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(5656,a,5751,a)].
% 51.52/51.51 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(5656,a,5752,a)].
% 51.52/51.51 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(5656,a,5753,a)].
% 53.63/53.59 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) != hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(5656,a,5754,a)].
% 53.63/53.59 5755 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) # label(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 53.63/53.59 5756 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | B = D | C = E # label(fact_crossproduct__eq) # label(axiom). [clausify(496)].
% 53.63/53.59 5757 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | B != D # label(fact_crossproduct__eq) # label(axiom). [clausify(496)].
% 53.63/53.59 5758 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) | C != E # label(fact_crossproduct__eq) # label(axiom). [clausify(496)].
% 53.63/53.59 5759 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B = C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(501)].
% 53.63/53.59 5760 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(501)].
% 53.63/53.59 5761 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | B != C | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)) # label(fact_crossproduct__noteq) # label(axiom). [clausify(501)].
% 53.63/53.59 5762 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) != B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__0__iff) # label(axiom). [clausify(854)].
% 53.63/53.59 5763 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) = B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__0__iff) # label(axiom). [clausify(854)].
% 53.63/53.59 5764 -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A) | c_Groups_Ozero__class_Ozero(A) = B | C != D | E = F | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)) # label(fact_add__scale__eq__noteq) # label(axiom). [clausify(963)].
% 53.63/53.59 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | A = C | B = D. [resolve(5755,a,5756,a)].
% 53.63/53.60 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | A != C. [resolve(5755,a,5757,a)].
% 53.63/53.60 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) | B != D. [resolve(5755,a,5758,a)].
% 53.63/53.60 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(5755,a,5759,a)].
% 53.63/53.60 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(5755,a,5760,a)].
% 53.63/53.60 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5755,a,5762,a)].
% 53.63/53.61 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5755,a,5763,a)].
% 53.63/53.61 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)). [resolve(5755,a,5764,a)].
% 53.63/53.61 5765 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) # label(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) # label(axiom). [assumption].
% 53.63/53.61 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | A = C | B = D. [resolve(5765,a,5756,a)].
% 53.63/53.61 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | A != C. [resolve(5765,a,5757,a)].
% 53.63/53.61 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) | B != D. [resolve(5765,a,5758,a)].
% 53.63/53.61 Derived: A = B | C = D | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)). [resolve(5765,a,5759,a)].
% 55.83/55.73 Derived: A != B | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)). [resolve(5765,a,5760,a)].
% 55.83/55.73 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(5765,a,5762,a)].
% 55.83/55.73 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(5765,a,5763,a)].
% 55.83/55.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | B != C | D = E | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),E)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D)). [resolve(5765,a,5764,a)].
% 55.83/55.73 5766 class_Rings_Osemiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring) # label(axiom). [assumption].
% 55.83/55.73 5767 -class_Rings_Osemiring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)),E) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),E)) # label(fact_combine__common__factor) # label(axiom). [clausify(497)].
% 55.83/55.73 5768 -class_Int_Onumber(A) | -class_Rings_Osemiring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Int_Onumber__class_Onumber__of(A),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(c_Int_Onumber__class_Onumber__of(A),C))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(c_Int_Onumber__class_Onumber__of(A),C)) # label(fact_left__distrib__number__of) # label(axiom). [clausify(1169)].
% 55.83/55.73 5769 -class_Int_Onumber(A) | -class_Rings_Osemiring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_right__distrib__number__of) # label(axiom). [clausify(1170)].
% 55.83/55.73 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),D)). [resolve(5766,a,5767,a)].
% 55.83/55.73 5770 class_Rings_Osemiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring) # label(axiom). [assumption].
% 55.83/55.73 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),D)). [resolve(5770,a,5767,a)].
% 55.83/55.73 5771 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) # label(axiom). [assumption].
% 55.83/55.73 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)),D)). [resolve(5771,a,5767,a)].
% 60.04/59.96 5772 class_Rings_Ocomm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 60.04/59.96 5773 -class_Rings_Ocomm__semiring(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C) # label(fact_comm__semiring__class_Odistrib) # label(axiom). [clausify(500)].
% 60.04/59.96 5774 class_Rings_Ocomm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 60.04/59.96 5775 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) # label(axiom). [assumption].
% 60.04/59.96 5776 class_Groups_Omonoid__mult(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__mult) # label(axiom). [assumption].
% 60.04/59.96 5777 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B) = B # label(fact_mult__1__left) # label(axiom). [clausify(691)].
% 60.04/59.96 5778 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_mult__1__right) # label(axiom). [clausify(693)].
% 60.04/59.96 5779 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),B) # label(fact_power3__eq__cube) # label(axiom). [clausify(1876)].
% 60.04/59.96 5780 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) # label(fact_power2__eq__square) # label(axiom). [clausify(1891)].
% 60.04/59.96 5781 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C)) # label(fact_power__even__eq) # label(axiom). [clausify(1894)].
% 60.04/59.96 5782 -class_Groups_Omonoid__mult(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Int_Onumber__class_Onumber__of(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(A),B)) # label(fact_power2__eq__square__number__of) # label(axiom). [clausify(1903)].
% 60.04/59.96 5783 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_power__odd__eq) # label(axiom). [clausify(1918)].
% 60.04/59.96 5784 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_power__commutes) # label(axiom). [clausify(1938)].
% 60.04/59.96 5785 -class_Groups_Omonoid__mult(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B) # label(fact_power__one) # label(axiom). [clausify(1939)].
% 60.04/59.97 5786 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)) # label(fact_power__mult) # label(axiom). [clausify(1941)].
% 60.04/59.97 5787 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = B # label(fact_power__one__right) # label(axiom). [clausify(1944)].
% 60.04/59.97 5788 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(fact_power__Suc2) # label(axiom). [clausify(1953)].
% 60.04/59.97 5789 -class_Groups_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(fact_power__add) # label(axiom). [clausify(1956)].
% 60.04/59.97 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),A). [resolve(5776,a,5779,a)].
% 60.04/59.97 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)). [resolve(5776,a,5781,a)].
% 60.04/59.97 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(5776,a,5783,a)].
% 60.04/59.97 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A). [resolve(5776,a,5785,a)].
% 60.04/59.97 5790 class_Groups_Omonoid__mult(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__mult) # label(axiom). [assumption].
% 60.04/59.97 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),A)),A). [resolve(5790,a,5779,a)].
% 60.04/59.97 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)). [resolve(5790,a,5781,a)].
% 60.04/59.97 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(5790,a,5783,a)].
% 62.22/62.13 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A). [resolve(5790,a,5785,a)].
% 62.22/62.13 5791 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) # label(axiom). [assumption].
% 62.22/62.13 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),A)),A). [resolve(5791,a,5779,a)].
% 62.22/62.13 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)). [resolve(5791,a,5781,a)].
% 62.22/62.13 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(5791,a,5783,a)].
% 62.22/62.13 Derived: c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A). [resolve(5791,a,5785,a)].
% 62.22/62.13 5792 class_Rings_Olinordered__semidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 62.22/62.13 5793 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A)))) # label(fact_less__add__one) # label(axiom). [clausify(701)].
% 62.22/62.13 5794 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_less__1__mult) # label(axiom). [clausify(702)].
% 62.22/62.13 5795 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_pos__add__strict) # label(axiom). [clausify(938)].
% 62.22/62.13 5796 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__one__le__zero) # label(axiom). [clausify(964)].
% 62.22/62.13 5797 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))) # label(fact_zero__le__one) # label(axiom). [clausify(965)].
% 62.22/62.13 5798 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))) # label(fact_zero__less__one) # label(axiom). [clausify(966)].
% 62.22/62.13 5799 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__one__less__zero) # label(axiom). [clausify(967)].
% 62.22/62.13 5800 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A)))) # label(fact_zero__less__two) # label(axiom). [clausify(1021)].
% 62.22/62.13 5801 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_member(B),f106(C,D,B,A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),C),D))) # label(fact_setprod__pos) # label(axiom). [clausify(1191)].
% 62.22/62.13 5802 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(B,f106(B,C,D,A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(D,A),B),C))) # label(fact_setprod__pos) # label(axiom). [clausify(1191)].
% 62.22/62.13 5803 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_member(B),f107(C,D,B,A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),C),D))) # label(fact_setprod__nonneg) # label(axiom). [clausify(1192)].
% 62.22/62.13 5804 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(B,f107(B,C,D,A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(D,A),B),C))) # label(fact_setprod__nonneg) # label(axiom). [clausify(1192)].
% 62.22/62.13 5805 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) # label(fact_of__nat__0__le__iff) # label(axiom). [clausify(1273)].
% 62.22/62.13 5806 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) # label(fact_zero__le__imp__of__nat) # label(axiom). [clausify(1274)].
% 62.22/62.13 5807 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_of__nat__less__0__iff) # label(axiom). [clausify(1275)].
% 62.22/62.13 5808 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) # label(fact_of__nat__less__imp__less) # label(axiom). [clausify(1280)].
% 62.22/62.13 5809 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) # label(fact_less__imp__of__nat__less) # label(axiom). [clausify(1281)].
% 62.22/62.13 5810 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) # label(fact_of__nat__less__iff) # label(axiom). [clausify(1282)].
% 62.22/62.13 5811 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) # label(fact_of__nat__less__iff) # label(axiom). [clausify(1282)].
% 62.22/62.13 5812 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) # label(fact_of__nat__le__iff) # label(axiom). [clausify(1283)].
% 62.22/62.13 5813 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) # label(fact_of__nat__le__iff) # label(axiom). [clausify(1283)].
% 62.22/62.13 5814 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) # label(fact_of__nat__0__less__iff) # label(axiom). [clausify(1299)].
% 62.22/62.13 5815 -class_Rings_Olinordered__semidom(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) # label(fact_of__nat__0__less__iff) # label(axiom). [clausify(1299)].
% 62.22/62.13 5816 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | B = C # label(fact_power2__eq__imp__eq) # label(axiom). [clausify(1897)].
% 62.22/62.13 5817 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_power2__le__imp__le) # label(axiom). [clausify(1898)].
% 62.22/62.13 5818 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) # label(fact_power2__less__imp__less) # label(axiom). [clausify(1909)].
% 62.22/62.13 5819 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))) # label(fact_power__strict__mono) # label(axiom). [clausify(1928)].
% 62.22/62.13 5820 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_one__less__power) # label(axiom). [clausify(1930)].
% 62.22/62.13 5821 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) # label(fact_power__increasing__iff) # label(axiom). [clausify(1931)].
% 62.22/62.13 5822 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) # label(fact_power__increasing__iff) # label(axiom). [clausify(1931)].
% 62.22/62.13 5823 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_zero__le__power) # label(axiom). [clausify(1945)].
% 62.22/62.13 5824 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))) # label(fact_power__mono) # label(axiom). [clausify(1946)].
% 62.22/62.13 5825 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_zero__less__power) # label(axiom). [clausify(1947)].
% 62.22/62.13 5826 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_one__le__power) # label(axiom). [clausify(1949)].
% 62.22/62.13 5827 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | C = D # label(fact_power__inject__exp) # label(axiom). [clausify(1951)].
% 62.22/62.13 5828 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | C != D # label(fact_power__inject__exp) # label(axiom). [clausify(1951)].
% 62.22/62.13 5829 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_power__less__imp__less__base) # label(axiom). [clausify(1960)].
% 62.22/62.13 5830 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Nat_OSuc,C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | B = D # label(fact_power__inject__base) # label(axiom). [clausify(1961)].
% 62.22/62.13 5831 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Nat_OSuc,C)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_power__le__imp__le__base) # label(axiom). [clausify(1962)].
% 62.22/62.13 5832 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) # label(fact_power__gt1__lemma) # label(axiom). [clausify(1963)].
% 62.22/62.13 5833 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) # label(fact_power__less__power__Suc) # label(axiom). [clausify(1964)].
% 62.22/62.13 5834 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)))) # label(fact_power__gt1) # label(axiom). [clausify(1966)].
% 62.22/62.13 5835 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) # label(fact_power__strict__increasing__iff) # label(axiom). [clausify(1967)].
% 62.22/62.13 5836 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) # label(fact_power__strict__increasing__iff) # label(axiom). [clausify(1967)].
% 62.22/62.13 5837 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) # label(fact_power__less__imp__less__exp) # label(axiom). [clausify(1968)].
% 62.22/62.13 5838 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) # label(fact_power__strict__increasing) # label(axiom). [clausify(1969)].
% 62.22/62.13 5839 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Oone__class_Oone(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) # label(fact_power__increasing) # label(axiom). [clausify(1971)].
% 62.22/62.13 5840 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(fact_power__Suc__less) # label(axiom). [clausify(1973)].
% 62.22/62.13 5841 -class_Rings_Olinordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | B = D # label(fact_power__eq__imp__eq__base) # label(axiom). [clausify(1974)].
% 62.22/62.13 5842 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),c_Groups_Oone__class_Oone(A))) # label(fact_power__Suc__less__one) # label(axiom). [clausify(1975)].
% 62.22/62.14 5843 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B))) # label(fact_power__strict__decreasing) # label(axiom). [clausify(1976)].
% 62.22/62.14 5844 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),c_Groups_Oone__class_Oone(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B))) # label(fact_power__decreasing) # label(axiom). [clausify(1977)].
% 62.22/62.14 5845 -class_Rings_Olinordered__semidom(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) # label(fact_power__le__imp__le__exp) # label(axiom). [clausify(1978)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)))). [resolve(5792,a,5793,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(5792,a,5794,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(5792,a,5795,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5792,a,5796,a)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(5792,a,5797,a)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(5792,a,5798,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5792,a,5799,a)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))). [resolve(5792,a,5800,a)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_member(A),f106(B,C,A,tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),B),C))). [resolve(5792,a,5801,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(A,f106(A,B,C,tc_Int_Oint)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(C,tc_Int_Oint),A),B))). [resolve(5792,a,5802,a)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_member(A),f107(B,C,A,tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),B),C))). [resolve(5792,a,5803,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(A,f107(A,B,C,tc_Int_Oint)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(C,tc_Int_Oint),A),B))). [resolve(5792,a,5804,a)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))). [resolve(5792,a,5805,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5792,a,5807,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5792,a,5808,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))). [resolve(5792,a,5809,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5792,a,5812,a)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5792,a,5813,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(5792,a,5814,a)].
% 62.22/62.14 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(5792,a,5815,a)].
% 62.22/62.14 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | A = B. [resolve(5792,a,5816,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(5792,a,5817,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(5792,a,5818,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C))). [resolve(5792,a,5819,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(5792,a,5820,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5792,a,5821,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5792,a,5822,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(5792,a,5823,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C))). [resolve(5792,a,5824,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(5792,a,5825,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(5792,a,5826,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | B = C. [resolve(5792,a,5827,a)].
% 62.22/62.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | B != C. [resolve(5792,a,5828,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(5792,a,5829,a)].
% 62.22/62.15 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(c_Nat_OSuc,B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | A = C. [resolve(5792,a,5830,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(c_Nat_OSuc,B)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(5792,a,5831,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)))). [resolve(5792,a,5832,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)))). [resolve(5792,a,5833,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B)))). [resolve(5792,a,5834,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5792,a,5835,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5792,a,5836,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))). [resolve(5792,a,5839,a)].
% 62.22/62.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(5792,a,5840,a)].
% 62.22/62.15 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(5792,a,5841,a)].
% 62.22/62.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Nat_OSuc,B))),c_Groups_Oone__class_Oone(tc_Int_Oint))). [resolve(5792,a,5842,a)].
% 62.22/62.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A))). [resolve(5792,a,5843,a)].
% 62.22/62.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),c_Groups_Oone__class_Oone(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A))). [resolve(5792,a,5844,a)].
% 62.22/62.16 5846 class_Rings_Olinordered__semidom(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 62.22/62.16 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). [resolve(5846,a,5793,a)].
% 62.22/62.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))). [resolve(5846,a,5794,a)].
% 62.22/62.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(5846,a,5795,a)].
% 62.22/62.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5846,a,5796,a)].
% 62.22/62.16 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(5846,a,5797,a)].
% 62.22/62.16 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(5846,a,5798,a)].
% 62.22/62.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5846,a,5799,a)].
% 62.22/62.16 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))). [resolve(5846,a,5800,a)].
% 62.22/62.16 Derived: hBOOL(hAPP(hAPP(c_member(A),f106(B,C,A,tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),B),C))). [resolve(5846,a,5801,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(A,f106(A,B,C,tc_Nat_Onat)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(C,tc_Nat_Onat),A),B))). [resolve(5846,a,5802,a)].
% 62.22/62.17 Derived: hBOOL(hAPP(hAPP(c_member(A),f107(B,C,A,tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),B),C))). [resolve(5846,a,5803,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(A,f107(A,B,C,tc_Nat_Onat)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(C,tc_Nat_Onat),A),B))). [resolve(5846,a,5804,a)].
% 62.22/62.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A))). [resolve(5846,a,5805,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5846,a,5807,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5846,a,5808,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),B))). [resolve(5846,a,5809,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5846,a,5812,a)].
% 62.22/62.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5846,a,5813,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(5846,a,5814,a)].
% 62.22/62.17 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(5846,a,5815,a)].
% 62.22/62.17 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | A = B. [resolve(5846,a,5816,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5846,a,5817,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5846,a,5818,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C))). [resolve(5846,a,5819,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(5846,a,5820,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5846,a,5821,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5846,a,5822,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(5846,a,5823,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C))). [resolve(5846,a,5824,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(5846,a,5825,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(5846,a,5826,a)].
% 62.22/62.17 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C) | B = C. [resolve(5846,a,5827,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C) | B != C. [resolve(5846,a,5828,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(5846,a,5829,a)].
% 62.22/62.18 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),hAPP(c_Nat_OSuc,B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | A = C. [resolve(5846,a,5830,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),hAPP(c_Nat_OSuc,B)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(5846,a,5831,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))). [resolve(5846,a,5832,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))). [resolve(5846,a,5833,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B)))). [resolve(5846,a,5834,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5846,a,5835,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5846,a,5836,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B))). [resolve(5846,a,5839,a)].
% 62.22/62.18 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))). [resolve(5846,a,5840,a)].
% 62.30/62.20 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(5846,a,5841,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B))),c_Groups_Oone__class_Oone(tc_Nat_Onat))). [resolve(5846,a,5842,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A))). [resolve(5846,a,5843,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),c_Groups_Oone__class_Oone(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),C),A))). [resolve(5846,a,5844,a)].
% 62.30/62.20 5847 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) # label(axiom). [assumption].
% 62.30/62.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))). [resolve(5847,a,5793,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5847,a,5794,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))). [resolve(5847,a,5795,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5847,a,5796,a)].
% 62.30/62.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). [resolve(5847,a,5797,a)].
% 62.30/62.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). [resolve(5847,a,5798,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5847,a,5799,a)].
% 62.30/62.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))). [resolve(5847,a,5800,a)].
% 62.30/62.20 Derived: hBOOL(hAPP(hAPP(c_member(A),f106(B,C,A,tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(5847,a,5801,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(A,f106(A,B,C,tc_Code__Numeral_Ocode__numeral)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(C,tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5847,a,5802,a)].
% 62.30/62.20 Derived: hBOOL(hAPP(hAPP(c_member(A),f107(B,C,A,tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(5847,a,5803,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(A,f107(A,B,C,tc_Code__Numeral_Ocode__numeral)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(C,tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5847,a,5804,a)].
% 62.30/62.20 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A))). [resolve(5847,a,5805,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5847,a,5807,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)). [resolve(5847,a,5808,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),B))). [resolve(5847,a,5809,a)].
% 62.30/62.20 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5847,a,5812,a)].
% 62.30/62.21 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)). [resolve(5847,a,5813,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(5847,a,5814,a)].
% 62.30/62.21 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(5847,a,5815,a)].
% 62.30/62.21 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | A = B. [resolve(5847,a,5816,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5847,a,5817,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)). [resolve(5847,a,5818,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(5847,a,5819,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5847,a,5820,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5847,a,5821,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(5847,a,5822,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5847,a,5823,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(5847,a,5824,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5847,a,5825,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5847,a,5826,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C) | B = C. [resolve(5847,a,5827,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C) | B != C. [resolve(5847,a,5828,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5847,a,5829,a)].
% 62.30/62.21 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Nat_OSuc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),hAPP(c_Nat_OSuc,B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | A = C. [resolve(5847,a,5830,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Nat_OSuc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),hAPP(c_Nat_OSuc,B)))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5847,a,5831,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)))). [resolve(5847,a,5832,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)))). [resolve(5847,a,5833,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Nat_OSuc,B)))). [resolve(5847,a,5834,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5847,a,5835,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(5847,a,5836,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(5847,a,5839,a)].
% 62.30/62.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5847,a,5840,a)].
% 66.60/66.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),B) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | A = C. [resolve(5847,a,5841,a)].
% 66.60/66.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_Nat_OSuc,B))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))). [resolve(5847,a,5842,a)].
% 66.60/66.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),A))). [resolve(5847,a,5843,a)].
% 66.60/66.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),C),A))). [resolve(5847,a,5844,a)].
% 66.60/66.50 5848 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1__strict) # label(axiom). [assumption].
% 66.60/66.50 5849 -class_Rings_Olinordered__semiring__1__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),F)) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)) # label(fact_convex__bound__lt) # label(axiom). [clausify(845)].
% 66.60/66.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),E)) | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),D),E) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),C))),B)). [resolve(5848,a,5849,a)].
% 68.71/68.63 5850 class_Groups_Omonoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Omonoid__add) # label(axiom). [assumption].
% 68.71/68.63 5851 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) = B # label(fact_add__0__left) # label(axiom). [clausify(857)].
% 68.71/68.63 5852 -class_Groups_Omonoid__add(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A)) = B # label(fact_add__0__right) # label(axiom). [clausify(860)].
% 68.71/68.63 5853 -class_Groups_Omonoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Olist_OCons(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_List_Omonoid__add__class_Olistsum(A),C)) # label(fact_listsum__simps_I2_J) # label(axiom). [clausify(3760)].
% 68.71/68.63 5854 -class_Groups_Omonoid__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_List_Omonoid__add__class_Olistsum(A),c_List_Olist_ONil(A)) # label(fact_listsum__simps_I1_J) # label(axiom). [clausify(3829)].
% 68.71/68.63 5855 -class_Groups_Omonoid__add(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Oappend(A),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),B)),hAPP(c_List_Omonoid__add__class_Olistsum(A),C)) # label(fact_listsum__append) # label(axiom). [clausify(3884)].
% 68.71/68.63 5856 -class_Groups_Omonoid__add(A) | hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_foldl__absorb0) # label(axiom). [clausify(3997)].
% 68.71/68.63 5857 -class_Groups_Omonoid__add(A) | c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)) = c_List_Omonoid__add__class_Olistsum(A) # label(fact_listsum__foldl) # label(axiom). [clausify(4000)].
% 68.71/68.63 5858 -class_Groups_Omonoid__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),hAPP(c_COMBK(A,B),c_Groups_Ozero__class_Ozero(A))),C)) # label(fact_listsum__0) # label(axiom). [clausify(4067)].
% 68.71/68.63 5859 -class_Groups_Omonoid__add(A) | -class_Groups_Oordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_member(B),f434(C,D,E,B,A)),hAPP(c_List_Oset(B),E))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),D),E))),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),C),E)))) # label(fact_listsum__mono) # label(axiom). [clausify(4121)].
% 68.71/68.63 5860 -class_Groups_Omonoid__add(A) | -class_Groups_Oordered__ab__semigroup__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(B,f434(C,B,D,E,A))),hAPP(C,f434(C,B,D,E,A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(E,A),B),D))),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(E,A),C),D)))) # label(fact_listsum__mono) # label(axiom). [clausify(4121)].
% 68.71/68.63 5861 -class_Groups_Omonoid__add(A) | c_List_Ofoldr(A,A,c_Groups_Oplus__class_Oplus(A),B,c_Groups_Ozero__class_Ozero(A)) = hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_foldl__foldr1) # label(axiom). [clausify(4288)].
% 68.71/68.63 5862 -class_Groups_Omonoid__add(A) | hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_List_Ofoldr(A,A,c_Groups_Oplus__class_Oplus(A),C,c_Groups_Ozero__class_Ozero(A))) # label(fact_foldl__foldr1__lemma) # label(axiom). [clausify(4289)].
% 68.71/68.64 5863 -class_Groups_Omonoid__add(A) | hBOOL(hAPP(hAPP(c_member(B),f456(C,D,E,B,A)),hAPP(c_List_Oset(B),E))) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),C),hAPP(c_List_Ofilter(B,D),E))) = hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),C),E)) # label(fact_listsum__map__filter) # label(axiom). [clausify(4434)].
% 68.71/68.64 5864 -class_Groups_Omonoid__add(A) | -hBOOL(hAPP(B,f456(C,B,D,E,A))) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(E,A),C),hAPP(c_List_Ofilter(E,B),D))) = hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(E,A),C),D)) # label(fact_listsum__map__filter) # label(axiom). [clausify(4434)].
% 68.71/68.64 5865 -class_Groups_Omonoid__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(B,f456(B,C,D,E,A)) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(E,A),B),hAPP(c_List_Ofilter(E,C),D))) = hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(E,A),B),D)) # label(fact_listsum__map__filter) # label(axiom). [clausify(4434)].
% 68.71/68.64 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),B)). [resolve(5850,a,5853,a)].
% 68.71/68.64 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),c_List_Olist_ONil(tc_Int_Oint)). [resolve(5850,a,5854,a)].
% 68.71/68.64 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Oappend(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),A)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),B)). [resolve(5850,a,5855,a)].
% 68.71/68.64 Derived: hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(5850,a,5856,a)].
% 68.71/68.64 Derived: c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_List_Omonoid__add__class_Olistsum(tc_Int_Oint). [resolve(5850,a,5857,a)].
% 68.71/68.64 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),hAPP(c_COMBK(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),B)). [resolve(5850,a,5858,a)].
% 68.71/68.64 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_member(A),f434(B,C,D,A,tc_Int_Oint)),hAPP(c_List_Oset(A),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),C),D))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D)))). [resolve(5850,a,5859,a)].
% 68.71/68.64 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(A,f434(B,A,C,D,tc_Int_Oint))),hAPP(B,f434(B,A,C,D,tc_Int_Oint)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(D,tc_Int_Oint),A),C))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(D,tc_Int_Oint),B),C)))). [resolve(5850,a,5860,a)].
% 68.71/68.64 Derived: hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_List_Ofoldr(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),B,c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5850,a,5862,a)].
% 68.71/68.64 Derived: hBOOL(hAPP(hAPP(c_member(A),f456(B,C,D,A,tc_Int_Oint)),hAPP(c_List_Oset(A),D))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),hAPP(c_List_Ofilter(A,C),D))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D)). [resolve(5850,a,5863,a)].
% 68.71/68.65 Derived: -hBOOL(hAPP(A,f456(B,A,C,D,tc_Int_Oint))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(D,tc_Int_Oint),B),hAPP(c_List_Ofilter(D,A),C))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(D,tc_Int_Oint),B),C)). [resolve(5850,a,5864,a)].
% 68.71/68.65 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(A,f456(A,B,C,D,tc_Int_Oint)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(D,tc_Int_Oint),A),hAPP(c_List_Ofilter(D,B),C))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(D,tc_Int_Oint),A),C)). [resolve(5850,a,5865,a)].
% 68.71/68.65 5866 class_Groups_Omonoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Omonoid__add) # label(axiom). [assumption].
% 68.71/68.65 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),B)). [resolve(5866,a,5853,a)].
% 68.71/68.65 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat)). [resolve(5866,a,5854,a)].
% 68.71/68.65 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),A)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),B)). [resolve(5866,a,5855,a)].
% 68.71/68.65 Derived: hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)). [resolve(5866,a,5856,a)].
% 68.71/68.65 Derived: c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat). [resolve(5866,a,5857,a)].
% 68.71/68.65 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B)). [resolve(5866,a,5858,a)].
% 68.71/68.65 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_member(A),f434(B,C,D,A,tc_Nat_Onat)),hAPP(c_List_Oset(A),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),C),D))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),D)))). [resolve(5866,a,5859,a)].
% 68.71/68.65 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(A,f434(B,A,C,D,tc_Nat_Onat))),hAPP(B,f434(B,A,C,D,tc_Nat_Onat)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(D,tc_Nat_Onat),A),C))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(D,tc_Nat_Onat),B),C)))). [resolve(5866,a,5860,a)].
% 68.71/68.65 Derived: hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_List_Ofoldr(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5866,a,5862,a)].
% 68.71/68.65 Derived: hBOOL(hAPP(hAPP(c_member(A),f456(B,C,D,A,tc_Nat_Onat)),hAPP(c_List_Oset(A),D))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),hAPP(c_List_Ofilter(A,C),D))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),D)). [resolve(5866,a,5863,a)].
% 68.71/68.65 Derived: -hBOOL(hAPP(A,f456(B,A,C,D,tc_Nat_Onat))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(D,tc_Nat_Onat),B),hAPP(c_List_Ofilter(D,A),C))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(D,tc_Nat_Onat),B),C)). [resolve(5866,a,5864,a)].
% 68.71/68.67 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(A,f456(A,B,C,D,tc_Nat_Onat)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(D,tc_Nat_Onat),A),hAPP(c_List_Ofilter(D,B),C))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(D,tc_Nat_Onat),A),C)). [resolve(5866,a,5865,a)].
% 68.71/68.67 5867 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) # label(axiom). [assumption].
% 68.71/68.67 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Olist_OCons(tc_Code__Numeral_Ocode__numeral),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5867,a,5853,a)].
% 68.71/68.67 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),c_List_Olist_ONil(tc_Code__Numeral_Ocode__numeral)). [resolve(5867,a,5854,a)].
% 68.71/68.67 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Oappend(tc_Code__Numeral_Ocode__numeral),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),B)). [resolve(5867,a,5855,a)].
% 68.71/68.67 Derived: hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)). [resolve(5867,a,5856,a)].
% 68.71/68.67 Derived: c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral). [resolve(5867,a,5857,a)].
% 68.71/68.67 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBK(tc_Code__Numeral_Ocode__numeral,A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),B)). [resolve(5867,a,5858,a)].
% 68.71/68.67 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(hAPP(c_member(A),f434(B,C,D,A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(A),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),C),D))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),D)))). [resolve(5867,a,5859,a)].
% 68.71/68.67 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(A,f434(B,A,C,D,tc_Code__Numeral_Ocode__numeral))),hAPP(B,f434(B,A,C,D,tc_Code__Numeral_Ocode__numeral)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(D,tc_Code__Numeral_Ocode__numeral),A),C))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(D,tc_Code__Numeral_Ocode__numeral),B),C)))). [resolve(5867,a,5860,a)].
% 68.71/68.67 Derived: hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_List_Ofoldr(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5867,a,5862,a)].
% 70.81/70.74 Derived: hBOOL(hAPP(hAPP(c_member(A),f456(B,C,D,A,tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Oset(A),D))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),hAPP(c_List_Ofilter(A,C),D))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),D)). [resolve(5867,a,5863,a)].
% 70.81/70.74 Derived: -hBOOL(hAPP(A,f456(B,A,C,D,tc_Code__Numeral_Ocode__numeral))) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(D,tc_Code__Numeral_Ocode__numeral),B),hAPP(c_List_Ofilter(D,A),C))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(D,tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(5867,a,5864,a)].
% 70.81/70.74 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(A,f456(A,B,C,D,tc_Code__Numeral_Ocode__numeral)) | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(D,tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Ofilter(D,B),C))) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(D,tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(5867,a,5865,a)].
% 70.81/70.74 5868 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__group__add) # label(axiom). [assumption].
% 70.81/70.74 5869 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__zero__sym) # label(axiom). [clausify(859)].
% 70.81/70.74 5870 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__zero__sym) # label(axiom). [clausify(859)].
% 70.81/70.74 5871 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(914)].
% 70.81/70.74 5872 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(914)].
% 70.81/70.74 5873 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(915)].
% 70.81/70.74 5874 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(915)].
% 70.81/70.74 5875 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(939)].
% 70.81/70.74 5876 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(939)].
% 70.81/70.74 5877 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(940)].
% 70.81/70.74 5878 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(940)].
% 70.81/70.74 5879 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_double__eq__0__iff) # label(axiom). [clausify(1054)].
% 70.81/70.74 5880 -class_Groups_Olinordered__ab__group__add(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_double__eq__0__iff) # label(axiom). [clausify(1054)].
% 70.81/70.74 5881 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_equal__neg__zero) # label(axiom). [clausify(1508)].
% 70.81/70.74 5882 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_equal__neg__zero) # label(axiom). [clausify(1508)].
% 70.81/70.74 5883 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != B | c_Groups_Ozero__class_Ozero(A) = B # label(fact_neg__equal__zero) # label(axiom). [clausify(1510)].
% 70.81/70.74 5884 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = B | c_Groups_Ozero__class_Ozero(A) != B # label(fact_neg__equal__zero) # label(axiom). [clausify(1510)].
% 70.81/70.74 5885 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__minus__self__iff) # label(axiom). [clausify(1558)].
% 70.81/70.74 5886 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_le__minus__self__iff) # label(axiom). [clausify(1558)].
% 70.81/70.74 5887 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_minus__le__self__iff) # label(axiom). [clausify(1560)].
% 70.81/70.74 5888 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_minus__le__self__iff) # label(axiom). [clausify(1560)].
% 70.81/70.74 5889 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__less__nonneg) # label(axiom). [clausify(1564)].
% 70.81/70.74 5890 -class_Groups_Olinordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_neg__less__nonneg) # label(axiom). [clausify(1564)].
% 70.81/70.75 5891 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_minus__max__eq__min) # label(axiom). [clausify(2507)].
% 70.81/70.75 5892 -class_Groups_Olinordered__ab__group__add(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Orderings_Oord__class_Omin(A),B),C)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) # label(fact_minus__min__eq__max) # label(axiom). [clausify(2508)].
% 70.81/70.75 5893 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(A,hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),B)) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Big__Operators_Olinorder__class_OMin(A,B)) # label(fact_minus__Min__eq__Max) # label(axiom). [clausify(3002)].
% 70.81/70.75 5894 -class_Groups_Olinordered__ab__group__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(A,hAPP(c_Set_Oimage(A,A,c_Groups_Ouminus__class_Ouminus(A)),B)) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Big__Operators_Olinorder__class_OMax(A,B)) # label(fact_minus__Max__eq__Min) # label(axiom). [clausify(3003)].
% 70.81/70.75 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5868,a,5869,a)].
% 70.81/70.75 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(5868,a,5870,a)].
% 70.81/70.75 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5868,a,5871,a)].
% 70.81/70.75 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5868,a,5872,a)].
% 70.81/70.75 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5868,a,5873,a)].
% 70.81/70.75 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5868,a,5874,a)].
% 70.81/70.75 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5868,a,5875,a)].
% 70.81/70.75 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5868,a,5881,a)].
% 70.81/70.75 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(5868,a,5882,a)].
% 70.81/70.75 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5868,a,5885,a)].
% 72.97/72.88 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5868,a,5886,a)].
% 72.97/72.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5868,a,5887,a)].
% 72.97/72.88 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5868,a,5888,a)].
% 72.97/72.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5868,a,5889,a)].
% 72.97/72.88 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(5868,a,5890,a)].
% 72.97/72.88 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(5868,a,5891,a)].
% 72.97/72.88 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(5868,a,5892,a)].
% 72.97/72.88 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),A)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)). [resolve(5868,a,5893,a)].
% 72.97/72.88 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),A)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)). [resolve(5868,a,5894,a)].
% 72.97/72.88 5895 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__no__zero__divisors) # label(axiom). [assumption].
% 72.97/72.88 5896 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(864)].
% 72.97/72.88 5897 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_mult__eq__0__iff) # label(axiom). [clausify(864)].
% 72.97/72.88 5898 -class_Rings_Oring__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_mult__eq__0__iff) # label(axiom). [clausify(864)].
% 72.97/72.88 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5895,a,5896,a)].
% 72.97/72.88 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(5895,a,5897,a)].
% 75.15/75.09 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5895,a,5898,a)].
% 75.15/75.09 5899 class_Rings_Omult__zero(tc_Int_Oint) # label(arity_Int__Oint__Rings_Omult__zero) # label(axiom). [assumption].
% 75.15/75.09 5900 -class_Rings_Omult__zero(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_mult__zero__right) # label(axiom). [clausify(866)].
% 75.15/75.09 5901 -class_Rings_Omult__zero(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_mult__zero__left) # label(axiom). [clausify(868)].
% 75.15/75.09 5902 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_power__eq__0__iff) # label(axiom). [clausify(1948)].
% 75.15/75.09 5903 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != C # label(fact_power__eq__0__iff) # label(axiom). [clausify(1948)].
% 75.15/75.09 5904 -class_Power_Opower(A) | -class_Rings_Omult__zero(A) | -class_Rings_Ono__zero__divisors(A) | -class_Rings_Ozero__neq__one(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = C # label(fact_power__eq__0__iff) # label(axiom). [clausify(1948)].
% 75.15/75.09 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5899,a,5902,b)].
% 75.15/75.09 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(5899,a,5903,b)].
% 75.15/75.09 Derived: -class_Power_Opower(tc_Int_Oint) | -class_Rings_Ono__zero__divisors(tc_Int_Oint) | -class_Rings_Ozero__neq__one(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(5899,a,5904,b)].
% 75.15/75.09 5905 class_Rings_Omult__zero(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Omult__zero) # label(axiom). [assumption].
% 75.15/75.09 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(5905,a,5902,b)].
% 75.15/75.09 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(5905,a,5903,b)].
% 75.15/75.09 Derived: -class_Power_Opower(tc_Nat_Onat) | -class_Rings_Ono__zero__divisors(tc_Nat_Onat) | -class_Rings_Ozero__neq__one(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(5905,a,5904,b)].
% 75.15/75.09 5906 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) # label(axiom). [assumption].
% 77.29/77.21 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A. [resolve(5906,a,5902,b)].
% 77.29/77.21 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(5906,a,5903,b)].
% 77.29/77.21 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) | -class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),A),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(5906,a,5904,b)].
% 77.29/77.21 5907 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 77.29/77.21 5908 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__nonneg__nonneg) # label(axiom). [clausify(916)].
% 77.29/77.21 5909 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(917)].
% 77.29/77.21 5910 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(917)].
% 77.29/77.21 5911 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_add__nonneg__eq__0__iff) # label(axiom). [clausify(917)].
% 77.29/77.21 5912 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__increasing) # label(axiom). [clausify(918)].
% 77.29/77.21 5913 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B))) # label(fact_add__increasing2) # label(axiom). [clausify(919)].
% 77.29/77.21 5914 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__nonpos__nonpos) # label(axiom). [clausify(920)].
% 77.29/77.21 5915 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__pos__pos) # label(axiom). [clausify(941)].
% 77.29/77.21 5916 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__neg__neg) # label(axiom). [clausify(942)].
% 77.29/77.21 5917 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__nonpos__neg) # label(axiom). [clausify(997)].
% 77.29/77.21 5918 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_add__neg__nonpos) # label(axiom). [clausify(998)].
% 77.29/77.21 5919 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__strict__increasing2) # label(axiom). [clausify(999)].
% 77.29/77.21 5920 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))) # label(fact_add__strict__increasing) # label(axiom). [clausify(1000)].
% 77.29/77.21 5921 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__nonneg__pos) # label(axiom). [clausify(1001)].
% 77.29/77.21 5922 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))) # label(fact_add__pos__nonneg) # label(axiom). [clausify(1002)].
% 77.29/77.21 5923 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | hBOOL(hAPP(hAPP(c_member(B),f85(E,D,C,B,A)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,tc_HOL_Obool)),C),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C))) # label(fact_setsum__mono2) # label(axiom). [clausify(1047)].
% 77.29/77.21 5924 -class_Groups_Oordered__comm__monoid__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(B,tc_HOL_Obool)),D),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(E,f85(E,D,C,B,A)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),E),C))) # label(fact_setsum__mono2) # label(axiom). [clausify(1047)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B))). [resolve(5907,a,5908,a)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5907,a,5909,a)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5907,a,5910,a)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5907,a,5911,a)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(5907,a,5912,a)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),A))). [resolve(5907,a,5913,a)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5907,a,5914,a)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5907,a,5916,a)].
% 77.29/77.21 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5907,a,5917,a)].
% 77.29/77.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5907,a,5918,a)].
% 77.29/77.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(5907,a,5919,a)].
% 77.29/77.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C))). [resolve(5907,a,5920,a)].
% 77.29/77.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f85(D,C,B,A,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B))). [resolve(5907,a,5923,a)].
% 77.29/77.22 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(D,f85(D,C,B,A,tc_Int_Oint)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),D),B))). [resolve(5907,a,5924,a)].
% 77.29/77.22 5925 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 77.29/77.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B))). [resolve(5925,a,5908,a)].
% 77.29/77.22 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(5925,a,5909,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B. [resolve(5925,a,5910,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B. [resolve(5925,a,5911,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(5925,a,5912,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),A))). [resolve(5925,a,5913,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5925,a,5914,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5925,a,5916,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5925,a,5917,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5925,a,5918,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(5925,a,5919,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C))). [resolve(5925,a,5920,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f85(D,C,B,A,tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B))). [resolve(5925,a,5923,a)].
% 77.29/77.23 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(D,f85(D,C,B,A,tc_Nat_Onat)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),D),B))). [resolve(5925,a,5924,a)].
% 77.34/77.25 5926 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) # label(axiom). [assumption].
% 77.34/77.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5926,a,5908,a)].
% 77.34/77.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A. [resolve(5926,a,5909,a)].
% 77.34/77.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B. [resolve(5926,a,5910,a)].
% 77.34/77.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != B. [resolve(5926,a,5911,a)].
% 77.34/77.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))). [resolve(5926,a,5912,a)].
% 77.34/77.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),A))). [resolve(5926,a,5913,a)].
% 77.34/77.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5926,a,5914,a)].
% 77.34/77.25 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5926,a,5916,a)].
% 79.42/79.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5926,a,5917,a)].
% 79.42/79.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5926,a,5918,a)].
% 79.42/79.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))). [resolve(5926,a,5919,a)].
% 79.42/79.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C))). [resolve(5926,a,5920,a)].
% 79.42/79.36 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | hBOOL(hAPP(hAPP(c_member(A),f85(D,C,B,A,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool)),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B))). [resolve(5926,a,5923,a)].
% 79.42/79.36 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(A,tc_HOL_Obool)),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(D,f85(D,C,B,A,tc_Code__Numeral_Ocode__numeral)))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),D),B))). [resolve(5926,a,5924,a)].
% 79.42/79.36 5927 class_Rings_Olinordered__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring) # label(axiom). [assumption].
% 79.42/79.36 5928 -class_Rings_Olinordered__ring(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B))) # label(fact_zero__le__square) # label(axiom). [clausify(921)].
% 81.57/81.50 5929 -class_Rings_Olinordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__square__less__zero) # label(axiom). [clausify(959)].
% 81.57/81.50 5930 -class_Rings_Olinordered__ring(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))) # label(fact_sum__squares__ge__zero) # label(axiom). [clausify(1015)].
% 81.57/81.50 5931 -class_Rings_Olinordered__ring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))) # label(fact_not__sum__squares__lt__zero) # label(axiom). [clausify(1018)].
% 81.57/81.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A))). [resolve(5927,a,5928,a)].
% 81.57/81.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5927,a,5929,a)].
% 81.57/81.50 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)))). [resolve(5927,a,5930,a)].
% 81.57/81.50 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5927,a,5931,a)].
% 81.57/81.50 5932 class_Rings_Olinordered__ring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__ring__strict) # label(axiom). [assumption].
% 81.57/81.50 5933 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(922)].
% 81.57/81.50 5934 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(922)].
% 81.57/81.50 5935 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(922)].
% 81.57/81.50 5936 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(922)].
% 81.57/81.50 5937 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(922)].
% 81.57/81.50 5938 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) # label(fact_zero__le__mult__iff) # label(axiom). [clausify(922)].
% 81.57/81.50 5939 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(923)].
% 81.57/81.50 5940 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(923)].
% 81.57/81.50 5941 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(923)].
% 81.57/81.50 5942 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(923)].
% 81.57/81.50 5943 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__le__0__iff) # label(axiom). [clausify(923)].
% 81.57/81.50 5944 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_mult__le__0__iff) # label(axiom). [clausify(923)].
% 81.57/81.50 5945 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))) # label(fact_mult__strict__left__mono__neg) # label(axiom). [clausify(943)].
% 81.57/81.50 5946 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) # label(fact_mult__strict__right__mono__neg) # label(axiom). [clausify(944)].
% 81.57/81.50 5947 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_mult__neg__neg) # label(axiom). [clausify(948)].
% 81.57/81.50 5948 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(950)].
% 81.57/81.50 5949 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__neg) # label(axiom). [clausify(950)].
% 81.57/81.50 5950 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(956)].
% 81.57/81.50 5951 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__less__cancel__left__pos) # label(axiom). [clausify(956)].
% 81.57/81.50 5952 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(957)].
% 81.57/81.50 5953 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(957)].
% 81.57/81.50 5954 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(957)].
% 81.57/81.50 5955 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(957)].
% 81.57/81.50 5956 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(957)].
% 81.57/81.50 5957 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),C)) # label(fact_mult__less__cancel__left__disj) # label(axiom). [clausify(957)].
% 81.57/81.50 5958 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(958)].
% 81.57/81.50 5959 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(958)].
% 81.57/81.50 5960 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(958)].
% 81.57/81.50 5961 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(958)].
% 81.57/81.50 5962 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(958)].
% 81.57/81.50 5963 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),B)) # label(fact_mult__less__cancel__right__disj) # label(axiom). [clausify(958)].
% 81.57/81.50 5964 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(962)].
% 81.57/81.50 5965 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(962)].
% 81.57/81.50 5966 -class_Rings_Olinordered__ring__strict(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__eq__zero__iff) # label(axiom). [clausify(962)].
% 81.57/81.51 5967 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(1003)].
% 81.57/81.51 5968 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_mult__le__cancel__left__pos) # label(axiom). [clausify(1003)].
% 81.57/81.51 5969 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),C)) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(1004)].
% 81.57/81.51 5970 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),C)) # label(fact_mult__le__cancel__left__neg) # label(axiom). [clausify(1004)].
% 81.57/81.51 5971 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(1016)].
% 81.57/81.51 5972 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(1016)].
% 81.57/81.51 5973 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__le__zero__iff) # label(axiom). [clausify(1016)].
% 81.57/81.51 5974 -class_Rings_Olinordered__ring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) != C # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(1017)].
% 81.57/81.51 5975 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(1017)].
% 81.57/81.51 5976 -class_Rings_Olinordered__ring__strict(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))) | c_Groups_Ozero__class_Ozero(A) = C # label(fact_sum__squares__gt__zero__iff) # label(axiom). [clausify(1017)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5932,a,5934,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5932,a,5935,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(5932,a,5940,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5932,a,5941,a)].
% 81.57/81.51 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5932,a,5943,a)].
% 81.57/81.51 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(5932,a,5944,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A))). [resolve(5932,a,5945,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))). [resolve(5932,a,5946,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(5932,a,5947,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(5932,a,5948,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(5932,a,5950,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(5932,a,5951,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5932,a,5952,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(5932,a,5953,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5932,a,5954,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),B)). [resolve(5932,a,5955,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5932,a,5958,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),A)). [resolve(5932,a,5959,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(5932,a,5960,a)].
% 81.57/81.51 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),A)). [resolve(5932,a,5961,a)].
% 81.57/81.52 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(5932,a,5962,a)].
% 81.57/81.52 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5932,a,5964,a)].
% 81.57/81.52 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5932,a,5965,a)].
% 81.57/81.52 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5932,a,5966,a)].
% 81.57/81.52 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)). [resolve(5932,a,5967,a)].
% 81.57/81.52 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B),C)). [resolve(5932,a,5968,a)].
% 81.57/81.52 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),B)). [resolve(5932,a,5969,a)].
% 81.57/81.52 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),B)). [resolve(5932,a,5970,a)].
% 81.57/81.52 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5932,a,5971,a)].
% 81.57/81.52 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5932,a,5972,a)].
% 81.57/81.52 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5932,a,5973,a)].
% 83.80/83.72 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(5932,a,5974,a)].
% 83.80/83.72 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(5932,a,5975,a)].
% 83.80/83.72 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B. [resolve(5932,a,5976,a)].
% 83.80/83.72 5977 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 83.80/83.72 5978 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_mult__nonneg__nonneg) # label(axiom). [clausify(924)].
% 83.80/83.72 5979 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__nonneg__nonpos) # label(axiom). [clausify(925)].
% 83.80/83.72 5980 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__nonneg__nonpos2) # label(axiom). [clausify(926)].
% 83.80/83.72 5981 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__nonpos__nonneg) # label(axiom). [clausify(927)].
% 83.80/83.72 5982 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_split__mult__neg__le) # label(axiom). [clausify(937)].
% 83.80/83.72 5983 -class_Rings_Oordered__cancel__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_split__mult__neg__le) # label(axiom). [clausify(937)].
% 83.80/83.72 5984 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 83.80/83.72 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))). [resolve(5984,a,5978,a)].
% 85.93/85.87 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5984,a,5979,a)].
% 85.93/85.87 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(5984,a,5980,a)].
% 85.93/85.87 5985 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) # label(axiom). [assumption].
% 85.93/85.87 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(5985,a,5978,a)].
% 85.93/85.87 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5985,a,5979,a)].
% 85.93/85.87 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(5985,a,5980,a)].
% 85.93/85.87 5986 class_Rings_Oordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__semiring) # label(axiom). [assumption].
% 85.93/85.87 5987 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) # label(fact_mult__right__mono) # label(axiom). [clausify(929)].
% 85.93/85.87 5988 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_mult__left__mono) # label(axiom). [clausify(930)].
% 85.93/85.88 5989 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__mono_H) # label(axiom). [clausify(934)].
% 85.93/85.88 5990 -class_Rings_Oordered__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__mono) # label(axiom). [clausify(935)].
% 85.93/85.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(5986,a,5987,a)].
% 85.93/85.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(5986,a,5988,a)].
% 85.93/85.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(5986,a,5989,a)].
% 85.93/85.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(5986,a,5990,a)].
% 85.93/85.88 5991 class_Rings_Oordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__semiring) # label(axiom). [assumption].
% 85.93/85.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))). [resolve(5991,a,5987,a)].
% 85.93/85.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))). [resolve(5991,a,5988,a)].
% 85.93/85.88 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(5991,a,5989,a)].
% 88.06/87.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(5991,a,5990,a)].
% 88.06/87.98 5992 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) # label(axiom). [assumption].
% 88.06/87.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(5992,a,5987,a)].
% 88.06/87.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(5992,a,5988,a)].
% 88.06/87.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(5992,a,5989,a)].
% 88.06/87.98 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(5992,a,5990,a)].
% 88.06/87.98 5993 class_Rings_Oordered__comm__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 88.06/87.98 5994 -class_Rings_Oordered__comm__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_comm__mult__left__mono) # label(axiom). [clausify(931)].
% 92.39/92.32 5995 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 92.39/92.32 5996 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) # label(axiom). [assumption].
% 92.39/92.32 5997 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 92.39/92.32 5998 -class_Rings_Olinordered__comm__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_comm__mult__strict__left__mono) # label(axiom). [clausify(945)].
% 92.39/92.32 5999 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 92.39/92.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))). [resolve(5999,a,5998,a)].
% 92.39/92.32 6000 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption].
% 92.39/92.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))). [resolve(6000,a,5998,a)].
% 92.39/92.32 6001 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 92.39/92.32 6002 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) # label(fact_mult__strict__left__mono) # label(axiom). [clausify(946)].
% 92.39/92.32 6003 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) # label(fact_mult__strict__right__mono) # label(axiom). [clausify(947)].
% 92.39/92.32 6004 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__neg__pos) # label(axiom). [clausify(949)].
% 92.39/92.32 6005 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) # label(fact_zero__less__mult__pos2) # label(axiom). [clausify(951)].
% 92.39/92.32 6006 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) # label(fact_zero__less__mult__pos) # label(axiom). [clausify(952)].
% 92.39/92.32 6007 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__pos__neg2) # label(axiom). [clausify(953)].
% 92.39/92.32 6008 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),c_Groups_Ozero__class_Ozero(A))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))) # label(fact_mult__pos__neg) # label(axiom). [clausify(954)].
% 92.39/92.32 6009 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))) # label(fact_mult__pos__pos) # label(axiom). [clausify(955)].
% 92.39/92.32 6010 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__strict__mono) # label(axiom). [clausify(1005)].
% 92.39/92.32 6011 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__strict__mono_H) # label(axiom). [clausify(1006)].
% 92.39/92.32 6012 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__less__le__imp__less) # label(axiom). [clausify(1007)].
% 92.39/92.32 6013 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))) # label(fact_mult__le__less__imp__less) # label(axiom). [clausify(1008)].
% 92.39/92.32 6014 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_mult__less__imp__less__right) # label(axiom). [clausify(1010)].
% 92.39/92.32 6015 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__less__imp__less__left) # label(axiom). [clausify(1012)].
% 92.39/92.32 6016 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),D)) # label(fact_mult__right__le__imp__le) # label(axiom). [clausify(1013)].
% 92.39/92.32 6017 -class_Rings_Olinordered__semiring__strict(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),D)) # label(fact_mult__left__le__imp__le) # label(axiom). [clausify(1014)].
% 92.39/92.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(6001,a,6004,a)].
% 92.39/92.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(6001,a,6005,a)].
% 92.39/92.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(6001,a,6006,a)].
% 92.39/92.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(6001,a,6008,a)].
% 92.39/92.32 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(6001,a,6009,a)].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(6001,a,6010,a)].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(6001,a,6011,a)].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(6001,a,6012,a)].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D))). [resolve(6001,a,6013,a)].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(6001,a,6014,a)].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(6001,a,6015,a)].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),C)). [resolve(6001,a,6016,a)].
% 92.44/92.34 6018 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))). [resolve(6018,a,6003,a)].
% 92.44/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(6018,a,6004,a)].
% 92.45/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)). [resolve(6018,a,6005,a)].
% 92.45/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)). [resolve(6018,a,6006,a)].
% 92.45/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))). [resolve(6018,a,6008,a)].
% 92.45/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))). [resolve(6018,a,6009,a)].
% 92.45/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(6018,a,6010,a)].
% 92.45/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(6018,a,6011,a)].
% 92.45/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(6018,a,6012,a)].
% 92.45/92.34 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))). [resolve(6018,a,6013,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),A),C)). [resolve(6018,a,6014,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B),C)). [resolve(6018,a,6015,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),C)). [resolve(6018,a,6016,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)). [resolve(6018,a,6017,a)].
% 92.45/92.36 6019 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) # label(axiom). [assumption].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C))). [resolve(6019,a,6003,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(6019,a,6004,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)). [resolve(6019,a,6005,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)). [resolve(6019,a,6006,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))). [resolve(6019,a,6008,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B))). [resolve(6019,a,6009,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(6019,a,6010,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(6019,a,6011,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(6019,a,6012,a)].
% 92.45/92.36 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),C),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D))). [resolve(6019,a,6013,a)].
% 96.69/96.60 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(6019,a,6014,a)].
% 96.69/96.60 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(6019,a,6015,a)].
% 96.69/96.60 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(6019,a,6016,a)].
% 96.69/96.60 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(6019,a,6017,a)].
% 96.69/96.60 6020 class_Rings_Olinordered__semiring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 96.69/96.60 6021 -class_Rings_Olinordered__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),D)) # label(fact_mult__right__less__imp__less) # label(axiom). [clausify(1009)].
% 96.69/96.60 6022 -class_Rings_Olinordered__semiring(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),C),D)) # label(fact_mult__left__less__imp__less) # label(axiom). [clausify(1011)].
% 96.69/96.60 6023 class_Rings_Olinordered__semiring(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 96.69/96.60 6024 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) # label(axiom). [assumption].
% 96.69/96.60 6025 class_Rings_Olinordered__semiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Olinordered__semiring__1) # label(axiom). [assumption].
% 96.69/96.60 6026 -class_Rings_Olinordered__semiring__1(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),D),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),E)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),F)) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)) # label(fact_convex__bound__le) # label(axiom). [clausify(1038)].
% 105.25/105.14 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),C),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),E)) | c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),D),E) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),C))),B)). [resolve(6025,a,6026,a)].
% 105.25/105.14 6027 class_Rings_Oring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1) # label(axiom). [assumption].
% 105.25/105.14 6028 -class_Rings_Oring__1(A) | hBOOL(hAPP(hAPP(c_member(A),c_Groups_Ozero__class_Ozero(A)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__0) # label(axiom). [clausify(1075)].
% 105.25/105.14 6029 -class_Rings_Oring__1(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | -hBOOL(hAPP(hAPP(c_member(A),C),c_Int_Oring__1__class_OInts(A))) | hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__add) # label(axiom). [clausify(1076)].
% 105.25/105.14 6030 -class_Rings_Oring__1(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | -hBOOL(hAPP(hAPP(c_member(A),C),c_Int_Oring__1__class_OInts(A))) | hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__mult) # label(axiom). [clausify(1077)].
% 105.25/105.14 6031 -class_Rings_Oring__1(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | -hBOOL(hAPP(hAPP(c_member(A),C),c_Int_Oring__1__class_OInts(A))) | hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__diff) # label(axiom). [clausify(1078)].
% 105.25/105.14 6032 -class_Rings_Oring__1(A) | hBOOL(hAPP(hAPP(c_member(A),c_Groups_Oone__class_Oone(A)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__1) # label(axiom). [clausify(1079)].
% 105.25/105.14 6033 -class_Rings_Oring__1(A) | hBOOL(hAPP(hAPP(c_member(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__of__nat) # label(axiom). [clausify(1287)].
% 105.25/105.14 6034 -class_Rings_Oring__1(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B),C)) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)) # label(fact_of__nat__diff) # label(axiom). [clausify(1295)].
% 105.25/105.14 6035 -class_Rings_Oring__1(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | hBOOL(hAPP(hAPP(c_member(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__minus) # label(axiom). [clausify(1624)].
% 105.25/105.14 6036 -class_Rings_Oring__1(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__power) # label(axiom). [clausify(1857)].
% 105.25/105.14 6037 -class_Rings_Oring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) # label(fact_power2__minus) # label(axiom). [clausify(1893)].
% 105.25/105.14 6038 -class_Rings_Oring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),C)) # label(fact_power__minus__even) # label(axiom). [clausify(1907)].
% 105.25/105.14 6039 -class_Rings_Oring__1(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)) # label(fact_power__minus1__even) # label(axiom). [clausify(1919)].
% 105.25/105.14 6040 -class_Rings_Oring__1(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))) # label(fact_power__minus1__odd) # label(axiom). [clausify(1925)].
% 105.25/105.14 6041 -class_Rings_Oring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(fact_power__minus) # label(axiom). [clausify(1972)].
% 105.25/105.14 6042 -class_Rings_Oring__1(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Int_Oring__1__class_Oof__int(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)))) # label(fact_of__int__of__nat) # label(axiom). [clausify(1981)].
% 105.25/105.14 6043 -class_Rings_Oring__1(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Int_Oring__1__class_Oof__int(A),B) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,B)) # label(fact_of__int__of__nat) # label(axiom). [clausify(1981)].
% 105.25/105.14 6044 -class_Rings_Oring__1(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Int_Oring__1__class_Oof__int(A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) # label(fact_of__int__0) # label(axiom). [clausify(1991)].
% 105.25/105.14 6045 -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),hAPP(c_Int_Oring__1__class_Oof__int(A),C)) # label(fact_of__int__add) # label(axiom). [clausify(1996)].
% 105.25/105.14 6046 -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),hAPP(c_Int_Oring__1__class_Oof__int(A),C)) # label(fact_of__int__mult) # label(axiom). [clausify(1998)].
% 105.25/105.14 6047 -class_Rings_Oring__1(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Int_Oring__1__class_Oof__int(A),c_Groups_Oone__class_Oone(tc_Int_Oint)) # label(fact_of__int__1) # label(axiom). [clausify(1999)].
% 105.25/105.14 6048 -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),hAPP(c_Int_Oring__1__class_Oof__int(A),C)) # label(fact_of__int__diff) # label(axiom). [clausify(2000)].
% 105.25/105.14 6049 -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B) # label(fact_of__int__of__nat__eq) # label(axiom). [clausify(2001)].
% 105.25/105.14 6050 -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)) # label(fact_of__int__minus) # label(axiom). [clausify(2002)].
% 105.25/105.14 6051 -class_Rings_Oring__1(A) | hBOOL(hAPP(hAPP(c_member(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),c_Int_Oring__1__class_OInts(A))) # label(fact_Ints__of__int) # label(axiom). [clausify(2006)].
% 105.25/105.14 6052 -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Int_Oring__1__class_Oof__int(A),B)),C) # label(fact_of__int__power) # label(axiom). [clausify(2007)].
% 105.25/105.14 6053 -class_Rings_Oring__1(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hAPP(c_Int_Oring__1__class_Oof__int(A),B) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,B)) # label(fact_of__nat__nat) # label(axiom). [clausify(2020)].
% 105.25/105.14 6054 -class_Groups_Ocomm__monoid__mult(A) | -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,tc_Int_Oint),C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),hAPP(hAPP(c_COMBB(tc_Int_Oint,A,B),c_Int_Oring__1__class_Oof__int(A)),C)),D) # label(fact_of__int__setprod) # label(axiom). [clausify(2296)].
% 105.25/105.14 6055 -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint),C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBB(tc_Int_Oint,A,B),c_Int_Oring__1__class_Oof__int(A)),C)),D) # label(fact_of__int__setsum) # label(axiom). [clausify(2297)].
% 105.25/105.14 6056 -class_Rings_Oring__1(A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Int_Oring__1__class_Oof__int(A),B) # label(fact_of__int__num) # label(axiom). [clausify(2374)].
% 105.25/105.14 6057 -class_Rings_Oring__1(A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Int_Oring__1__class_Oof__int(A),B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) # label(fact_of__int__num) # label(axiom). [clausify(2374)].
% 105.25/105.14 6058 -class_Rings_Oring__1(A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Int_Oring__1__class_Oof__int(A),B) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,A),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(A,A)),tc_fun(tc_Int_Oint,A)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(A,A),A),tc_fun(tc_fun(tc_Int_Oint,tc_fun(A,A)),tc_fun(tc_Int_Oint,A)),tc_Int_Oint),c_COMBB(tc_fun(A,A),A,tc_Int_Oint)),hAPP(hAPP(c_COMBB(A,tc_fun(tc_fun(A,A),A),tc_Int_Oint),c_HOL_OLet(A,A)),c_Int_Oring__1__class_Oof__int(A)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(A,A),tc_fun(A,A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(A,A)),tc_fun(tc_fun(A,A),tc_fun(A,A)),tc_Int_Oint),c_COMBS(A,A,A)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(A,A),tc_fun(A,tc_fun(A,A))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(A,A)),tc_fun(tc_fun(A,A),tc_fun(A,tc_fun(A,A))),tc_Int_Oint),c_COMBB(A,tc_fun(A,A),A)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),tc_Int_Oint),c_If(A)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(A,A,A),c_Groups_Oplus__class_Oplus(A)),c_COMBI(A))))),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_Groups_Oplus__class_Oplus(A)),hAPP(hAPP(c_COMBS(A,A,A),c_Groups_Oplus__class_Oplus(A)),c_COMBI(A)))),c_Groups_Oone__class_Oone(A))))),c_Divides_Odivmod__int(B,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) # label(fact_of__int__num) # label(axiom). [clausify(2374)].
% 105.25/105.15 6059 -class_Rings_Oring__1(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B),C)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)) # label(fact_of__int) # label(axiom). [clausify(2400)].
% 105.25/105.15 6060 -class_Rings_Oinverse(A) | -class_Rings_Oring__1(A) | c_Nitpick_Oof__frac(B,A,C) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(A),hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(c_Nitpick_Onum(B),C))),hAPP(c_Int_Oring__1__class_Oof__int(A),hAPP(c_Nitpick_Odenom(B),C))) # label(fact_Nitpick_Oof__frac__def) # label(axiom). [clausify(3641)].
% 105.25/105.15 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6028,a)].
% 105.25/105.15 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6029,a)].
% 105.25/105.15 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6030,a)].
% 105.25/105.15 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6031,a)].
% 105.25/105.15 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6032,a)].
% 105.25/105.15 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6033,a)].
% 105.25/105.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),A),B)) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),A)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)). [resolve(6027,a,6034,a)].
% 105.25/105.15 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6035,a)].
% 105.25/105.15 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6036,a)].
% 105.25/105.15 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(6027,a,6037,a)].
% 105.25/105.15 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B)). [resolve(6027,a,6038,a)].
% 105.25/105.15 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),A)). [resolve(6027,a,6039,a)].
% 105.25/105.15 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),A))). [resolve(6027,a,6040,a)].
% 105.25/105.15 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(6027,a,6041,a)].
% 105.25/105.15 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)))). [resolve(6027,a,6042,a)].
% 105.25/105.15 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,A)). [resolve(6027,a,6043,a)].
% 105.25/105.15 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(6027,a,6044,a)].
% 105.25/105.15 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B)). [resolve(6027,a,6045,a)].
% 105.25/105.15 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B)). [resolve(6027,a,6046,a)].
% 105.25/105.15 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(6027,a,6047,a)].
% 105.25/105.15 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B)). [resolve(6027,a,6048,a)].
% 105.25/105.15 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A). [resolve(6027,a,6049,a)].
% 105.25/105.15 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)). [resolve(6027,a,6050,a)].
% 105.25/105.15 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),c_Int_Oring__1__class_OInts(tc_Int_Oint))). [resolve(6027,a,6051,a)].
% 105.25/105.15 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A)),B). [resolve(6027,a,6052,a)].
% 105.25/105.16 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,A)). [resolve(6027,a,6053,a)].
% 105.25/105.16 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,A),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)),B)),C). [resolve(6027,a,6054,b)].
% 105.25/105.16 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,A),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)),B)),C). [resolve(6027,a,6055,a)].
% 105.25/105.16 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A). [resolve(6027,a,6056,a)].
% 105.25/105.16 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A))). [resolve(6027,a,6057,a)].
% 105.25/105.16 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),tc_fun(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint),c_HOL_OLet(tc_Int_Oint,tc_Int_Oint)),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_If(tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),c_COMBI(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),c_COMBI(tc_Int_Oint)))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Divides_Odivmod__int(A,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))). [resolve(6027,a,6058,a)].
% 105.25/105.16 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),A),B)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)). [resolve(6027,a,6059,a)].
% 107.42/107.35 Derived: -class_Rings_Oinverse(tc_Int_Oint) | c_Nitpick_Oof__frac(A,tc_Int_Oint,B) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nitpick_Onum(A),B))),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nitpick_Odenom(A),B))). [resolve(6027,a,6060,b)].
% 107.42/107.35 6061 class_Int_Oring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 107.42/107.35 6062 -class_Int_Oring__char__0(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_Ints__double__eq__0__iff) # label(axiom). [clausify(1080)].
% 107.42/107.35 6063 -class_Int_Oring__char__0(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_Ints__double__eq__0__iff) # label(axiom). [clausify(1080)].
% 107.42/107.35 6064 -class_Int_Oring__char__0(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Int_Oring__1__class_OInts(A))) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),B)),B) # label(fact_Ints__odd__nonzero) # label(axiom). [clausify(1081)].
% 107.42/107.35 6065 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | hAPP(c_Int_Onumber__class_Onumber__of(A),B) != hAPP(c_Int_Onumber__class_Onumber__of(A),C) | B = C # label(fact_eq__number__of) # label(axiom). [clausify(1157)].
% 107.42/107.35 6066 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | hAPP(c_Int_Onumber__class_Onumber__of(A),B) = hAPP(c_Int_Onumber__class_Onumber__of(A),C) | B != C # label(fact_eq__number__of) # label(axiom). [clausify(1157)].
% 107.42/107.35 6067 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | -c_Int_Oiszero(A,hAPP(c_Int_Onumber__class_Onumber__of(A),c_Int_OBit1(B))) # label(fact_iszero__number__of__Bit1) # label(axiom). [clausify(1788)].
% 107.42/107.35 6068 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | -c_Int_Oiszero(A,hAPP(c_Int_Onumber__class_Onumber__of(A),c_Int_OBit0(B))) | c_Int_Oiszero(A,hAPP(c_Int_Onumber__class_Onumber__of(A),B)) # label(fact_iszero__number__of__Bit0) # label(axiom). [clausify(1789)].
% 107.42/107.35 6069 -class_Int_Onumber__ring(A) | -class_Int_Oring__char__0(A) | c_Int_Oiszero(A,hAPP(c_Int_Onumber__class_Onumber__of(A),c_Int_OBit0(B))) | -c_Int_Oiszero(A,hAPP(c_Int_Onumber__class_Onumber__of(A),B)) # label(fact_iszero__number__of__Bit0) # label(axiom). [clausify(1789)].
% 107.42/107.35 6070 -class_Int_Oring__char__0(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),B) != hAPP(c_Int_Oring__1__class_Oof__int(A),C) | B = C # label(fact_of__int__eq__iff) # label(axiom). [clausify(1984)].
% 107.42/107.35 6071 -class_Int_Oring__char__0(A) | hAPP(c_Int_Oring__1__class_Oof__int(A),B) = hAPP(c_Int_Oring__1__class_Oof__int(A),C) | B != C # label(fact_of__int__eq__iff) # label(axiom). [clausify(1984)].
% 107.42/107.35 6072 -class_Int_Oring__char__0(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Int_Oring__1__class_Oof__int(A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B # label(fact_of__int__0__eq__iff) # label(axiom). [clausify(1992)].
% 107.42/107.35 6073 -class_Int_Oring__char__0(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Int_Oring__1__class_Oof__int(A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B # label(fact_of__int__0__eq__iff) # label(axiom). [clausify(1992)].
% 107.42/107.35 6074 -class_Int_Oring__char__0(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Int_Oring__1__class_Oof__int(A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B # label(fact_of__int__eq__0__iff) # label(axiom). [clausify(1993)].
% 115.66/115.60 6075 -class_Int_Oring__char__0(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Int_Oring__1__class_Oof__int(A),B) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B # label(fact_of__int__eq__0__iff) # label(axiom). [clausify(1993)].
% 115.66/115.60 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Int_Oring__1__class_OInts(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A). [resolve(6061,a,6064,a)].
% 115.66/115.60 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),B) | A = B. [resolve(6061,a,6065,b)].
% 115.66/115.60 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),B) | A != B. [resolve(6061,a,6066,b)].
% 115.66/115.60 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Int_Oiszero(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(A))). [resolve(6061,a,6067,b)].
% 115.66/115.60 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Int_Oiszero(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(A))) | c_Int_Oiszero(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)). [resolve(6061,a,6068,b)].
% 115.66/115.60 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Oiszero(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(A))) | -c_Int_Oiszero(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),A)). [resolve(6061,a,6069,b)].
% 115.66/115.60 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B) | A = B. [resolve(6061,a,6070,a)].
% 115.66/115.60 Derived: hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),B) | A != B. [resolve(6061,a,6071,a)].
% 115.66/115.60 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(6061,a,6072,a)].
% 115.66/115.60 6076 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(arity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 115.66/115.60 6077 -class_Nat_Osemiring__char__0(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C) | B = C # label(fact_of__nat__eq__iff) # label(axiom). [clausify(1255)].
% 115.66/115.60 6078 -class_Nat_Osemiring__char__0(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C) | B != C # label(fact_of__nat__eq__iff) # label(axiom). [clausify(1255)].
% 115.66/115.60 6079 -class_Nat_Osemiring__char__0(A) | c_Fun_Oinj__on(tc_Nat_Onat,A,c_Nat_Osemiring__1__class_Oof__nat(A),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) # label(fact_inj__of__nat) # label(axiom). [clausify(2862)].
% 115.66/115.60 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B) | A = B. [resolve(6076,a,6077,a)].
% 115.66/115.60 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B) | A != B. [resolve(6076,a,6078,a)].
% 115.66/115.60 Derived: c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))). [resolve(6076,a,6079,a)].
% 115.66/115.60 6080 class_Nat_Osemiring__char__0(tc_Nat_Onat) # label(arity_Nat__Onat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 115.66/115.60 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),B) | A = B. [resolve(6080,a,6077,a)].
% 115.66/115.60 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),B) | A != B. [resolve(6080,a,6078,a)].
% 115.66/115.60 Derived: c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))). [resolve(6080,a,6079,a)].
% 115.66/115.60 6081 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 117.69/117.64 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),B) | A = B. [resolve(6081,a,6077,a)].
% 117.69/117.64 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),B) | A != B. [resolve(6081,a,6078,a)].
% 117.69/117.64 Derived: c_Fun_Oinj__on(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))). [resolve(6081,a,6079,a)].
% 117.69/117.64 6082 class_Rings_Osemiring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__1) # label(axiom). [assumption].
% 117.69/117.64 6083 -class_Rings_Osemiring__1(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) # label(fact_of__nat__0) # label(axiom). [clausify(1279)].
% 117.69/117.64 6084 -class_Rings_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)) # label(fact_of__nat__add) # label(axiom). [clausify(1284)].
% 117.69/117.64 6085 -class_Rings_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)) # label(fact_of__nat__mult) # label(axiom). [clausify(1285)].
% 117.69/117.64 6086 -class_Rings_Osemiring__1(A) | c_Groups_Oone__class_Oone(A) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) # label(fact_of__nat__1) # label(axiom). [clausify(1286)].
% 117.69/117.64 6087 -class_Rings_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Nat_OSuc,B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)) # label(fact_of__nat__Suc) # label(axiom). [clausify(1294)].
% 117.69/117.64 6088 -class_Groups_Oordered__ab__semigroup__add(A) | -class_Rings_Osemiring__1(A) | hBOOL(hAPP(hAPP(c_member(B),f115(C,D,E,B,A)),E)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Finite__Set_Ocard(B),E))),C))) # label(fact_setsum__bounded) # label(axiom). [clausify(1303)].
% 117.69/117.64 6089 -class_Groups_Oordered__ab__semigroup__add(A) | -class_Rings_Osemiring__1(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(B,f115(C,B,D,E,A))),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Finite__Set_Ocard(E),D))),C))) # label(fact_setsum__bounded) # label(axiom). [clausify(1303)].
% 117.69/117.64 6090 -class_Rings_Osemiring__1(A) | hBOOL(hAPP(hAPP(c_member(A),c_Groups_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_ONats(A))) # label(fact_Nats__0) # label(axiom). [clausify(1377)].
% 117.69/117.64 6091 -class_Rings_Osemiring__1(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Nat_Osemiring__1__class_ONats(A))) | -hBOOL(hAPP(hAPP(c_member(A),C),c_Nat_Osemiring__1__class_ONats(A))) | hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Nat_Osemiring__1__class_ONats(A))) # label(fact_Nats__add) # label(axiom). [clausify(1378)].
% 117.69/117.64 6092 -class_Rings_Osemiring__1(A) | -hBOOL(hAPP(hAPP(c_member(A),B),c_Nat_Osemiring__1__class_ONats(A))) | -hBOOL(hAPP(hAPP(c_member(A),C),c_Nat_Osemiring__1__class_ONats(A))) | hBOOL(hAPP(hAPP(c_member(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Nat_Osemiring__1__class_ONats(A))) # label(fact_Nats__mult) # label(axiom). [clausify(1379)].
% 117.69/117.64 6093 -class_Rings_Osemiring__1(A) | hBOOL(hAPP(hAPP(c_member(A),c_Groups_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_ONats(A))) # label(fact_Nats__1) # label(axiom). [clausify(1380)].
% 117.69/117.64 6094 -class_Rings_Osemiring__1(A) | hBOOL(hAPP(hAPP(c_member(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),c_Nat_Osemiring__1__class_ONats(A))) # label(fact_of__nat__in__Nats) # label(axiom). [clausify(1381)].
% 117.69/117.64 6095 -class_Rings_Osemiring__1(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,B))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,B))) # label(fact_of__nat__double) # label(axiom). [clausify(1692)].
% 117.69/117.64 6096 -class_Rings_Osemiring__1(A) | c_Int_Oiszero(A,c_Groups_Ozero__class_Ozero(A)) # label(fact_iszero__0) # label(axiom). [clausify(1707)].
% 117.69/117.64 6097 -class_Rings_Osemiring__1(A) | -c_Int_Oiszero(A,B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_iszero__def) # label(axiom). [clausify(1708)].
% 117.69/117.64 6098 -class_Rings_Osemiring__1(A) | c_Int_Oiszero(A,B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_iszero__def) # label(axiom). [clausify(1708)].
% 117.69/117.64 6099 -class_Rings_Osemiring__1(A) | -c_Int_Oiszero(A,c_Groups_Oone__class_Oone(A)) # label(fact_not__iszero__1) # label(axiom). [clausify(1710)].
% 117.69/117.64 6100 -class_Rings_Osemiring__1(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) # label(fact_zero__power2) # label(axiom). [clausify(1888)].
% 117.69/117.64 6101 -class_Rings_Osemiring__1(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) # label(fact_one__power2) # label(axiom). [clausify(1892)].
% 117.69/117.64 6102 -class_Rings_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),C) # label(fact_of__nat__power) # label(axiom). [clausify(1940)].
% 117.69/117.64 6103 -class_Rings_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,B),c_Nat_Osemiring__1__class_Oof__nat(A)),C)),D) # label(fact_of__nat__setsum) # label(axiom). [clausify(2311)].
% 117.69/117.64 6104 -class_Groups_Ocomm__monoid__mult(A) | -class_Rings_Osemiring__1(A) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(B,A),hAPP(hAPP(c_COMBB(tc_Nat_Onat,A,B),c_Nat_Osemiring__1__class_Oof__nat(A)),C)),D) # label(fact_of__nat__setprod) # label(axiom). [clausify(2314)].
% 117.69/117.64 6105 -class_Rings_Osemiring__1(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Finite__Set_Ocard(B),C))),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(c_COMBK(A,B),D)),C) # label(fact_setsum__constant) # label(axiom). [clausify(2321)].
% 117.69/117.64 6106 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,hAPP(hAPP(c_COMBC(A,A,A),c_Groups_Oplus__class_Oplus(A)),c_Groups_Oone__class_Oone(A)),B,c_Groups_Ozero__class_Ozero(A)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B) # label(fact_semiring__1__class_Oof__nat__code) # label(axiom). [clausify(2420)].
% 117.69/117.64 6107 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C) = C # label(fact_of__nat__aux_Osimps_I1_J) # label(axiom). [clausify(2425)].
% 117.69/117.64 6108 -class_Rings_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,hAPP(c_Nat_OSuc,C),D) = c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,C,hAPP(B,D)) # label(fact_of__nat__aux_Osimps_I2_J) # label(axiom). [clausify(2426)].
% 117.69/117.64 6109 -class_Rings_Osemiring__1(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),hAPP(c_COMBK(A,B),C)),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),D))),C) # label(fact_listsum__triv) # label(axiom). [clausify(4098)].
% 117.69/117.64 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(6082,a,6083,a)].
% 117.69/117.64 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)). [resolve(6082,a,6084,a)].
% 117.69/117.64 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)). [resolve(6082,a,6085,a)].
% 117.69/117.64 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(6082,a,6086,a)].
% 117.69/117.64 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)). [resolve(6082,a,6087,a)].
% 117.69/117.64 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_member(A),f115(B,C,D,A,tc_Int_Oint)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(A),D))),B))). [resolve(6082,a,6088,b)].
% 117.69/117.64 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(A,f115(B,A,C,D,tc_Int_Oint))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(D),C))),B))). [resolve(6082,a,6089,b)].
% 117.69/117.64 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))). [resolve(6082,a,6090,a)].
% 117.69/117.64 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))). [resolve(6082,a,6091,a)].
% 117.69/117.64 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),A),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))) | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))). [resolve(6082,a,6092,a)].
% 117.69/117.64 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))). [resolve(6082,a,6093,a)].
% 117.69/117.64 Derived: hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Nat_Osemiring__1__class_ONats(tc_Int_Oint))). [resolve(6082,a,6094,a)].
% 117.69/117.64 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),A))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,A))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,A))). [resolve(6082,a,6095,a)].
% 117.69/117.66 Derived: c_Int_Oiszero(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(6082,a,6096,a)].
% 117.69/117.66 Derived: -c_Int_Oiszero(tc_Int_Oint,A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(6082,a,6097,a)].
% 117.69/117.66 Derived: c_Int_Oiszero(tc_Int_Oint,A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(6082,a,6098,a)].
% 117.69/117.66 Derived: -c_Int_Oiszero(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(6082,a,6099,a)].
% 117.69/117.66 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(6082,a,6100,a)].
% 117.69/117.66 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),B). [resolve(6082,a,6102,a)].
% 117.69/117.66 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,A),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),B)),C). [resolve(6082,a,6103,a)].
% 117.69/117.66 Derived: -class_Groups_Ocomm__monoid__mult(tc_Int_Oint) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,A),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),B)),C). [resolve(6082,a,6104,b)].
% 117.69/117.66 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(A),B))),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(c_COMBK(tc_Int_Oint,A),C)),B). [resolve(6082,a,6105,a)].
% 117.69/117.66 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A). [resolve(6082,a,6106,a)].
% 117.69/117.66 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) = B. [resolve(6082,a,6107,a)].
% 117.69/117.66 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Int_Oint,A,hAPP(c_Nat_OSuc,B),C) = c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Int_Oint,A,B,hAPP(A,C)). [resolve(6082,a,6108,a)].
% 117.69/117.66 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),hAPP(c_COMBK(tc_Int_Oint,A),B)),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C))),B). [resolve(6082,a,6109,a)].
% 117.69/117.66 6110 class_Rings_Osemiring__1(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__1) # label(axiom). [assumption].
% 117.69/117.66 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(6110,a,6083,a)].
% 117.69/117.66 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),B)). [resolve(6110,a,6084,a)].
% 117.69/117.66 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),B)). [resolve(6110,a,6085,a)].
% 117.69/117.66 Derived: c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(6110,a,6086,a)].
% 117.69/117.66 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)). [resolve(6110,a,6087,a)].
% 117.69/117.66 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) | hBOOL(hAPP(hAPP(c_member(A),f115(B,C,D,A,tc_Nat_Onat)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(A),D))),B))). [resolve(6110,a,6088,b)].
% 117.69/117.66 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(A,f115(B,A,C,D,tc_Nat_Onat))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(D),C))),B))). [resolve(6110,a,6089,b)].
% 117.69/117.66 Derived: hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))). [resolve(6110,a,6090,a)].
% 117.69/117.66 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))). [resolve(6110,a,6091,a)].
% 117.69/117.66 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))) | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))). [resolve(6110,a,6092,a)].
% 117.69/117.66 Derived: hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))). [resolve(6110,a,6093,a)].
% 117.69/117.66 Derived: hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),c_Nat_Osemiring__1__class_ONats(tc_Nat_Onat))). [resolve(6110,a,6094,a)].
% 117.69/117.66 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),A))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(c_Int_Onat,A))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(c_Int_Onat,A))). [resolve(6110,a,6095,a)].
% 117.69/117.66 Derived: c_Int_Oiszero(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(6110,a,6096,a)].
% 117.69/117.66 Derived: -c_Int_Oiszero(tc_Nat_Onat,A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A. [resolve(6110,a,6097,a)].
% 117.69/117.66 Derived: c_Int_Oiszero(tc_Nat_Onat,A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A. [resolve(6110,a,6098,a)].
% 117.69/117.66 Derived: -c_Int_Oiszero(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(6110,a,6099,a)].
% 117.69/117.66 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(6110,a,6100,a)].
% 117.78/117.68 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A)),B). [resolve(6110,a,6102,a)].
% 117.78/117.68 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,A),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat)),B)),C). [resolve(6110,a,6103,a)].
% 117.78/117.68 Derived: -class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,A),c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat)),B)),C). [resolve(6110,a,6104,b)].
% 117.78/117.68 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(A),B))),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,A),C)),B). [resolve(6110,a,6105,a)].
% 117.78/117.68 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),A). [resolve(6110,a,6106,a)].
% 117.78/117.68 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) = B. [resolve(6110,a,6107,a)].
% 117.78/117.68 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B),C) = c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Nat_Onat,A,B,hAPP(A,C)). [resolve(6110,a,6108,a)].
% 117.78/117.68 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,A),B)),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C))),B). [resolve(6110,a,6109,a)].
% 117.78/117.68 6111 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) # label(axiom). [assumption].
% 117.78/117.68 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(6111,a,6083,a)].
% 117.78/117.68 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),B)). [resolve(6111,a,6084,a)].
% 117.78/117.68 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),B)). [resolve(6111,a,6085,a)].
% 117.78/117.68 Derived: c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(6111,a,6086,a)].
% 117.78/117.68 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_OSuc,A)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)). [resolve(6111,a,6087,a)].
% 117.78/117.68 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(hAPP(c_member(A),f115(B,C,D,A,tc_Code__Numeral_Ocode__numeral)),D)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ocard(A),D))),B))). [resolve(6111,a,6088,b)].
% 117.78/117.68 Derived: -class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(A,f115(B,A,C,D,tc_Code__Numeral_Ocode__numeral))),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Code__Numeral_Ocode__numeral),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ocard(D),C))),B))). [resolve(6111,a,6089,b)].
% 117.78/117.68 Derived: hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))). [resolve(6111,a,6090,a)].
% 117.78/117.68 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),A),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))). [resolve(6111,a,6091,a)].
% 117.78/117.68 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),A),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))) | -hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),B),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))) | hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))). [resolve(6111,a,6092,a)].
% 117.78/117.68 Derived: hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))). [resolve(6111,a,6093,a)].
% 117.78/117.68 Derived: hBOOL(hAPP(hAPP(c_member(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),c_Nat_Osemiring__1__class_ONats(tc_Code__Numeral_Ocode__numeral))). [resolve(6111,a,6094,a)].
% 117.78/117.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),A))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onat,A))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onat,A))). [resolve(6111,a,6095,a)].
% 117.78/117.68 Derived: c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(6111,a,6096,a)].
% 117.78/117.68 Derived: -c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,A) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A. [resolve(6111,a,6097,a)].
% 117.78/117.68 Derived: c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,A) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A. [resolve(6111,a,6098,a)].
% 117.78/117.68 Derived: -c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)). [resolve(6111,a,6099,a)].
% 119.78/119.67 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))). [resolve(6111,a,6100,a)].
% 119.78/119.67 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A)),B). [resolve(6111,a,6102,a)].
% 119.78/119.67 Derived: hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,A),c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)),B)),C). [resolve(6111,a,6103,a)].
% 119.78/119.67 Derived: -class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Nat_Onat),B),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,A),c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral)),B)),C). [resolve(6111,a,6104,b)].
% 119.78/119.67 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Finite__Set_Ocard(A),B))),C) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBK(tc_Code__Numeral_Ocode__numeral,A),C)),B). [resolve(6111,a,6105,a)].
% 119.78/119.67 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),A). [resolve(6111,a,6106,a)].
% 119.78/119.67 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B) = B. [resolve(6111,a,6107,a)].
% 119.78/119.67 Derived: c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Code__Numeral_Ocode__numeral,A,hAPP(c_Nat_OSuc,B),C) = c_Nat_Osemiring__1__class_Oof__nat__aux(tc_Code__Numeral_Ocode__numeral,A,B,hAPP(A,C)). [resolve(6111,a,6108,a)].
% 119.78/119.67 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBK(tc_Code__Numeral_Ocode__numeral,A),B)),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C))),B). [resolve(6111,a,6109,a)].
% 119.78/119.67 6112 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption].
% 119.78/119.67 6113 -class_Groups_Oordered__ab__group__add__abs(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)) = hAPP(c_Groups_Oabs__class_Oabs(A),B) # label(fact_abs__idempotent) # label(axiom). [clausify(1345)].
% 119.78/119.67 6114 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_abs__le__D1) # label(axiom). [clausify(1346)].
% 119.78/119.67 6115 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),hAPP(c_Groups_Oabs__class_Oabs(A),B))) # label(fact_abs__ge__self) # label(axiom). [clausify(1347)].
% 119.78/119.67 6116 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Oabs__class_Oabs(A),c_Groups_Ozero__class_Ozero(A)) # label(fact_abs__zero) # label(axiom). [clausify(1348)].
% 119.78/119.67 6117 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(c_Groups_Oabs__class_Oabs(A),B) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_abs__eq__0) # label(axiom). [clausify(1349)].
% 119.78/119.67 6118 -class_Groups_Oordered__ab__group__add__abs(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(c_Groups_Oabs__class_Oabs(A),B) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_abs__eq__0) # label(axiom). [clausify(1349)].
% 119.78/119.67 6119 -class_Groups_Oordered__ab__group__add__abs(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__add__abs) # label(axiom). [clausify(1350)].
% 119.78/119.67 6120 -class_Groups_Oordered__ab__group__add__abs(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)) = hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B)) # label(fact_abs__minus__commute) # label(axiom). [clausify(1353)].
% 119.78/119.67 6121 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Groups_Oabs__class_Oabs(A),B))) # label(fact_abs__ge__zero) # label(axiom). [clausify(1358)].
% 119.78/119.67 6122 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_abs__le__zero__iff) # label(axiom). [clausify(1359)].
% 119.78/119.67 6123 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),c_Groups_Ozero__class_Ozero(A))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_abs__le__zero__iff) # label(axiom). [clausify(1359)].
% 119.78/119.67 6124 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | hAPP(c_Groups_Oabs__class_Oabs(A),B) = B # label(fact_abs__of__nonneg) # label(axiom). [clausify(1360)].
% 119.78/119.67 6125 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),c_Groups_Ozero__class_Ozero(A))) # label(fact_abs__not__less__zero) # label(axiom). [clausify(1361)].
% 119.78/119.67 6126 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Groups_Oabs__class_Oabs(A),B))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__less__abs__iff) # label(axiom). [clausify(1362)].
% 119.78/119.67 6127 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Groups_Oabs__class_Oabs(A),B))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__less__abs__iff) # label(axiom). [clausify(1362)].
% 119.78/119.67 6128 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | hAPP(c_Groups_Oabs__class_Oabs(A),B) = B # label(fact_abs__of__pos) # label(axiom). [clausify(1363)].
% 119.78/119.67 6129 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)))) # label(fact_abs__triangle__ineq) # label(axiom). [clausify(1364)].
% 119.78/119.67 6130 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C))),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B)))) # label(fact_abs__triangle__ineq2__sym) # label(axiom). [clausify(1366)].
% 119.78/119.67 6131 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C))),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)))) # label(fact_abs__triangle__ineq2) # label(axiom). [clausify(1367)].
% 119.78/119.67 6132 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)))),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)))) # label(fact_abs__triangle__ineq3) # label(axiom). [clausify(1368)].
% 119.78/119.67 6133 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D))),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),E))))) # label(fact_abs__diff__triangle__ineq) # label(axiom). [clausify(1373)].
% 119.78/119.67 6134 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)))) # label(fact_abs__triangle__ineq4) # label(axiom). [clausify(1374)].
% 119.78/119.67 6135 -class_Groups_Oordered__ab__group__add__abs(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) = hAPP(c_Groups_Oabs__class_Oabs(A),B) # label(fact_abs__minus__cancel) # label(axiom). [clausify(1545)].
% 119.78/119.67 6136 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) # label(fact_abs__le__D2) # label(axiom). [clausify(1587)].
% 119.78/119.67 6137 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) # label(fact_abs__leI) # label(axiom). [clausify(1588)].
% 119.78/119.67 6138 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) # label(fact_abs__le__iff) # label(axiom). [clausify(1589)].
% 119.78/119.67 6139 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) # label(fact_abs__le__iff) # label(axiom). [clausify(1589)].
% 119.78/119.67 6140 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),C)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) # label(fact_abs__le__iff) # label(axiom). [clausify(1589)].
% 119.78/119.67 6141 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),B))) # label(fact_abs__ge__minus__self) # label(axiom). [clausify(1590)].
% 119.78/119.67 6142 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(c_Groups_Oabs__class_Oabs(A),B) # label(fact_abs__of__nonpos) # label(axiom). [clausify(1636)].
% 119.78/119.68 6143 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Groups_Oabs__class_Oabs(A),B))),c_Groups_Ozero__class_Ozero(A))) # label(fact_abs__minus__le__zero) # label(axiom). [clausify(1637)].
% 119.78/119.68 6144 -class_Groups_Oordered__ab__group__add__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(c_Groups_Oabs__class_Oabs(A),B) # label(fact_abs__of__neg) # label(axiom). [clausify(1639)].
% 119.78/119.68 6145 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),D))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBB(A,A,B),c_Groups_Oabs__class_Oabs(A)),C)),D))) # label(fact_setsum__abs) # label(axiom). [clausify(2270)].
% 119.78/119.68 6146 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBB(A,A,B),c_Groups_Oabs__class_Oabs(A)),C)),D))) # label(fact_setsum__abs__ge__zero) # label(axiom). [clausify(2271)].
% 119.78/119.68 6147 -class_Groups_Oordered__ab__group__add__abs(A) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBB(A,A,B),c_Groups_Oabs__class_Oabs(A)),C)),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBB(A,A,B),c_Groups_Oabs__class_Oabs(A)),C)),D) # label(fact_abs__setsum__abs) # label(axiom). [clausify(2280)].
% 119.78/119.68 6148 -class_Groups_Oordered__ab__group__add__abs(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),B))),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(A,A),c_Groups_Oabs__class_Oabs(A)),B)))) # label(fact_listsum__abs) # label(axiom). [clausify(4092)].
% 119.78/119.68 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(6112,a,6113,a)].
% 119.78/119.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)). [resolve(6112,a,6114,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A))). [resolve(6112,a,6115,a)].
% 119.78/119.68 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(6112,a,6116,a)].
% 119.78/119.68 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(6112,a,6117,a)].
% 119.78/119.68 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(6112,a,6118,a)].
% 119.78/119.68 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(6112,a,6119,a)].
% 119.78/119.68 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),A)). [resolve(6112,a,6120,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A))). [resolve(6112,a,6121,a)].
% 119.78/119.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(6112,a,6122,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(6112,a,6123,a)].
% 119.78/119.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) = A. [resolve(6112,a,6124,a)].
% 119.78/119.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(6112,a,6125,a)].
% 119.78/119.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(6112,a,6126,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(6112,a,6127,a)].
% 119.78/119.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) = A. [resolve(6112,a,6128,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)))). [resolve(6112,a,6129,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),A)))). [resolve(6112,a,6130,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B))),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)))). [resolve(6112,a,6131,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)))),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)))). [resolve(6112,a,6132,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),D)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),C))),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),D))))). [resolve(6112,a,6133,a)].
% 119.78/119.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),B)))). [resolve(6112,a,6134,a)].
% 121.78/121.68 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(6112,a,6135,a)].
% 121.78/121.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)). [resolve(6112,a,6136,a)].
% 121.78/121.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A)),B)). [resolve(6112,a,6137,a)].
% 121.78/121.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A))). [resolve(6112,a,6141,a)].
% 121.78/121.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(6112,a,6142,a)].
% 121.78/121.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))). [resolve(6112,a,6143,a)].
% 121.78/121.68 Derived: -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(6112,a,6144,a)].
% 121.78/121.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),C))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint)),B)),C))). [resolve(6112,a,6145,a)].
% 121.78/121.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint)),B)),C))). [resolve(6112,a,6146,a)].
% 121.78/121.68 Derived: hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint)),B)),C)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,A),c_Groups_Oabs__class_Oabs(tc_Int_Oint)),B)),C). [resolve(6112,a,6147,a)].
% 121.78/121.68 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),A))),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint)),A)))). [resolve(6112,a,6148,a)].
% 121.78/121.68 6149 class_Rings_Oordered__ring__abs(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oordered__ring__abs) # label(axiom). [assumption].
% 121.78/121.68 6150 -class_Rings_Oordered__ring__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(1372)].
% 121.78/121.68 6151 -class_Rings_Oordered__ring__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(1372)].
% 123.80/123.69 6152 -class_Rings_Oordered__ring__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),c_Groups_Ozero__class_Ozero(A)),C)) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(1372)].
% 123.80/123.69 6153 -class_Rings_Oordered__ring__abs(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),B),c_Groups_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(A),C),c_Groups_Ozero__class_Ozero(A))) | hAPP(c_Groups_Oabs__class_Oabs(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Oabs__class_Oabs(A),B)),hAPP(c_Groups_Oabs__class_Oabs(A),C)) # label(fact_abs__eq__mult) # label(axiom). [clausify(1372)].
% 123.80/123.69 6154 class_Divides_Osemiring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 123.80/123.69 6155 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Divides_Odiv__class_Omod(A,B,C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mod__trivial) # label(axiom). [clausify(1389)].
% 123.80/123.69 6156 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,c_Groups_Ozero__class_Ozero(A),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__0) # label(axiom). [clausify(1390)].
% 123.80/123.69 6157 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Ozero__class_Ozero(A)) = B # label(fact_mod__by__0) # label(axiom). [clausify(1391)].
% 123.80/123.69 6158 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__self) # label(axiom). [clausify(1392)].
% 123.80/123.69 6159 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__add__self2) # label(axiom). [clausify(1393)].
% 123.80/123.69 6160 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),B) = c_Divides_Odiv__class_Omod(A,C,B) # label(fact_mod__add__self1) # label(axiom). [clausify(1394)].
% 123.80/123.69 6161 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),D) # label(fact_mod__add__right__eq) # label(axiom). [clausify(1395)].
% 123.80/123.69 6162 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_mod__add__left__eq) # label(axiom). [clausify(1396)].
% 123.80/123.69 6163 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_mod__add__eq) # label(axiom). [clausify(1397)].
% 123.80/123.69 6164 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C),D) # label(fact_zmod__simps_I2_J) # label(axiom). [clausify(1398)].
% 123.80/123.69 6165 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C) # label(fact_zmod__simps_I1_J) # label(axiom). [clausify(1399)].
% 123.80/123.69 6166 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),E),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),F),C) # label(fact_mod__add__cong) # label(axiom). [clausify(1400)].
% 123.80/123.69 6167 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),F),C) # label(fact_mod__mult__cong) # label(axiom). [clausify(1401)].
% 123.80/123.69 6168 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_zmod__simps_I4_J) # label(axiom). [clausify(1402)].
% 123.80/123.69 6169 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,D)),C) # label(fact_mod__mult__mult2) # label(axiom). [clausify(1403)].
% 123.80/123.69 6170 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(A,C,D)) # label(fact_mod__mult__mult1) # label(axiom). [clausify(1404)].
% 123.80/123.69 6171 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,C)),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_mod__mult__eq) # label(axiom). [clausify(1405)].
% 123.80/123.69 6172 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),C) # label(fact_mod__mult__left__eq) # label(axiom). [clausify(1406)].
% 123.80/123.69 6173 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D) # label(fact_mod__mult__right__eq) # label(axiom). [clausify(1407)].
% 123.80/123.69 6174 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),C) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self2__is__0) # label(axiom). [clausify(1424)].
% 123.80/123.69 6175 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),B) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__mult__self1__is__0) # label(axiom). [clausify(1425)].
% 123.80/123.69 6176 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),D) = c_Divides_Odiv__class_Omod(A,B,D) # label(fact_mod__mult__self1) # label(axiom). [clausify(1426)].
% 123.80/123.69 6177 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),C) = c_Divides_Odiv__class_Omod(A,B,C) # label(fact_mod__mult__self2) # label(axiom). [clausify(1427)].
% 123.80/123.69 6178 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(A,B,c_Groups_Oone__class_Oone(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_mod__by__1) # label(axiom). [clausify(1428)].
% 123.80/123.69 6179 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_div__0) # label(axiom). [clausify(1703)].
% 123.80/123.69 6180 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),B),c_Groups_Ozero__class_Ozero(A)) # label(fact_div__by__0) # label(axiom). [clausify(1704)].
% 123.80/123.69 6181 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),B),c_Groups_Oone__class_Oone(A)) = B # label(fact_div__by__1) # label(axiom). [clausify(1706)].
% 123.80/123.69 6182 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) # label(fact_div__mult__mult1__if) # label(axiom). [clausify(1735)].
% 123.80/123.69 6183 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),D) # label(fact_div__mult__mult1__if) # label(axiom). [clausify(1735)].
% 123.80/123.69 6184 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),B) = C # label(fact_div__mult__self2__is__id) # label(axiom). [clausify(1736)].
% 123.80/123.69 6185 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),B) = C # label(fact_div__mult__self1__is__id) # label(axiom). [clausify(1737)].
% 123.80/123.69 6186 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),D) # label(fact_div__mult__mult2) # label(axiom). [clausify(1738)].
% 123.80/123.69 6187 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),D) # label(fact_div__mult__mult1) # label(axiom). [clausify(1739)].
% 123.80/123.69 6188 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),B),B) # label(fact_div__self) # label(axiom). [clausify(1740)].
% 123.80/123.69 6189 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),c_Divides_Odiv__class_Omod(A,B,C)),C) # label(fact_mod__div__trivial) # label(axiom). [clausify(1741)].
% 123.80/123.69 6190 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)) # label(fact_div__mult__self1) # label(axiom). [clausify(1778)].
% 123.80/123.69 6191 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)) # label(fact_div__mult__self2) # label(axiom). [clausify(1779)].
% 123.80/123.69 6192 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)),c_Groups_Oone__class_Oone(A)) # label(fact_div__add__self2) # label(axiom). [clausify(1780)].
% 123.80/123.69 6193 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),B) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)),c_Groups_Oone__class_Oone(A)) # label(fact_div__add__self1) # label(axiom). [clausify(1781)].
% 123.80/123.69 6194 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),B),C)),C)),c_Divides_Odiv__class_Omod(A,B,C))),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D) # label(fact_div__mod__equality) # label(axiom). [clausify(1782)].
% 123.80/123.69 6195 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B))),c_Divides_Odiv__class_Omod(A,C,B))),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D) # label(fact_div__mod__equality2) # label(axiom). [clausify(1783)].
% 123.80/123.69 6196 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),B),C)),C)),c_Divides_Odiv__class_Omod(A,B,C)) = B # label(fact_mod__div__equality) # label(axiom). [clausify(1784)].
% 123.80/123.69 6197 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B))),c_Divides_Odiv__class_Omod(A,C,B)) = C # label(fact_mod__div__equality2) # label(axiom). [clausify(1785)].
% 123.80/123.69 6198 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(A,B,C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),B),C)),C)) = B # label(fact_semiring__div__class_Omod__div__equality_H) # label(axiom). [clausify(1786)].
% 123.80/123.69 6199 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),B),C)),C)),c_Divides_Odiv__class_Omod(A,B,C)) = B # label(fact_mod__div__decomp) # label(axiom). [clausify(2124)].
% 123.80/123.69 6200 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),E)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),D),B) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),E),C) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E) # label(fact_dvd__div__div__eq__mult) # label(axiom). [clausify(4806)].
% 123.80/123.69 6201 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) = C | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),E)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),D),B) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),E),C) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E) # label(fact_dvd__div__div__eq__mult) # label(axiom). [clausify(4806)].
% 123.80/123.69 6202 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B) != D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) = C # label(fact_dvd__div__eq__mult) # label(axiom). [clausify(4807)].
% 123.80/123.69 6203 -class_Divides_Osemiring__div(A) | c_Groups_Ozero__class_Ozero(A) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B) = D | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B) != C # label(fact_dvd__div__eq__mult) # label(axiom). [clausify(4807)].
% 123.80/123.69 6204 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)) = C # label(fact_dvd__mult__div__cancel) # label(axiom). [clausify(4809)].
% 123.80/123.69 6205 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)) # label(fact_div__mult__swap) # label(axiom). [clausify(4810)].
% 123.80/123.69 6206 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)),B) = C # label(fact_dvd__div__mult__self) # label(axiom). [clausify(4811)].
% 123.80/123.70 6207 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)),D) # label(fact_dvd__div__mult) # label(axiom). [clausify(4812)].
% 123.80/123.70 6208 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),D),E)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),E),D)) # label(fact_div__mult__div__if__dvd) # label(axiom). [clausify(4813)].
% 123.80/123.70 6209 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Omod(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__eq__mod__eq__0) # label(axiom). [clausify(4845)].
% 123.80/123.70 6210 -class_Divides_Osemiring__div(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Omod(A,C,B) != c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__eq__mod__eq__0) # label(axiom). [clausify(4845)].
% 123.80/123.70 6211 -class_Divides_Osemiring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | c_Divides_Odiv__class_Omod(A,C,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_dvd__imp__mod__0) # label(axiom). [clausify(4846)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(6154,a,6155,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(6154,a,6156,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(6154,a,6157,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(6154,a,6158,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(6154,a,6159,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),A) = c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A). [resolve(6154,a,6160,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B),C). [resolve(6154,a,6161,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),B). [resolve(6154,a,6162,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C),B). [resolve(6154,a,6163,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),E),B). [resolve(6154,a,6166,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),E),B). [resolve(6154,a,6167,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),B). [resolve(6154,a,6168,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,C)),B). [resolve(6154,a,6169,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)). [resolve(6154,a,6170,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C),B). [resolve(6154,a,6171,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C). [resolve(6154,a,6173,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(6154,a,6174,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(6154,a,6175,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,C). [resolve(6154,a,6176,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B). [resolve(6154,a,6177,a)].
% 123.80/123.70 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(6154,a,6178,a)].
% 123.80/123.70 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(6154,a,6179,a)].
% 123.80/123.70 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)). [resolve(6154,a,6180,a)].
% 123.80/123.70 Derived: hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(6154,a,6181,a)].
% 123.80/123.70 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(6154,a,6182,a)].
% 123.80/123.70 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),C). [resolve(6154,a,6183,a)].
% 123.80/123.70 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A)),A) = B. [resolve(6154,a,6184,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),A) = B. [resolve(6154,a,6185,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),C). [resolve(6154,a,6186,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),A),A). [resolve(6154,a,6188,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),B). [resolve(6154,a,6189,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)). [resolve(6154,a,6190,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)). [resolve(6154,a,6191,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(6154,a,6192,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(6154,a,6193,a)].
% 123.80/123.71 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),A),B)),B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C). [resolve(6154,a,6194,a)].
% 123.80/123.71 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A))),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C). [resolve(6154,a,6195,a)].
% 123.80/123.71 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),A),B)),B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)) = A. [resolve(6154,a,6196,a)].
% 123.80/123.71 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A))),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A)) = B. [resolve(6154,a,6197,a)].
% 123.80/123.71 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),A),B)),B)) = A. [resolve(6154,a,6198,a)].
% 123.80/123.71 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),C),A) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),D),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D). [resolve(6154,a,6200,a)].
% 123.80/123.72 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),C),A) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),D),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D). [resolve(6154,a,6201,a)].
% 123.80/123.72 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A) = B. [resolve(6154,a,6202,a)].
% 123.80/123.72 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A) != B. [resolve(6154,a,6203,a)].
% 123.80/123.72 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)) = B. [resolve(6154,a,6204,a)].
% 123.80/123.72 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)). [resolve(6154,a,6205,a)].
% 123.80/123.72 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)),A) = B. [resolve(6154,a,6206,a)].
% 123.80/123.72 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)),C). [resolve(6154,a,6207,a)].
% 123.80/123.72 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),C),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),D),C)). [resolve(6154,a,6208,a)].
% 123.80/123.72 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(6154,a,6209,a)].
% 123.80/123.72 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A) != c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(6154,a,6210,a)].
% 123.80/123.72 6212 class_Divides_Osemiring__div(tc_Nat_Onat) # label(arity_Nat__Onat__Divides_Osemiring__div) # label(axiom). [assumption].
% 123.80/123.72 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(6212,a,6155,a)].
% 123.80/123.72 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(6212,a,6156,a)].
% 123.80/123.72 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = A. [resolve(6212,a,6157,a)].
% 123.80/123.72 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(6212,a,6158,a)].
% 123.80/123.72 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(6212,a,6159,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),A) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A). [resolve(6212,a,6160,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B),C). [resolve(6212,a,6161,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),B). [resolve(6212,a,6162,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C),B). [resolve(6212,a,6163,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),E),B). [resolve(6212,a,6166,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,D,B) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,E,B) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),E),B). [resolve(6212,a,6167,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),B). [resolve(6212,a,6168,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C)),B). [resolve(6212,a,6169,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)). [resolve(6212,a,6170,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),B). [resolve(6212,a,6171,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),C). [resolve(6212,a,6173,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(6212,a,6174,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(6212,a,6175,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,C). [resolve(6212,a,6176,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B). [resolve(6212,a,6177,a)].
% 123.80/123.73 Derived: c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(6212,a,6178,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(6212,a,6179,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)). [resolve(6212,a,6180,a)].
% 123.80/123.73 Derived: hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = A. [resolve(6212,a,6181,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)). [resolve(6212,a,6182,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),C). [resolve(6212,a,6183,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)),A) = B. [resolve(6212,a,6184,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),A) = B. [resolve(6212,a,6185,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),C). [resolve(6212,a,6186,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),A),A). [resolve(6212,a,6188,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),B). [resolve(6212,a,6189,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)). [resolve(6212,a,6190,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)). [resolve(6212,a,6191,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(6212,a,6192,a)].
% 123.80/123.73 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)). [resolve(6212,a,6193,a)].
% 123.80/123.73 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),A),B)),B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C). [resolve(6212,a,6194,a)].
% 123.80/123.74 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C). [resolve(6212,a,6195,a)].
% 123.80/123.74 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),A),B)),B)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)) = A. [resolve(6212,a,6196,a)].
% 123.80/123.74 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A)) = B. [resolve(6212,a,6197,a)].
% 123.80/123.74 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),A),B)),B)) = A. [resolve(6212,a,6198,a)].
% 123.80/123.74 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),C),A) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),D),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D). [resolve(6212,a,6200,a)].
% 123.80/123.74 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),C),A) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),D),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),D). [resolve(6212,a,6201,a)].
% 123.80/123.74 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A) = B. [resolve(6212,a,6202,a)].
% 123.80/123.74 Derived: c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A) != B. [resolve(6212,a,6203,a)].
% 123.80/123.74 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)) = B. [resolve(6212,a,6204,a)].
% 123.80/123.74 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)). [resolve(6212,a,6205,a)].
% 123.80/123.74 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)),A) = B. [resolve(6212,a,6206,a)].
% 123.80/123.74 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)),C). [resolve(6212,a,6207,a)].
% 123.80/123.74 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),C),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),B),A)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),D),C)). [resolve(6212,a,6208,a)].
% 123.80/123.76 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(6212,a,6209,a)].
% 123.80/123.76 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),A),B)) | c_Divides_Odiv__class_Omod(tc_Nat_Onat,B,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat). [resolve(6212,a,6210,a)].
% 123.80/123.76 6213 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) # label(axiom). [assumption].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(6213,a,6155,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(6213,a,6156,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(6213,a,6157,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(6213,a,6158,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(6213,a,6159,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),A) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,A). [resolve(6213,a,6160,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B),C). [resolve(6213,a,6161,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C),B). [resolve(6213,a,6162,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C),B). [resolve(6213,a,6163,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,C,B) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,D,B) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,E,B) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),D),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),E),B). [resolve(6213,a,6166,a)].
% 123.80/123.76 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,C,B) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,D,B) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,E,B) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),D),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),E),B). [resolve(6213,a,6167,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),B). [resolve(6213,a,6168,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,C)),B). [resolve(6213,a,6169,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,C)). [resolve(6213,a,6170,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C),B). [resolve(6213,a,6171,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),C). [resolve(6213,a,6173,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),B) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(6213,a,6174,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B),A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(6213,a,6175,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)),C) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,C). [resolve(6213,a,6176,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)),B) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B). [resolve(6213,a,6177,a)].
% 123.80/123.77 Derived: c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(6213,a,6178,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A). [resolve(6213,a,6179,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)). [resolve(6213,a,6180,a)].
% 123.80/123.77 Derived: hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),A),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = A. [resolve(6213,a,6181,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != A | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)). [resolve(6213,a,6182,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),C). [resolve(6213,a,6183,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A)),A) = B. [resolve(6213,a,6184,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),B)),A) = B. [resolve(6213,a,6185,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),C). [resolve(6213,a,6186,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),A),A). [resolve(6213,a,6188,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B)),B). [resolve(6213,a,6189,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(6213,a,6190,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C))),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(6213,a,6191,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),A)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)). [resolve(6213,a,6192,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)). [resolve(6213,a,6193,a)].
% 123.80/123.77 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),A),B)),B)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),C). [resolve(6213,a,6194,a)].
% 123.80/123.77 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A))),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,A))),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C). [resolve(6213,a,6195,a)].
% 123.80/123.77 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),A),B)),B)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B)) = A. [resolve(6213,a,6196,a)].
% 123.80/123.77 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A))),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,A)) = B. [resolve(6213,a,6197,a)].
% 123.80/123.77 Derived: hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,A,B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),A),B)),B)) = A. [resolve(6213,a,6198,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),B),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),C),A) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),D),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),D). [resolve(6213,a,6200,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = B | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),B),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),C),A) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),D),B) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),D). [resolve(6213,a,6201,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A) != C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A) = B. [resolve(6213,a,6202,a)].
% 123.80/123.77 Derived: c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = A | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A) = C | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),A) != B. [resolve(6213,a,6203,a)].
% 125.94/125.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)) = B. [resolve(6213,a,6204,a)].
% 125.94/125.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),B)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),C),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)). [resolve(6213,a,6205,a)].
% 125.94/125.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)),A) = B. [resolve(6213,a,6206,a)].
% 125.94/125.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C)),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)),C). [resolve(6213,a,6207,a)].
% 125.94/125.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),C),D)) | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),C)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),B),A)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),D),C)). [resolve(6213,a,6208,a)].
% 125.94/125.86 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,A) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(6213,a,6209,a)].
% 125.94/125.86 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),A),B)) | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,B,A) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral). [resolve(6213,a,6210,a)].
% 125.94/125.86 6214 class_Divides_Oring__div(tc_Int_Oint) # label(arity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 125.94/125.86 6215 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Divides_Odiv__class_Omod(A,C,D)),D) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C),D) # label(fact_mod__diff__right__eq) # label(axiom). [clausify(1408)].
% 125.94/125.86 6216 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(A,B,C)),D),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D),C) # label(fact_mod__diff__left__eq) # label(axiom). [clausify(1409)].
% 125.94/125.86 6217 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(A,B,C)),c_Divides_Odiv__class_Omod(A,D,C)),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D),C) # label(fact_mod__diff__eq) # label(axiom). [clausify(1410)].
% 125.94/125.86 6218 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,E,C) != c_Divides_Odiv__class_Omod(A,F,C) | c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E),C) = c_Divides_Odiv__class_Omod(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),F),C) # label(fact_mod__diff__cong) # label(axiom). [clausify(1411)].
% 128.01/127.91 6219 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Divides_Odiv__class_Omod(A,B,C)),C) = c_Divides_Odiv__class_Omod(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C) # label(fact_mod__minus__eq) # label(axiom). [clausify(1526)].
% 128.01/127.91 6220 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(A,B,C) != c_Divides_Odiv__class_Omod(A,D,C) | c_Divides_Odiv__class_Omod(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C) = c_Divides_Odiv__class_Omod(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),D),C) # label(fact_mod__minus__cong) # label(axiom). [clausify(1527)].
% 128.01/127.91 6221 -class_Divides_Oring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),B) # label(fact_dvd__neg__div) # label(axiom). [clausify(4843)].
% 128.01/127.91 6222 -class_Divides_Oring__div(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),B)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(A),C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)) # label(fact_dvd__div__neg) # label(axiom). [clausify(4844)].
% 128.01/127.91 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)),C) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B),C). [resolve(6214,a,6215,a)].
% 128.01/127.91 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),C),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),C),B). [resolve(6214,a,6216,a)].
% 128.01/127.91 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),C),B). [resolve(6214,a,6217,a)].
% 128.01/127.91 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,D,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,E,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),D),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),E),B). [resolve(6214,a,6218,a)].
% 128.01/127.91 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B)),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A),B). [resolve(6214,a,6219,a)].
% 128.01/127.91 Derived: c_Divides_Odiv__class_Omod(tc_Int_Oint,A,B) != c_Divides_Odiv__class_Omod(tc_Int_Oint,C,B) | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A),B) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),C),B). [resolve(6214,a,6220,a)].
% 128.01/127.91 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B)),A). [resolve(6214,a,6221,a)].
% 128.01/127.91 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),A)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(6214,a,6222,a)].
% 128.01/127.91 6223 class_Rings_Oidom(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oidom) # label(axiom). [assumption].
% 128.01/127.91 6224 -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C) | B = C | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = C # label(fact_square__eq__iff) # label(axiom). [clausify(1518)].
% 128.01/127.91 6225 -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C) | B != C # label(fact_square__eq__iff) # label(axiom). [clausify(1518)].
% 128.01/127.91 6226 -class_Rings_Oidom(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) != C # label(fact_square__eq__iff) # label(axiom). [clausify(1518)].
% 128.01/127.91 6227 -class_Rings_Oidom(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | c_Groups_Ozero__class_Ozero(A) = B | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)) # label(fact_dvd__mult__cancel__left) # label(axiom). [clausify(4814)].
% 128.01/127.91 6228 -class_Rings_Oidom(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_dvd__mult__cancel__left) # label(axiom). [clausify(4814)].
% 128.01/127.91 6229 -class_Rings_Oidom(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)) # label(fact_dvd__mult__cancel__left) # label(axiom). [clausify(4814)].
% 128.01/127.91 6230 -class_Rings_Oidom(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | c_Groups_Ozero__class_Ozero(A) = C | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) # label(fact_dvd__mult__cancel__right) # label(axiom). [clausify(4815)].
% 128.01/127.91 6231 -class_Rings_Oidom(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | c_Groups_Ozero__class_Ozero(A) != C # label(fact_dvd__mult__cancel__right) # label(axiom). [clausify(4815)].
% 128.01/127.91 6232 -class_Rings_Oidom(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) # label(fact_dvd__mult__cancel__right) # label(axiom). [clausify(4815)].
% 128.01/127.91 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B) | A = B | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = B. [resolve(6223,a,6224,a)].
% 128.01/127.91 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B) | A != B. [resolve(6223,a,6225,a)].
% 128.01/127.91 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),B) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) != B. [resolve(6223,a,6226,a)].
% 128.01/127.91 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),C)). [resolve(6223,a,6227,a)].
% 128.01/127.91 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(6223,a,6228,a)].
% 128.01/127.91 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),C)). [resolve(6223,a,6229,a)].
% 128.01/127.91 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = B | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)). [resolve(6223,a,6230,a)].
% 129.98/129.94 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != B. [resolve(6223,a,6231,a)].
% 129.98/129.94 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)). [resolve(6223,a,6232,a)].
% 129.98/129.94 6233 class_Rings_Ocomm__ring__1(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__ring__1) # label(axiom). [assumption].
% 129.98/129.94 6234 -class_Rings_Ocomm__ring__1(A) | hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom). [clausify(1571)].
% 129.98/129.94 6235 -class_Rings_Ocomm__ring__1(A) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),B) # label(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom). [clausify(1575)].
% 129.98/129.94 6236 -class_Rings_Ocomm__ring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D))) # label(fact_dvd__diff) # label(axiom). [clausify(4840)].
% 129.98/129.94 6237 -class_Rings_Ocomm__ring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_dvd__minus__iff) # label(axiom). [clausify(4841)].
% 129.98/129.94 6238 -class_Rings_Ocomm__ring__1(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_dvd__minus__iff) # label(axiom). [clausify(4841)].
% 129.98/129.94 6239 -class_Rings_Ocomm__ring__1(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_minus__dvd__iff) # label(axiom). [clausify(4842)].
% 129.98/129.94 6240 -class_Rings_Ocomm__ring__1(A) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) # label(fact_minus__dvd__iff) # label(axiom). [clausify(4842)].
% 129.98/129.94 Derived: hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),A). [resolve(6233,a,6235,a)].
% 129.98/129.94 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B),C))). [resolve(6233,a,6236,a)].
% 129.98/129.94 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(6233,a,6237,a)].
% 129.98/129.94 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(6233,a,6238,a)].
% 129.98/129.94 Derived: -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(6233,a,6239,a)].
% 129.98/129.94 Derived: hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)). [resolve(6233,a,6240,a)].
% 132.06/131.96 6241 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) # label(arity_Int__Oint__Rings_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 132.06/131.96 6242 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | c_Groups_Oone__class_Oone(A) = B | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) = B # label(fact_square__eq__1__iff) # label(axiom). [clausify(1576)].
% 132.06/131.96 6243 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | c_Groups_Oone__class_Oone(A) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(1576)].
% 132.06/131.96 6244 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B) | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) != B # label(fact_square__eq__1__iff) # label(axiom). [clausify(1576)].
% 132.06/131.96 6245 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | c_Groups_Ozero__class_Ozero(A) = B # label(fact_zero__eq__power2) # label(axiom). [clausify(1889)].
% 132.06/131.96 6246 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | c_Groups_Ozero__class_Ozero(A) != B # label(fact_zero__eq__power2) # label(axiom). [clausify(1889)].
% 132.06/131.96 6247 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | c_Groups_Oone__class_Oone(A) = B | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) = B # label(fact_power2__eq__1__iff) # label(axiom). [clausify(1904)].
% 132.06/131.96 6248 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | c_Groups_Oone__class_Oone(A) != B # label(fact_power2__eq__1__iff) # label(axiom). [clausify(1904)].
% 132.06/131.96 6249 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) != B # label(fact_power2__eq__1__iff) # label(axiom). [clausify(1904)].
% 132.06/131.96 6250 -class_Rings_Oring__1__no__zero__divisors(A) | c_Groups_Ozero__class_Ozero(A) = B | c_Groups_Ozero__class_Ozero(A) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) # label(fact_field__power__not__zero) # label(axiom). [clausify(1932)].
% 132.06/131.96 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) | c_Groups_Oone__class_Oone(tc_Int_Oint) = A | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(6241,a,6242,a)].
% 132.06/131.96 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) | c_Groups_Oone__class_Oone(tc_Int_Oint) != A. [resolve(6241,a,6243,a)].
% 132.06/131.96 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),A) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) != A. [resolve(6241,a,6244,a)].
% 132.06/131.96 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(6241,a,6245,a)].
% 132.06/131.96 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != A. [resolve(6241,a,6246,a)].
% 138.18/138.10 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | c_Groups_Oone__class_Oone(tc_Int_Oint) = A | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(6241,a,6247,a)].
% 138.18/138.10 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | c_Groups_Oone__class_Oone(tc_Int_Oint) != A. [resolve(6241,a,6248,a)].
% 138.18/138.10 Derived: c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) != A. [resolve(6241,a,6249,a)].
% 138.18/138.10 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B). [resolve(6241,a,6250,a)].
% 138.18/138.10 6251 class_Groups_Oabs__if(tc_Int_Oint) # label(arity_Int__Oint__Groups_Oabs__if) # label(axiom). [assumption].
% 138.18/138.10 6252 -class_Groups_Oabs__if(A) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hAPP(c_Groups_Ouminus__class_Ouminus(A),B) = hAPP(c_Groups_Oabs__class_Oabs(A),B) # label(fact_abs__if) # label(axiom). [clausify(1638)].
% 138.18/138.10 6253 -class_Groups_Oabs__if(A) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),B),c_Groups_Ozero__class_Ozero(A))) | hAPP(c_Groups_Oabs__class_Oabs(A),B) = B # label(fact_abs__if) # label(axiom). [clausify(1638)].
% 138.18/138.10 Derived: hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),A) = A. [resolve(6251,a,6253,a)].
% 138.18/138.10 6254 class_Rings_Osemiring__0(tc_Int_Oint) # label(arity_Int__Oint__Rings_Osemiring__0) # label(axiom). [assumption].
% 138.18/138.10 6255 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_OSuc,B)) # label(fact_power__0__Suc) # label(axiom). [clausify(1950)].
% 138.18/138.10 6256 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != B | c_Groups_Oone__class_Oone(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_power__0__left) # label(axiom). [clausify(1965)].
% 138.18/138.10 6257 -class_Power_Opower(A) | -class_Rings_Osemiring__0(A) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = B | c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B) # label(fact_power__0__left) # label(axiom). [clausify(1965)].
% 138.18/138.10 6258 -class_Rings_Osemiring__0(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A),hAPP(hAPP(c_COMBB(A,A,C),hAPP(c_Groups_Otimes__class_Otimes(A),B)),D)),E) # label(fact_setsum__right__distrib) # label(axiom). [clausify(2282)].
% 138.18/138.10 6259 -class_Rings_Osemiring__0(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Otimes__class_Otimes(A)),C)),E)),D) # label(fact_setsum__left__distrib) # label(axiom). [clausify(2283)].
% 138.18/138.10 6260 -class_Rings_Osemiring__0(A) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),C),D)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,A),F),V6)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(E,tc_HOL_Obool),A),hAPP(hAPP(c_COMBB(tc_fun(E,A),tc_fun(tc_fun(E,tc_HOL_Obool),A),B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(E,A)),hAPP(hAPP(c_COMBC(B,tc_fun(E,A),tc_fun(E,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(E,A),tc_fun(E,A)),B),c_COMBB(A,A,E)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Otimes__class_Otimes(A)),C))),F))),V6)),D) # label(fact_setsum__product) # label(axiom). [clausify(2284)].
% 138.18/138.10 6261 -class_Rings_Osemiring__0(A) | -c_Fun_Oinj__on(tc_prod(B,C),A,hAPP(c_Product__Type_Oprod_Oprod__case(B,C,A),hAPP(hAPP(c_COMBC(B,tc_fun(C,A),tc_fun(C,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(C,A),tc_fun(C,A)),B),c_COMBB(A,A,C)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Otimes__class_Otimes(A)),D))),E)),hAPP(hAPP(c_Product__Type_OSigma(B,C),F),hAPP(c_COMBK(tc_fun(C,tc_HOL_Obool),B),V6))) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A),D),F)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A),E),V6)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,A),c_Fun_Oid(A)),hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(C,tc_HOL_Obool)),tc_fun(B,tc_HOL_Obool),A),hAPP(c_COMBB(tc_fun(C,tc_HOL_Obool),tc_HOL_Obool,B),c_HOL_OEx(C))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_fun(C,tc_HOL_Obool)),tc_fun(B,tc_fun(C,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool))),tc_fun(tc_fun(B,tc_fun(C,tc_HOL_Obool)),tc_fun(B,tc_fun(C,tc_HOL_Obool))),A),c_COMBS(B,tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(C,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(B,tc_fun(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool))),A),hAPP(c_COMBB(tc_fun(C,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool)),B),c_COMBS(C,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(C,tc_HOL_Obool)),tc_fun(B,tc_fun(C,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),A),hAPP(c_COMBB(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),B),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),C),c_fconj))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_fun(C,A)),tc_fun(B,tc_fun(C,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(C,A),tc_fun(C,tc_HOL_Obool)),tc_fun(tc_fun(B,tc_fun(C,A)),tc_fun(B,tc_fun(C,tc_HOL_Obool))),A),c_COMBB(tc_fun(C,A),tc_fun(C,tc_HOL_Obool),B)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(C,A),tc_fun(C,tc_HOL_Obool)),A),c_COMBB(A,tc_HOL_Obool,C)),c_fequal))),hAPP(hAPP(c_COMBC(B,tc_fun(C,A),tc_fun(C,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(C,A),tc_fun(C,A)),B),c_COMBB(A,A,C)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Otimes__class_Otimes(A)),D))),E)))))),hAPP(hAPP(c_COMBC(B,tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(C,tc_HOL_Obool),tc_fun(C,tc_HOL_Obool)),B),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,C)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),B),c_fconj),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),F)))),hAPP(hAPP(c_COMBC(C,tc_fun(C,tc_HOL_Obool),tc_HOL_Obool),c_member(C)),V6))))))) # label(fact_setsum__mult__setsum__if__inj) # label(axiom). [clausify(3237)].
% 138.18/138.10 6262 -class_Rings_Osemiring__0(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_Groups_Otimes__class_Otimes(A)),C)),D)),E)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),C),E))),D) # label(fact_listsum__mult__const) # label(axiom). [clausify(4065)].
% 138.18/138.10 6263 -class_Rings_Osemiring__0(A) | hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),hAPP(hAPP(c_COMBB(A,A,B),hAPP(c_Groups_Otimes__class_Otimes(A),C)),D)),E)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Omap(B,A),D),E))) # label(fact_listsum__const__mult) # label(axiom). [clausify(4066)].
% 138.18/138.10 6264 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),f581(C,B,A)),c_Groups_Ozero__class_Ozero(A)))) # label(fact_unity__coeff__ex) # label(axiom). [clausify(4808)].
% 138.18/138.10 6265 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))) | hBOOL(hAPP(B,f581(C,B,A))) # label(fact_unity__coeff__ex) # label(axiom). [clausify(4808)].
% 138.18/138.10 6266 -class_Rings_Odvd(A) | -class_Rings_Osemiring__0(A) | hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),f582(C,B,A)))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),c_Groups_Ozero__class_Ozero(A)))) | -hBOOL(hAPP(B,D)) # label(fact_unity__coeff__ex) # label(axiom). [clausify(4808)].
% 138.18/138.10 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_OSuc,A)). [resolve(6254,a,6255,b)].
% 138.18/138.10 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(6254,a,6256,b)].
% 138.18/138.10 Derived: -class_Power_Opower(tc_Int_Oint) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A). [resolve(6254,a,6257,b)].
% 138.18/138.10 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint),C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A)),C)),D). [resolve(6254,a,6258,a)].
% 138.18/138.10 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),C)),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),B)),D)),C). [resolve(6254,a,6259,a)].
% 138.18/138.10 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),B),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Int_Oint),E),F)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_HOL_Obool),tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(D,tc_Int_Oint),tc_fun(tc_fun(D,tc_HOL_Obool),tc_Int_Oint),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Int_Oint)),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_Int_Oint),tc_fun(D,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_fun(D,tc_Int_Oint),tc_fun(D,tc_Int_Oint)),A),c_COMBB(tc_Int_Oint,tc_Int_Oint,D)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),B))),E))),F)),C). [resolve(6254,a,6260,a)].
% 138.18/138.10 Derived: -c_Fun_Oinj__on(tc_prod(A,B),tc_Int_Oint,hAPP(c_Product__Type_Oprod_Oprod__case(A,B,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_Int_Oint),tc_fun(B,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_fun(B,tc_Int_Oint),tc_fun(B,tc_Int_Oint)),A),c_COMBB(tc_Int_Oint,tc_Int_Oint,B)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),C))),D)),hAPP(hAPP(c_Product__Type_OSigma(A,B),E),hAPP(c_COMBK(tc_fun(B,tc_HOL_Obool),A),F))) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Int_Oint),C),E)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Int_Oint),D),F)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,tc_Int_Oint),c_Fun_Oid(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(B))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),tc_fun(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),tc_Int_Oint),c_COMBS(A,tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(A,tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),tc_Int_Oint),hAPP(c_COMBB(tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),A),c_COMBS(B,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Int_Oint),hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),B),c_fconj))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(A,tc_fun(B,tc_Int_Oint)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(B,tc_Int_Oint),tc_fun(B,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_fun(B,tc_Int_Oint)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),tc_Int_Oint),c_COMBB(tc_fun(B,tc_Int_Oint),tc_fun(B,tc_HOL_Obool),A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_fun(B,tc_Int_Oint),tc_fun(B,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_HOL_Obool,B)),c_fequal))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_Int_Oint),tc_fun(B,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_fun(B,tc_Int_Oint),tc_fun(B,tc_Int_Oint)),A),c_COMBB(tc_Int_Oint,tc_Int_Oint,B)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),C))),D)))))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),A),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,B)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),E)))),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),F))))))). [resolve(6254,a,6261,a)].
% 138.18/138.10 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),hAPP(hAPP(c_COMBC(A,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),B)),C)),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),B),D))),C). [resolve(6254,a,6262,a)].
% 138.18/138.10 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B)),C)),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Int_Oint),hAPP(hAPP(c_List_Omap(A,tc_Int_Oint),C),D))). [resolve(6254,a,6263,a)].
% 138.18/138.10 Derived: -class_Rings_Odvd(tc_Int_Oint) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),f581(B,A,tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))). [resolve(6254,a,6264,b)].
% 138.18/138.10 Derived: -class_Rings_Odvd(tc_Int_Oint) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))) | hBOOL(hAPP(A,f581(B,A,tc_Int_Oint))). [resolve(6254,a,6265,b)].
% 138.18/138.10 Derived: -class_Rings_Odvd(tc_Int_Oint) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),f582(B,A,tc_Int_Oint)))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) | -hBOOL(hAPP(A,C)). [resolve(6254,a,6266,b)].
% 138.21/138.11 6267 class_Rings_Osemiring__0(tc_Nat_Onat) # label(arity_Nat__Onat__Rings_Osemiring__0) # label(axiom). [assumption].
% 138.21/138.11 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,A)). [resolve(6267,a,6255,b)].
% 138.21/138.11 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(6267,a,6256,b)].
% 138.21/138.11 Derived: -class_Power_Opower(tc_Nat_Onat) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A). [resolve(6267,a,6257,b)].
% 138.21/138.11 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat),C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A)),C)),D). [resolve(6267,a,6258,a)].
% 138.21/138.11 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),B),C)),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),B)),D)),C). [resolve(6267,a,6259,a)].
% 138.21/138.11 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),B),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Nat_Onat),E),F)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_HOL_Obool),tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(D,tc_Nat_Onat),tc_fun(tc_fun(D,tc_HOL_Obool),tc_Nat_Onat),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Nat_Onat)),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_Nat_Onat),tc_fun(D,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(D,tc_Nat_Onat),tc_fun(D,tc_Nat_Onat)),A),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,D)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),B))),E))),F)),C). [resolve(6267,a,6260,a)].
% 138.21/138.11 Derived: -c_Fun_Oinj__on(tc_prod(A,B),tc_Nat_Onat,hAPP(c_Product__Type_Oprod_Oprod__case(A,B,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_Nat_Onat),tc_fun(B,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(B,tc_Nat_Onat),tc_fun(B,tc_Nat_Onat)),A),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,B)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),C))),D)),hAPP(hAPP(c_Product__Type_OSigma(A,B),E),hAPP(c_COMBK(tc_fun(B,tc_HOL_Obool),A),F))) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat),C),E)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Nat_Onat),D),F)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),c_Fun_Oid(tc_Nat_Onat)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(B))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),tc_fun(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),tc_Nat_Onat),c_COMBS(A,tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(A,tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),A),c_COMBS(B,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),B),c_fconj))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(A,tc_fun(B,tc_Nat_Onat)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(B,tc_Nat_Onat),tc_fun(B,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_fun(B,tc_Nat_Onat)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),tc_Nat_Onat),c_COMBB(tc_fun(B,tc_Nat_Onat),tc_fun(B,tc_HOL_Obool),A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(B,tc_Nat_Onat),tc_fun(B,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,B)),c_fequal))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_Nat_Onat),tc_fun(B,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(B,tc_Nat_Onat),tc_fun(B,tc_Nat_Onat)),A),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,B)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),C))),D)))))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),A),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,B)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),E)))),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),F))))))). [resolve(6267,a,6261,a)].
% 138.21/138.13 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),hAPP(hAPP(c_COMBC(A,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),B)),C)),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),B),D))),C). [resolve(6267,a,6262,a)].
% 138.21/138.13 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B)),C)),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(A,tc_Nat_Onat),C),D))). [resolve(6267,a,6263,a)].
% 138.21/138.13 Derived: -class_Rings_Odvd(tc_Nat_Onat) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),f581(B,A,tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))). [resolve(6267,a,6264,b)].
% 138.21/138.13 Derived: -class_Rings_Odvd(tc_Nat_Onat) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))) | hBOOL(hAPP(A,f581(B,A,tc_Nat_Onat))). [resolve(6267,a,6265,b)].
% 138.21/138.13 Derived: -class_Rings_Odvd(tc_Nat_Onat) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),f582(B,A,tc_Nat_Onat)))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | -hBOOL(hAPP(A,C)). [resolve(6267,a,6266,b)].
% 138.21/138.13 6268 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) # label(axiom). [assumption].
% 138.21/138.13 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,A)). [resolve(6268,a,6255,b)].
% 138.21/138.13 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != A | c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A). [resolve(6268,a,6256,b)].
% 138.21/138.13 Derived: -class_Power_Opower(tc_Code__Numeral_Ocode__numeral) | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = A | c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),A). [resolve(6268,a,6257,b)].
% 138.21/138.13 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral),C),D)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,B),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),A)),C)),D). [resolve(6268,a,6258,a)].
% 138.21/138.13 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),B),C)),D) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),A),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),B)),D)),C). [resolve(6268,a,6259,a)].
% 138.21/138.13 Derived: hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),B),C)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Code__Numeral_Ocode__numeral),E),F)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(D,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(D,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),A),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(D,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_Code__Numeral_Ocode__numeral),tc_fun(D,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(D,tc_Code__Numeral_Ocode__numeral),tc_fun(D,tc_Code__Numeral_Ocode__numeral)),A),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,D)),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),A),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),B))),E))),F)),C). [resolve(6268,a,6260,a)].
% 138.21/138.13 Derived: -c_Fun_Oinj__on(tc_prod(A,B),tc_Code__Numeral_Ocode__numeral,hAPP(c_Product__Type_Oprod_Oprod__case(A,B,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(B,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(B,tc_Code__Numeral_Ocode__numeral)),A),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,B)),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),A),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),C))),D)),hAPP(hAPP(c_Product__Type_OSigma(A,B),E),hAPP(c_COMBK(tc_fun(B,tc_HOL_Obool),A),F))) | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Code__Numeral_Ocode__numeral),C),E)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,tc_Code__Numeral_Ocode__numeral),D),F)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),c_Fun_Oid(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Set_OCollect(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(B))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),tc_fun(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),c_COMBS(A,tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(A,tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),A),c_COMBS(B,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(B,tc_HOL_Obool)),tc_fun(A,tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),B),c_fconj))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(A,tc_fun(B,tc_Code__Numeral_Ocode__numeral)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(B,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_fun(B,tc_Code__Numeral_Ocode__numeral)),tc_fun(A,tc_fun(B,tc_HOL_Obool))),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(B,tc_HOL_Obool),A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(B,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,B)),c_fequal))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(B,tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_fun(B,tc_Code__Numeral_Ocode__numeral),tc_fun(B,tc_Code__Numeral_Ocode__numeral)),A),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,B)),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),A),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),C))),D)))))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(B,tc_HOL_Obool),tc_fun(B,tc_HOL_Obool)),A),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,B)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),E)))),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_HOL_Obool),tc_HOL_Obool),c_member(B)),F))))))). [resolve(6268,a,6261,a)].
% 138.21/138.13 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBC(A,tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),A),c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral)),B)),C)),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),B),D))),C). [resolve(6268,a,6262,a)].
% 138.21/138.13 Derived: hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,A),hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B)),C)),D)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(A,tc_Code__Numeral_Ocode__numeral),C),D))). [resolve(6268,a,6263,a)].
% 142.35/142.24 Derived: -class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),f581(B,A,tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))). [resolve(6268,a,6264,b)].
% 142.35/142.24 Derived: -class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) | -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),C))) | hBOOL(hAPP(A,f581(B,A,tc_Code__Numeral_Ocode__numeral))). [resolve(6268,a,6265,b)].
% 142.35/142.24 Derived: -class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) | hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),B),f582(B,A,tc_Code__Numeral_Ocode__numeral)))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Code__Numeral_Ocode__numeral),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),C),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))) | -hBOOL(hAPP(A,C)). [resolve(6268,a,6266,b)].
% 142.35/142.24 6269 class_Groups_Osgn__if(tc_Int_Oint) # label(arity_Int__Oint__Groups_Osgn__if) # label(axiom). [assumption].
% 142.35/142.24 6270 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) != B | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn__if) # label(axiom). [clausify(2025)].
% 142.35/142.24 6271 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) = B | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | c_Groups_Osgn__class_Osgn(A,B) = c_Groups_Oone__class_Oone(A) # label(fact_sgn__if) # label(axiom). [clausify(2025)].
% 142.35/142.24 6272 -class_Groups_Osgn__if(A) | c_Groups_Ozero__class_Ozero(A) = B | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(A),c_Groups_Ozero__class_Ozero(A)),B)) | c_Groups_Osgn__class_Osgn(A,B) = hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)) # label(fact_sgn__if) # label(axiom). [clausify(2025)].
% 142.35/142.24 6273 -class_Groups_Osgn__if(A) | c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A) # label(fact_sgn0) # label(axiom). [clausify(2029)].
% 142.35/142.24 Derived: c_Groups_Ozero__class_Ozero(tc_Int_Oint) = A | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)) | c_Groups_Osgn__class_Osgn(tc_Int_Oint,A) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)). [resolve(6269,a,6272,a)].
% 142.35/142.24 Derived: c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint). [resolve(6269,a,6273,a)].
% 142.35/142.24 6274 -class_Lattices_Obounded__lattice(A) | class_Lattices_Obounded__lattice__top(tc_fun(B,A)) # label(arity_fun__Lattices_Obounded__lattice__top) # label(axiom). [clausify(4857)].
% 142.35/142.24 6275 -class_Lattices_Obounded__lattice__top(A) | c_Orderings_Otop__class_Otop(A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),B),c_Orderings_Otop__class_Otop(A)) # label(fact_sup__top__right) # label(axiom). [clausify(2073)].
% 142.35/142.24 6276 -class_Lattices_Obounded__lattice__top(A) | c_Orderings_Otop__class_Otop(A) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(A),c_Orderings_Otop__class_Otop(A)),B) # label(fact_sup__top__left) # label(axiom). [clausify(2074)].
% 142.35/142.24 6277 -class_Lattices_Obounded__lattice__top(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),c_Orderings_Otop__class_Otop(A)),B) = B # label(fact_inf__top__left) # label(axiom). [clausify(2075)].
% 142.35/142.24 6278 -class_Lattices_Obounded__lattice__top(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),c_Orderings_Otop__class_Otop(A)) = B # label(fact_inf__top__right) # label(axiom). [clausify(2076)].
% 142.35/142.24 6279 -class_Lattices_Obounded__lattice__top(A) | c_Orderings_Otop__class_Otop(A) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) | c_Orderings_Otop__class_Otop(A) = B # label(fact_inf__eq__top__iff) # label(axiom). [clausify(2077)].
% 143.73/143.63 6280 -class_Lattices_Obounded__lattice__top(A) | c_Orderings_Otop__class_Otop(A) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) | c_Orderings_Otop__class_Otop(A) = C # label(fact_inf__eq__top__iff) # label(axiom). [clausify(2077)].
% 143.73/143.63 6281 -class_Lattices_Obounded__lattice__top(A) | c_Orderings_Otop__class_Otop(A) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(A),B),C) | c_Orderings_Otop__class_Otop(A) != B | c_Orderings_Otop__class_Otop(A) != C # label(fact_inf__eq__top__iff) # label(axiom). [clausify(2077)].
% 143.73/143.63 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),C),c_Orderings_Otop__class_Otop(tc_fun(B,A))). [resolve(6274,b,6275,a)].
% 143.73/143.63 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A)),c_Orderings_Otop__class_Otop(tc_fun(B,A))),C). [resolve(6274,b,6276,a)].
% 143.73/143.63 Derived: -class_Lattices_Obounded__lattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),c_Orderings_Otop__class_Otop(tc_fun(B,A))),C) = C. [resolve(6274,b,6277,a)].
% 143.73/143.63 Derived: -class_Lattices_Obounded__lattice(A) | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),c_Orderings_Otop__class_Otop(tc_fun(B,A))) = C. [resolve(6274,b,6278,a)].
% 143.73/143.63 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = C. [resolve(6274,b,6279,a)].
% 143.73/143.63 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = D. [resolve(6274,b,6280,a)].
% 143.73/143.63 Derived: -class_Lattices_Obounded__lattice(A) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A)),C),D) | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != C | c_Orderings_Otop__class_Otop(tc_fun(B,A)) != D. [resolve(6274,b,6281,a)].
% 143.73/143.63 6282 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) # label(arity_HOL__Obool__Lattices_Obounded__lattice__top) # label(axiom). [assumption].
% 143.73/143.63 Derived: c_Orderings_Otop__class_Otop(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),A),c_Orderings_Otop__class_Otop(tc_HOL_Obool)). [resolve(6282,a,6275,a)].
% 143.73/143.63 Derived: c_Orderings_Otop__class_Otop(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_HOL_Obool)),A). [resolve(6282,a,6276,a)].
% 143.73/143.63 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_HOL_Obool)),A) = A. [resolve(6282,a,6277,a)].
% 143.73/143.63 Derived: hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),c_Orderings_Otop__class_Otop(tc_HOL_Obool)) = A. [resolve(6282,a,6278,a)].
% 143.73/143.63 Derived: c_Orderings_Otop__class_Otop(tc_HOL_Obool) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) = A. [resolve(6282,a,6279,a)].
% 143.73/143.63 Derived: c_Orderings_Otop__class_Otop(tc_HOL_Obool) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) = B. [resolve(6282,a,6280,a)].
% 143.73/143.63 Derived: c_Orderings_Otop__class_Otop(tc_HOL_Obool) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),A),B) | c_Orderings_Otop__class_Otop(tc_HOL_Obool) != A | c_Orderings_Otop__class_Otop(tc_HOL_Obool) != B. [resolve(6282,a,6281,a)].
% 143.73/143.63 6283 c_Nitpick_Orefl_H(A,B) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f156(B,A)),f156(B,A))),B)) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(2155)].
% 143.73/143.63 6284 -c_Nitpick_Orefl_H(A,B) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),C),C)),B)) # label(fact_Nitpick_Orefl_H__def) # label(axiom). [clausify(2155)].
% 147.93/147.81 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f156(B,A)),f156(B,A))),B)) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),C),C)),B)). [resolve(6283,a,6284,a)].
% 147.93/147.81 6285 c_Relation_Oirrefl(A,B) | hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f171(B,A)),f171(B,A))),B)) # label(fact_irrefl__def) # label(axiom). [clausify(2428)].
% 147.93/147.81 6286 -c_Relation_Oirrefl(A,B) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),C),C)),B)) # label(fact_irrefl__def) # label(axiom). [clausify(2428)].
% 147.93/147.81 Derived: hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),f171(B,A)),f171(B,A))),B)) | -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),C),C)),B)). [resolve(6285,a,6286,a)].
% 147.93/147.81 6287 c_Relation_Oirrefl(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool)),B),c_Relation_OId(A))) # label(fact_irrefl__diff__Id) # label(axiom). [clausify(3548)].
% 147.93/147.81 Derived: -hBOOL(hAPP(hAPP(c_member(tc_prod(A,A)),hAPP(hAPP(c_Product__Type_OPair(A,A),B),B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(A,A),tc_HOL_Obool)),C),c_Relation_OId(A)))). [resolve(6287,a,6286,a)].
% 147.93/147.81 6288 -c_Typedef_Otype__definition(A,B,C,D,E) | -hBOOL(hAPP(hAPP(c_member(B),F),E)) | -hBOOL(hAPP(hAPP(c_member(B),V6),E)) | hAPP(D,V6) != hAPP(D,F) | V6 = F # label(fact_type__definition_OAbs__inject) # label(axiom). [clausify(2893)].
% 147.93/147.81 6289 c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) # label(fact_type__definition__Integ) # label(axiom). [assumption].
% 147.93/147.81 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),A),c_Int_OInteg)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B),c_Int_OInteg)) | hAPP(c_Int_OAbs__Integ,B) != hAPP(c_Int_OAbs__Integ,A) | B = A. [resolve(6288,a,6289,a)].
% 147.93/147.81 6290 -c_Typedef_Otype__definition(A,B,C,D,E) | -hBOOL(hAPP(hAPP(c_member(B),F),E)) | -hBOOL(hAPP(hAPP(c_member(B),V6),E)) | hAPP(D,V6) = hAPP(D,F) | V6 != F # label(fact_type__definition_OAbs__inject) # label(axiom). [clausify(2893)].
% 147.93/147.81 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),A),c_Int_OInteg)) | -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B),c_Int_OInteg)) | hAPP(c_Int_OAbs__Integ,B) = hAPP(c_Int_OAbs__Integ,A) | B != A. [resolve(6290,a,6289,a)].
% 147.93/147.81 6291 -c_Typedef_Otype__definition(A,B,C,D,E) | -hBOOL(hAPP(hAPP(c_member(B),F),E)) | hAPP(C,hAPP(D,F)) = F # label(fact_type__definition_OAbs__inverse) # label(axiom). [clausify(2894)].
% 147.93/147.81 Derived: -hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),A),c_Int_OInteg)) | hAPP(c_Int_ORep__Integ,hAPP(c_Int_OAbs__Integ,A)) = A. [resolve(6291,a,6289,a)].
% 147.93/147.81 6292 -c_Typedef_Otype__definition(A,B,C,D,E) | hBOOL(hAPP(hAPP(c_member(B),hAPP(C,F)),E)) # label(fact_type__definition_ORep) # label(axiom). [clausify(2895)].
% 147.93/147.81 Derived: hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,A)),c_Int_OInteg)). [resolve(6292,a,6289,a)].
% 147.93/147.81 6293 -c_Typedef_Otype__definition(A,B,C,D,E) | hAPP(D,hAPP(C,F)) = F # label(fact_type__definition_ORep__inverse) # label(axiom). [clausify(2896)].
% 147.93/147.81 Derived: hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,A)) = A. [resolve(6293,a,6289,a)].
% 147.93/147.81 6294 -c_Typedef_Otype__definition(A,B,C,D,E) | hAPP(C,F) != hAPP(C,V6) | F = V6 # label(fact_type__definition_ORep__inject) # label(axiom). [clausify(2897)].
% 147.93/147.81 Derived: hAPP(c_Int_ORep__Integ,A) != hAPP(c_Int_ORep__Integ,B) | A = B. [resolve(6294,a,6289,a)].
% 147.93/147.81 6295 -c_Typedef_Otype__definition(A,B,C,D,E) | hAPP(C,F) = hAPP(C,V6) | F != V6 # label(fact_type__definition_ORep__inject) # label(axiom). [clausify(2897)].
% 147.93/147.81 Derived: hAPP(c_Int_ORep__Integ,A) = hAPP(c_Int_ORep__Integ,B) | A != B. [resolve(6295,a,6289,a)].
% 147.93/147.81 6296 -c_Typedef_Otype__definition(A,B,C,D,E) | c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)) = hAPP(c_Set_Oimage(B,A,D),E) # label(fact_type__definition_OAbs__image) # label(axiom). [clausify(2942)].
% 150.55/150.49 Derived: c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Int_Oint,c_Int_OAbs__Integ),c_Int_OInteg). [resolve(6296,a,6289,a)].
% 150.55/150.49 6297 -c_Typedef_Otype__definition(A,B,C,D,E) | hAPP(c_Set_Oimage(A,B,C),c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))) = E # label(fact_type__definition_ORep__range) # label(axiom). [clausify(2943)].
% 150.55/150.49 Derived: hAPP(c_Set_Oimage(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))) = c_Int_OInteg. [resolve(6297,a,6289,a)].
% 150.55/150.49 6298 c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) # label(fact_type__definition__code__numeral) # label(axiom). [assumption].
% 150.55/150.49 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | hAPP(c_Code__Numeral_Oof__nat,B) != hAPP(c_Code__Numeral_Oof__nat,A) | B = A. [resolve(6298,a,6288,a)].
% 150.55/150.49 Derived: -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),A),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | -hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) | hAPP(c_Code__Numeral_Oof__nat,B) = hAPP(c_Code__Numeral_Oof__nat,A) | B != A. [resolve(6298,a,6290,a)].
% 150.55/150.49 Derived: hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,A)) = A. [resolve(6298,a,6293,a)].
% 150.55/150.49 Derived: hAPP(c_Code__Numeral_Onat__of,A) != hAPP(c_Code__Numeral_Onat__of,B) | A = B. [resolve(6298,a,6294,a)].
% 150.55/150.49 Derived: hAPP(c_Code__Numeral_Onat__of,A) = hAPP(c_Code__Numeral_Onat__of,B) | A != B. [resolve(6298,a,6295,a)].
% 150.55/150.49 Derived: c_Orderings_Otop__class_Otop(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,c_Code__Numeral_Oof__nat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))). [resolve(6298,a,6296,a)].
% 150.55/150.49 Derived: hAPP(c_Set_Oimage(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of),c_Orderings_Otop__class_Otop(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)). [resolve(6298,a,6297,a)].
% 150.55/150.49 6299 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) # label(axiom). [assumption].
% 150.55/150.49 6300 -class_Groups_Olinordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMin(A,hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(A)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),A),c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj)),hAPP(hAPP(c_COMBC(A,tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),A),c_COMBB(A,tc_HOL_Obool,A)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(A),C))))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),c_Big__Operators_Olinorder__class_OMin(A,B)) # label(fact_add__Min__commute) # label(axiom). [clausify(3225)].
% 150.55/150.49 6301 -class_Groups_Olinordered__ab__semigroup__add(A) | -hBOOL(hAPP(c_Finite__Set_Ofinite(A),B)) | c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = B | c_Big__Operators_Olinorder__class_OMax(A,hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool,A),c_HOL_OEx(A)),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_HOL_Obool)),A),c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(A,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),A),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A),c_fconj)),hAPP(hAPP(c_COMBC(A,tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_HOL_Obool),tc_fun(tc_fun(A,A),tc_fun(A,tc_HOL_Obool)),A),c_COMBB(A,tc_HOL_Obool,A)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(A),C))))),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_member(A)),B))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),c_Big__Operators_Olinorder__class_OMax(A,B)) # label(fact_add__Max__commute) # label(axiom). [clausify(3226)].
% 150.55/150.49 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Int_Oint)),A))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMin(tc_Int_Oint,A)). [resolve(6299,a,6300,a)].
% 150.55/150.49 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool,tc_Int_Oint),c_HOL_OEx(tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Int_Oint)),A))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Big__Operators_Olinorder__class_OMax(tc_Int_Oint,A)). [resolve(6299,a,6301,a)].
% 150.55/150.49 6302 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) # label(axiom). [assumption].
% 150.55/150.49 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),A))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMin(tc_Nat_Onat,A)). [resolve(6302,a,6300,a)].
% 150.55/150.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_Nat_Onat),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),A))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),c_Big__Operators_Olinorder__class_OMax(tc_Nat_Onat,A)). [resolve(6302,a,6301,a)].
% 150.55/150.51 6303 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) # label(axiom). [assumption].
% 150.55/150.51 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,hAPP(c_Set_OCollect(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBS(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_fconj)),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B))))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Code__Numeral_Ocode__numeral)),A))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMin(tc_Code__Numeral_Ocode__numeral,A)). [resolve(6303,a,6300,a)].
% 152.56/152.46 Derived: -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Code__Numeral_Ocode__numeral),A)) | c_Orderings_Obot__class_Obot(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)) = A | c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,hAPP(c_Set_OCollect(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral),c_HOL_OEx(tc_Code__Numeral_Ocode__numeral)),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBS(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_fconj)),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool)),tc_Code__Numeral_Ocode__numeral),c_COMBB(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool,tc_Code__Numeral_Ocode__numeral)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B))))),hAPP(hAPP(c_COMBC(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Code__Numeral_Ocode__numeral)),A))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),c_Big__Operators_Olinorder__class_OMax(tc_Code__Numeral_Ocode__numeral,A)). [resolve(6303,a,6301,a)].
% 152.56/152.46 6304 c_Predicate_Oreflp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) # label(fact_reflp__def) # label(axiom). [clausify(3236)].
% 152.56/152.46 6305 -c_Predicate_Oreflp(A,B) | c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) # label(fact_reflp__def) # label(axiom). [clausify(3236)].
% 152.56/152.46 6306 -c_Predicate_Oreflp(A,B) | hBOOL(hAPP(hAPP(B,C),C)) # label(fact_reflpE) # label(axiom). [clausify(3241)].
% 152.56/152.46 Derived: hBOOL(hAPP(hAPP(A,B),B)) | -c_Relation_Orefl__on(C,c_Orderings_Otop__class_Otop(tc_fun(C,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(C,C)),hAPP(c_Product__Type_Oprod_Oprod__case(C,C,tc_HOL_Obool),A))). [resolve(6306,a,6304,a)].
% 152.56/152.46 6307 -c_Equiv__Relations_Oequivp(A,B) | c_Predicate_Oreflp(A,B) # label(fact_equivpE) # label(axiom). [clausify(4648)].
% 152.56/152.46 Derived: -c_Equiv__Relations_Oequivp(A,B) | c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6307,b,6305,a)].
% 168.83/168.75 Derived: -c_Equiv__Relations_Oequivp(A,B) | hBOOL(hAPP(hAPP(B,C),C)). [resolve(6307,b,6306,a)].
% 168.83/168.75 6308 -c_Predicate_Oreflp(A,B) | -c_Predicate_Osymp(A,B) | -c_Predicate_Otransp(A,B) | c_Equiv__Relations_Oequivp(A,B) # label(fact_equivpI) # label(axiom). [clausify(4649)].
% 168.83/168.75 Derived: -c_Predicate_Osymp(A,B) | -c_Predicate_Otransp(A,B) | c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6308,a,6304,a)].
% 168.83/168.75 6309 -c_Equiv__Relations_Oequivp(A,B) | c_Predicate_Oreflp(A,B) # label(fact_equivp__reflp__symp__transp) # label(axiom). [clausify(4651)].
% 168.83/168.75 6310 c_Equiv__Relations_Oequivp(A,B) | -c_Predicate_Oreflp(A,B) | -c_Predicate_Osymp(A,B) | -c_Predicate_Otransp(A,B) # label(fact_equivp__reflp__symp__transp) # label(axiom). [clausify(4651)].
% 168.83/168.75 6311 class_Orderings_Owellorder(tc_Nat_Onat) # label(arity_Nat__Onat__Orderings_Owellorder) # label(axiom). [assumption].
% 168.83/168.75 6312 -class_Orderings_Owellorder(A) | c_Wellfounded_Owf(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),c_Orderings_Oord__class_Oless(A)))) # label(fact_wf) # label(axiom). [clausify(3329)].
% 168.83/168.75 Derived: c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))). [resolve(6311,a,6312,a)].
% 168.83/168.75 6313 c_Nitpick_Owf_H(A,B) | -c_Wellfounded_Oacyclic(A,B) | -hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(A,A)),B)) # label(fact_Nitpick_Owf_H__def) # label(axiom). [clausify(3372)].
% 168.83/168.75 6314 -c_Nitpick_Owf_H(A,B) | c_Wellfounded_Oacyclic(A,B) # label(fact_Nitpick_Owf_H__def) # label(axiom). [clausify(3372)].
% 168.83/168.75 6315 -c_Nitpick_Owf_H(A,B) | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(A,A)),B)) | c_Nitpick_Ounknown(tc_HOL_Obool) # label(fact_Nitpick_Owf_H__def) # label(axiom). [clausify(3372)].
% 168.83/168.75 6316 c_Nitpick_Owf_H(A,B) | -c_Wellfounded_Oacyclic(A,B) | -c_Nitpick_Ounknown(tc_HOL_Obool) # label(fact_Nitpick_Owf_H__def) # label(axiom). [clausify(3372)].
% 168.83/168.75 6317 c_Nitpick_Oless__frac(A,B,C) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(A),c_Nitpick_Oplus__frac(A,B,c_Nitpick_Ouminus__frac(A,C)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_Nitpick_Oless__frac__def) # label(axiom). [clausify(3644)].
% 168.83/168.75 6318 -c_Nitpick_Oless__frac(A,B,C) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(A),c_Nitpick_Oplus__frac(A,B,c_Nitpick_Ouminus__frac(A,C)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_Nitpick_Oless__frac__def) # label(axiom). [clausify(3644)].
% 168.83/168.75 6319 c_Nitpick_Oless__eq__frac(A,B,C) | -hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(A),c_Nitpick_Oplus__frac(A,B,c_Nitpick_Ouminus__frac(A,C)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_Nitpick_Oless__eq__frac__def) # label(axiom). [clausify(3645)].
% 168.83/168.75 6320 -c_Nitpick_Oless__eq__frac(A,B,C) | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(A),c_Nitpick_Oplus__frac(A,B,c_Nitpick_Ouminus__frac(A,C)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) # label(fact_Nitpick_Oless__eq__frac__def) # label(axiom). [clausify(3645)].
% 168.83/168.75 6321 c_List_Onat__list(A) | -c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),A)) # label(fact_nat__list__def) # label(axiom). [clausify(3763)].
% 168.83/168.75 6322 -c_List_Onat__list(A) | c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),A)) # label(fact_nat__list__def) # label(axiom). [clausify(3763)].
% 168.83/168.75 6323 -c_List_Onat__list(A) | c_List_Oembed__list(c_List_Oreturn__list(A)) = A # label(fact_transfer__nat__int__list__return__embed) # label(axiom). [clausify(4416)].
% 168.83/168.75 Derived: c_List_Oembed__list(c_List_Oreturn__list(A)) = A | -c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),A)). [resolve(6323,a,6321,a)].
% 173.10/172.98 6324 class_Groups_Osemigroup__add(tc_Int_Oint) # label(arity_Int__Oint__Groups_Osemigroup__add) # label(axiom). [assumption].
% 173.10/172.98 6325 -class_Groups_Osemigroup__add(A) | hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),C),D)) # label(fact_foldl__assoc) # label(axiom). [clausify(3996)].
% 173.10/172.98 Derived: hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_List_Ofoldl(tc_Int_Oint,tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(6324,a,6325,a)].
% 173.10/172.98 6326 class_Groups_Osemigroup__add(tc_Nat_Onat) # label(arity_Nat__Onat__Groups_Osemigroup__add) # label(axiom). [assumption].
% 173.10/172.98 Derived: hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C)). [resolve(6326,a,6325,a)].
% 173.10/172.98 6327 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) # label(axiom). [assumption].
% 173.10/172.98 Derived: hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),B)),C) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),A),hAPP(c_List_Ofoldl(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral,c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),B),C)). [resolve(6327,a,6325,a)].
% 173.10/172.98 6328 class_Nat_Osize(tc_Com_Ocom) # label(arity_Com__Ocom__Nat_Osize) # label(axiom). [assumption].
% 173.10/172.98 6329 -class_Nat_Osize(A) | c_FunDef_Ois__measure(A,c_Nat_Osize__class_Osize(A)) # label(fact_measure__size) # label(axiom). [clausify(4490)].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_Com_Ocom,c_Nat_Osize__class_Osize(tc_Com_Ocom)). [resolve(6328,a,6329,a)].
% 173.10/172.98 6330 class_Nat_Osize(tc_Nat_Onat) # label(arity_Nat__Onat__Nat_Osize) # label(axiom). [assumption].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat)). [resolve(6330,a,6329,a)].
% 173.10/172.98 6331 class_Nat_Osize(tc_HOL_Obool) # label(arity_HOL__Obool__Nat_Osize) # label(axiom). [assumption].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_HOL_Obool,c_Nat_Osize__class_Osize(tc_HOL_Obool)). [resolve(6331,a,6329,a)].
% 173.10/172.98 6332 class_Nat_Osize(tc_Com_Ostate) # label(arity_Com__Ostate__Nat_Osize) # label(axiom). [assumption].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_Com_Ostate,c_Nat_Osize__class_Osize(tc_Com_Ostate)). [resolve(6332,a,6329,a)].
% 173.10/172.98 6333 class_Nat_Osize(tc_List_Olist(A)) # label(arity_List__Olist__Nat_Osize) # label(axiom). [clausify(4874)].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_List_Olist(A),c_Nat_Osize__class_Osize(tc_List_Olist(A))). [resolve(6333,a,6329,a)].
% 173.10/172.98 6334 class_Nat_Osize(tc_sum(A,B)) # label(arity_sum__Nat_Osize) # label(axiom). [clausify(4877)].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_sum(A,B),c_Nat_Osize__class_Osize(tc_sum(A,B))). [resolve(6334,a,6329,a)].
% 173.10/172.98 6335 class_Nat_Osize(tc_Option_Ooption(A)) # label(arity_Option__Ooption__Nat_Osize) # label(axiom). [clausify(4880)].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_Option_Ooption(A),c_Nat_Osize__class_Osize(tc_Option_Ooption(A))). [resolve(6335,a,6329,a)].
% 173.10/172.98 6336 class_Nat_Osize(tc_Nitpick_Opair__box(A,B)) # label(arity_Nitpick__Opair____box__Nat_Osize) # label(axiom). [clausify(4881)].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_Nitpick_Opair__box(A,B),c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(A,B))). [resolve(6336,a,6329,a)].
% 173.10/172.98 6337 class_Nat_Osize(tc_prod(A,B)) # label(arity_prod__Nat_Osize) # label(axiom). [clausify(4885)].
% 173.10/172.98 Derived: c_FunDef_Ois__measure(tc_prod(A,B),c_Nat_Osize__class_Osize(tc_prod(A,B))). [resolve(6337,a,6329,a)].
% 175.02/174.98 6338 class_Nat_Osize(tc_Product__Type_Ounit) # label(arity_Product____Type__Ounit__Nat_Osize) # label(axiom). [assumption].
% 175.02/174.98 Derived: c_FunDef_Ois__measure(tc_Product__Type_Ounit,c_Nat_Osize__class_Osize(tc_Product__Type_Ounit)). [resolve(6338,a,6329,a)].
% 175.02/174.98 6339 class_Nat_Osize(tc_Code__Evaluation_Oterm) # label(arity_Code____Evaluation__Oterm__Nat_Osize) # label(axiom). [assumption].
% 175.02/174.98 Derived: c_FunDef_Ois__measure(tc_Code__Evaluation_Oterm,c_Nat_Osize__class_Osize(tc_Code__Evaluation_Oterm)). [resolve(6339,a,6329,a)].
% 175.02/174.98 6340 class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(A)) # label(arity_Hoare____Mirabelle__Otriple__Nat_Osize) # label(axiom). [clausify(4886)].
% 175.02/174.98 Derived: c_FunDef_Ois__measure(tc_Hoare__Mirabelle_Otriple(A),c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(A))). [resolve(6340,a,6329,a)].
% 175.02/174.98 6341 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) # label(arity_Code____Numeral__Ocode____numeral__Nat_Osize) # label(axiom). [assumption].
% 175.02/174.98 Derived: c_FunDef_Ois__measure(tc_Code__Numeral_Ocode__numeral,c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral)). [resolve(6341,a,6329,a)].
% 175.02/174.98 6342 class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(A)) # label(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) # label(axiom). [clausify(4887)].
% 175.02/174.98 Derived: c_FunDef_Ois__measure(tc_Lazy__Sequence_Olazy__sequence(A),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(A))). [resolve(6342,a,6329,a)].
% 175.02/174.98 6343 c_Predicate_Otransp(A,B) | -c_Relation_Otrans(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) # label(fact_transp__def) # label(axiom). [clausify(4646)].
% 175.02/174.98 6344 -c_Predicate_Otransp(A,B) | c_Relation_Otrans(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) # label(fact_transp__def) # label(axiom). [clausify(4646)].
% 175.02/174.98 6345 -c_Predicate_Otransp(A,B) | -hBOOL(hAPP(hAPP(B,C),D)) | -hBOOL(hAPP(hAPP(B,D),E)) | hBOOL(hAPP(hAPP(B,C),E)) # label(fact_transpE) # label(axiom). [clausify(4647)].
% 175.02/174.98 Derived: -hBOOL(hAPP(hAPP(A,B),C)) | -hBOOL(hAPP(hAPP(A,C),D)) | hBOOL(hAPP(hAPP(A,B),D)) | -c_Relation_Otrans(E,hAPP(c_Set_OCollect(tc_prod(E,E)),hAPP(c_Product__Type_Oprod_Oprod__case(E,E,tc_HOL_Obool),A))). [resolve(6345,a,6343,a)].
% 175.02/174.98 6346 -c_Equiv__Relations_Oequivp(A,B) | c_Predicate_Otransp(A,B) # label(fact_equivpE) # label(axiom). [clausify(4648)].
% 175.02/174.98 Derived: -c_Equiv__Relations_Oequivp(A,B) | c_Relation_Otrans(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6346,b,6344,a)].
% 175.02/174.98 Derived: -c_Equiv__Relations_Oequivp(A,B) | -hBOOL(hAPP(hAPP(B,C),D)) | -hBOOL(hAPP(hAPP(B,D),E)) | hBOOL(hAPP(hAPP(B,C),E)). [resolve(6346,b,6345,a)].
% 175.02/174.98 6347 -c_Equiv__Relations_Oequivp(A,B) | c_Predicate_Otransp(A,B) # label(fact_equivp__reflp__symp__transp) # label(axiom). [clausify(4651)].
% 175.02/174.98 6348 -hBOOL(hAPP(hAPP(A,B),B)) | -c_Predicate_Osymp(C,A) | -c_Predicate_Otransp(C,A) | c_Equiv__Relations_Opart__equivp(C,A) # label(fact_part__equivpI) # label(axiom). [clausify(4683)].
% 175.02/174.98 Derived: -hBOOL(hAPP(hAPP(A,B),B)) | -c_Predicate_Osymp(C,A) | c_Equiv__Relations_Opart__equivp(C,A) | -c_Relation_Otrans(C,hAPP(c_Set_OCollect(tc_prod(C,C)),hAPP(c_Product__Type_Oprod_Oprod__case(C,C,tc_HOL_Obool),A))). [resolve(6348,c,6343,a)].
% 175.02/174.98 6349 -c_Equiv__Relations_Opart__equivp(A,B) | c_Predicate_Otransp(A,B) # label(fact_part__equivp__refl__symp__transp) # label(axiom). [clausify(4684)].
% 175.02/174.98 Derived: -c_Equiv__Relations_Opart__equivp(A,B) | c_Relation_Otrans(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6349,b,6344,a)].
% 175.02/174.98 6350 c_Equiv__Relations_Opart__equivp(A,B) | -hBOOL(hAPP(hAPP(B,C),C)) | -c_Predicate_Osymp(A,B) | -c_Predicate_Otransp(A,B) # label(fact_part__equivp__refl__symp__transp) # label(axiom). [clausify(4684)].
% 175.02/174.98 6351 -c_Equiv__Relations_Opart__equivp(A,B) | c_Predicate_Otransp(A,B) # label(fact_part__equivpE) # label(axiom). [clausify(4689)].
% 175.02/174.98 Derived: -c_Equiv__Relations_Opart__equivp(A,B) | -hBOOL(hAPP(hAPP(B,C),D)) | -hBOOL(hAPP(hAPP(B,D),E)) | hBOOL(hAPP(hAPP(B,C),E)). [resolve(6351,b,6345,a)].
% 178.10/177.99 6352 -c_Predicate_Osymp(A,B) | -c_Predicate_Otransp(A,B) | c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6308,a,6304,a)].
% 178.10/177.99 Derived: -c_Predicate_Osymp(A,B) | c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Relation_Otrans(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6352,b,6343,a)].
% 178.10/177.99 Derived: -c_Predicate_Osymp(A,B) | c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Equiv__Relations_Opart__equivp(A,B). [resolve(6352,b,6349,b)].
% 178.10/177.99 6353 -c_Predicate_Osymp(A,B) | -hBOOL(hAPP(hAPP(B,C),D)) | hBOOL(hAPP(hAPP(B,D),C)) # label(fact_sympE) # label(axiom). [clausify(4650)].
% 178.10/177.99 6354 -c_Equiv__Relations_Oequivp(A,B) | c_Predicate_Osymp(A,B) # label(fact_equivpE) # label(axiom). [clausify(4648)].
% 178.10/177.99 Derived: -hBOOL(hAPP(hAPP(A,B),C)) | hBOOL(hAPP(hAPP(A,C),B)) | -c_Equiv__Relations_Oequivp(D,A). [resolve(6353,a,6354,b)].
% 178.10/177.99 6355 -c_Equiv__Relations_Oequivp(A,B) | c_Predicate_Osymp(A,B) # label(fact_equivp__reflp__symp__transp) # label(axiom). [clausify(4651)].
% 178.10/177.99 6356 -c_Predicate_Osymp(A,B) | c_Relation_Osym(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) # label(fact_symp__def) # label(axiom). [clausify(4682)].
% 178.10/177.99 Derived: c_Relation_Osym(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Equiv__Relations_Oequivp(A,B). [resolve(6356,a,6354,b)].
% 178.10/177.99 6357 c_Predicate_Osymp(A,B) | -c_Relation_Osym(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) # label(fact_symp__def) # label(axiom). [clausify(4682)].
% 178.10/177.99 Derived: -c_Relation_Osym(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -hBOOL(hAPP(hAPP(B,C),D)) | hBOOL(hAPP(hAPP(B,D),C)). [resolve(6357,a,6353,a)].
% 178.10/177.99 6358 -c_Equiv__Relations_Opart__equivp(A,B) | c_Predicate_Osymp(A,B) # label(fact_part__equivp__refl__symp__transp) # label(axiom). [clausify(4684)].
% 178.10/177.99 Derived: -c_Equiv__Relations_Opart__equivp(A,B) | c_Relation_Osym(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6358,b,6356,a)].
% 178.10/177.99 6359 -c_Equiv__Relations_Opart__equivp(A,B) | c_Predicate_Osymp(A,B) # label(fact_part__equivpE) # label(axiom). [clausify(4689)].
% 178.10/177.99 Derived: -c_Equiv__Relations_Opart__equivp(A,B) | -hBOOL(hAPP(hAPP(B,C),D)) | hBOOL(hAPP(hAPP(B,D),C)). [resolve(6359,b,6353,a)].
% 178.10/177.99 6360 -hBOOL(hAPP(hAPP(A,B),B)) | -c_Predicate_Osymp(C,A) | c_Equiv__Relations_Opart__equivp(C,A) | -c_Relation_Otrans(C,hAPP(c_Set_OCollect(tc_prod(C,C)),hAPP(c_Product__Type_Oprod_Oprod__case(C,C,tc_HOL_Obool),A))). [resolve(6348,c,6343,a)].
% 178.10/177.99 Derived: -hBOOL(hAPP(hAPP(A,B),B)) | c_Equiv__Relations_Opart__equivp(C,A) | -c_Relation_Otrans(C,hAPP(c_Set_OCollect(tc_prod(C,C)),hAPP(c_Product__Type_Oprod_Oprod__case(C,C,tc_HOL_Obool),A))) | -c_Equiv__Relations_Oequivp(C,A). [resolve(6360,b,6354,b)].
% 178.10/177.99 Derived: -hBOOL(hAPP(hAPP(A,B),B)) | c_Equiv__Relations_Opart__equivp(C,A) | -c_Relation_Otrans(C,hAPP(c_Set_OCollect(tc_prod(C,C)),hAPP(c_Product__Type_Oprod_Oprod__case(C,C,tc_HOL_Obool),A))) | -c_Relation_Osym(C,hAPP(c_Set_OCollect(tc_prod(C,C)),hAPP(c_Product__Type_Oprod_Oprod__case(C,C,tc_HOL_Obool),A))). [resolve(6360,b,6357,a)].
% 178.10/177.99 6361 -c_Predicate_Osymp(A,B) | c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Relation_Otrans(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6352,b,6343,a)].
% 179.21/179.10 Derived: c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Relation_Otrans(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Relation_Osym(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6361,a,6357,a)].
% 179.21/179.10 Derived: c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Relation_Otrans(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Equiv__Relations_Opart__equivp(A,B). [resolve(6361,a,6358,b)].
% 179.21/179.10 6362 -c_Predicate_Osymp(A,B) | c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Equiv__Relations_Opart__equivp(A,B). [resolve(6352,b,6349,b)].
% 179.21/179.10 Derived: c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Equiv__Relations_Opart__equivp(A,B) | -c_Relation_Osym(A,hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))). [resolve(6362,a,6357,a)].
% 179.21/179.10 Derived: c_Equiv__Relations_Oequivp(A,B) | -c_Relation_Orefl__on(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(A,A)),hAPP(c_Product__Type_Oprod_Oprod__case(A,A,tc_HOL_Obool),B))) | -c_Equiv__Relations_Opart__equivp(A,B) | -c_Equiv__Relations_Opart__equivp(A,B). [resolve(6362,a,6358,b)].
% 179.21/179.10 6363 class_Rings_Ocomm__ring(tc_Int_Oint) # label(arity_Int__Oint__Rings_Ocomm__ring) # label(axiom). [assumption].
% 179.21/179.10 6364 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))) # label(fact_inf__period_I4_J) # label(axiom). [clausify(4804)].
% 179.21/179.10 6365 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))) # label(fact_inf__period_I4_J) # label(axiom). [clausify(4804)].
% 179.21/179.10 6366 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))) # label(fact_inf__period_I3_J) # label(axiom). [clausify(4805)].
% 179.21/179.10 6367 -class_Rings_Ocomm__ring(A) | -class_Rings_Odvd(A) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))) # label(fact_inf__period_I3_J) # label(axiom). [clausify(4805)].
% 179.21/179.10 Derived: -class_Rings_Odvd(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),D))) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),B))),D))). [resolve(6363,a,6364,a)].
% 192.14/192.08 Derived: -class_Rings_Odvd(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),B)) | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),B))),D))). [resolve(6363,a,6365,a)].
% 192.14/192.08
% 192.14/192.08 ============================== end predicate elimination =============
% 192.14/192.08
% 192.14/192.08 Auto_denials: (non-Horn, no changes).
% 192.14/192.08
% 192.14/192.08 Term ordering decisions:
% 192.14/192.08 Function symbol KB weights: tc_Int_Oint=1. tc_Nat_Onat=1. tc_HOL_Obool=1. tc_Code__Numeral_Ocode__numeral=1. c_Nat_OSuc=1. c_Int_OPls=1. c_Int_Onat=1. c_fconj=1. c_fequal=1. c_Int_OMin=1. c_Nat__Numeral_Oneg=1. c_fNot=1. c_Code__Numeral_Oof__nat=1. c_Code__Numeral_Onat__of=1. tc_Com_Ostate=1. c_Int_OAbs__Integ=1. c_Int_Ointrel=1. c_fimplies=1. tc_Com_Ocom=1. c_Int_ORep__Integ=1. c_fdisj=1. c_Int_OInteg=1. tc_Product__Type_Ounit=1. c_Divides_OnegateSnd=1. c_Wellfounded_Oless__than=1. c_FunDef_Opair__less=1. c_Nitpick_Onorm__frac__rel=1. tc_Code__Evaluation_Oterm=1. c_Divides_OnegDivAlg__rel=1. c_Divides_OposDivAlg__rel=1. c_FunDef_Opair__leq=1. c_Wellfounded_Opred__nat=1. c_fFalse=1. c_Code__Numeral_Oint__of=1. c_Lazy__Sequence_Osmall__lazy_H__rel=1. c_List_Oupto__rel=1. c_Nitpick_Onat__gcd__rel=1. c_FunDef_Omax__strict=1. c_FunDef_Omax__weak=1. c_FunDef_Omin__strict=1. c_FunDef_Omin__weak=1. c_Com_Ocom_OSKIP=1. c_Nitpick_Oint__gcd=1. c_fTrue=1. c_Code__Numeral_Osubtract__code__numeral=1. c_Nitpick_OFrac=1. t_a=1. v_G=1. v_c=1. hAPP=1. tc_fun=1. tc_prod=1. c_Product__Type_OPair=1. c_Big__Operators_Ocomm__monoid__add__class_Osetsum=1. c_List_Omap=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_Big__Operators_Ocomm__monoid__mult__class_Osetprod=1. c_Transitive__Closure_Ortrancl=1. c_Complete__Lattice_OSup__class_OSup=1. c_COMBK=1. c_Product__Type_OSigma=1. c_List_Ofilter=1. c_Big__Operators_Olinorder__class_OMax=1. c_Big__Operators_Olinorder__class_OMin=1. c_Product__Type_Osnd=1. c_Product__Type_Ofst=1. c_Finite__Set_Ofold1=1. c_List_Ozip=1. c_Relation_Oconverse=1. c_List_Oupt=1. c_Transitive__Closure_Otrancl=1. c_Nat_Ocompow=1. c_Wellfounded_Oaccp=1. c_Complete__Lattice_OInf__class_OInf=1. c_List_Olist__update=1. c_List_Olistrel1=1. c_List_Oconcat=1. c_List_Olistrel=1. c_Big__Operators_Olattice__class_OInf__fin=1. c_Big__Operators_Olattice__class_OSup__fin=1. c_List_Olists=1. c_List_Oremdups=1. c_Relation_ODomain=1. c_HOL_OLet=1. c_List_Obutlast=1. c_List_Olistsp=1. c_List_Olexord=1. c_Relation_ORange=1. c_List_Olast=1. c_List_Otranspose=1. c_Wellfounded_Oacc=1. c_Divides_OposDivAlg=1. c_Divides_Odivmod__int__rel=1. c_Divides_Odivmod__nat__rel=1. c_Divides_OnegDivAlg=1. c_List_Olinorder__class_Osorted__list__of__set=1. c_List_Orotate=1. c_Groups_Osgn__class_Osgn=1. c_List_Oupto=1. tc_sum=1. c_Relation_OId__on=1. c_Hilbert__Choice_OEps=1. c_Wellfounded_Omax__ext=1. c_List_OremoveAll=1. c_HOL_OThe=1. c_List_Olex=1. c_Divides_Odivmod__int=1. c_Relation_Oinv__image=1. c_Divides_Odivmod__nat=1. c_Com_Ocom_OWhile=1. c_List_Omeasures=1. c_Nitpick_Onorm__frac=1. c_Com_Ocom_OSemi=1. c_Quotient_ORespects=1. c_Nitpick_Onat__gcd=1. c_Random_Opick=1. c_Divides_Opdivmod=1. c_Lazy__Sequence_Osmall__lazy_H=1. c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy=1. c_List_Olexn=1. c_Nat__Transfer_Otsub=1. c_Predicate_OPowp=1. c_Random_Oselect__weight=1. c_Enum_Osublists=1. c_Wellfounded_Omin__ext=1. c_Code__Numeral_Onat__of__aux=1. c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size=1. c_Nitpick_OAbs__Frac=1. c_Lazy__Sequence_Oflat=1. c_Orderings_Oord_Omax=1. c_Orderings_Oord_Omin=1. c_Random_Olog=1. c_List_Olenlex=1. c_List_Olistset=1. c_Quickcheck_Obeyond=1. c_Random_Oselect=1. c_Set_Othe__elem=1. tc_Nitpick_Opair__box=1. c_FunDef_Orp__inv__image=1. c_New__DSequence_Oneg__single=1. c_New__DSequence_Opos__single=1. c_Nitpick_Ocard_H=1. c_Nitpick_Oint__lcm=1. c_Nitpick_Onat__lcm=1. c_Random_Oinc__shift=1. c_SMT_Oz3div=1. c_SMT_Oz3mod=1. c_Code__Numeral_Odiv__mod__code__numeral=1. c_Enum_Oenum__the=1. c_Int_Onat__aux=1. c_Lazy__Sequence_Ohb__single=1. c_Nitpick_Oinverse__frac=1. c_Nitpick_Onumber__of__frac=1. c_Nitpick_Ouminus__frac=1. f1=1. f16=1. f17=1. f18=1. f19=1. f27=1. f28=1. f38=1. f39=1. f40=1. f41=1. f42=1. f53=1. f54=1. f61=1. f67=1. f75=1. f92=1. f99=1. f113=1. f114=1. f125=1. f130=1. f137=1. f156=1. f171=1. f178=1. f180=1. f184=1. f185=1. f201=1. f202=1. f203=1. f204=1. f232=1. f233=1. f234=1. f235=1. f243=1. f244=1. f250=1. f251=1. f252=1. f253=1. f306=1. f308=1. f309=1. f313=1. f314=1. f319=1. f321=1. f327=1. f334=1. f336=1. f347=1. f348=1. f359=1. f366=1. f382=1. f384=1. f385=1. f387=1. f394=1. f415=1. f416=1. f428=1. f440=1. f441=1. f446=1. f452=1. f453=1. f457=1. f458=1. f462=1. f463=1. f465=1. f466=1. f467=1. f469=1. f470=1. f473=1. f482=1. f483=1. f515=1. f519=1. f520=1. f521=1. f523=1. f524=1. f530=1. f531=1. f532=1. f533=1. f534=1. f535=1. f536=1. f537=1. f538=1. f539=1. f545=1. f547=1. f550=1. f552=1. f553=1. c_Orderings_Oord__class_Oless__eq=1. c_Groups_Ozero__class_Ozero=1. c_member=1. c_Orderings_Oord__class_Oless=1. tc_List_Olist=1. c_Groups_Otimes__class_Otimes=1. c_Groups_Oplus__class_Oplus=1. c_Finite__Set_Ofinite=1. c_Orderings_Obot__class_Obot=1. c_Int_Onumber__class_Onumber__of=1. c_Groups_Ominus__class_Ominus=1. c_Set_Oinsert=1. c_Groups_Oone__class_Oone=1. c_Lattices_Osemilattice__sup__class_Osup=1. c_Lattices_Osemilattice__inf__class_Oinf=1. c_Nat_Osize__class_Osize=1. c_Orderings_Oord__class_Omin=1. c_List_Olist_OCons=1. c_Orderings_Oord__class_Omax=1. c_List_Oset=1. c_Orderings_Otop__class_Otop=1. c_List_Olist_ONil=1. c_Groups_Ouminus__class_Ouminus=1. c_Divides_Odiv__class_Odiv=1. c_Power_Opower__class_Opower=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Int_OBit1=1. c_List_Oappend=1. c_Rings_Odvd__class_Odvd=1. c_Int_OBit0=1. c_Set_OCollect=1. c_Finite__Set_Ocard=1. c_List_Onth=1. c_List_Odistinct=1. c_Groups_Oabs__class_Oabs=1. c_List_Omonoid__add__class_Olistsum=1. c_List_Otake=1. c_COMBI=1. tc_Hoare__Mirabelle_Otriple=1. c_List_Orev=1. c_SetInterval_Oord__class_OlessThan=1. tc_Lazy__Sequence_Olazy__sequence=1. c_List_Odrop=1. c_SetInterval_Oord__class_OatMost=1. c_HOL_OEx=1. c_Int_Oring__1__class_Oof__int=1. c_SetInterval_Oord__class_OgreaterThan=1. c_SetInterval_Oord__class_OatLeast=1. c_If=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Equiv__Relations_Oquotient=1. c_Fun_Oid=1. tc_Option_Ooption=1. c_Int_Opred=1. c_Set_OPow=1. c_Relation_OId=1. c_Nat_Osemiring__1__class_ONats=1. c_List_Otl=1. c_List_Ohd=1. c_Int_Oring__1__class_OInts=1. c_Relation_OField=1. c_List_Orotate1=1. c_Int_Osucc=1. c_Divides_Oadjust=1. c_Enum_Oenum__class_Oenum__all=1. c_Enum_Oenum__class_Oenum__ex=1. c_Com_Ocom_Ocom__size=1. c_Code__Numeral_OSuc__code__numeral=1. c_List_Omember=1. c_Nitpick_Odenom=1. c_Lazy__Sequence_Olazy__sequence_OEmpty=1. c_Nitpick_Onum=1. c_Lazy__Sequence_Osingle=1. c_Wellfounded_Ofinite__psubset=1. c_HOL_OAll=1. c_Lazy__Sequence_Oempty=1. c_Lazy__Sequence_Oyield=1. c_List_Oembed__list=1. c_List_Oreturn__list=1. c_Nitpick_Ofrac=1. c_Wellfounded_Omeasure=1. c_Code__Numeral_Ocode__numeral_Ocode__numeral__size=1. c_List_Otranspose__rel=1. c_Nat_Onat_Onat__size=1. c_Random_Orange=1. c_DSequence_Oempty=1. c_DSequence_Osingle=1. c_HOL_Obool_Obool__size=1. c_Int_Oint__ge__less__than=1. c_Int_Oint__ge__less__than2=1. c_New__DSequence_Opos__empty=1. c_New__DSequence_Opos__not__seq=1. c_New__Random__Sequence_Oneg__single=1. c_New__Random__Sequence_Opos__single=1. c_Nitpick_ORep__Frac=1. c_Random__Sequence_Osingle=1. c_DSequence_Ounion=1. c_Lazy__Sequence_Ohb__not__seq=1. c_Lazy__Sequence_Ohit__bound=1. c_Lazy__Sequence_Oyieldn=1. c_Nat_Ofunpow=1. c_Nitpick_Oone__frac=1. c_Nitpick_Ozero__frac=1. c_Rings_Oinverse__class_Odivide=1. c_Set_OBall=1. c_Set_OBex=1. f76=1. f109=1. f110=1. f111=1. f112=1. f118=1. f133=1. f134=1. f135=1. f136=1. f149=1. f175=1. f176=1. f177=1. f179=1. f268=1. f304=1. f333=1. f411=1. f546=1. f548=1. c_COMBB=1. c_COMBC=1. c_Divides_Odiv__class_Omod=1. c_Set_Oimage=1. c_COMBS=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_Product__Type_Oprod_Oprod__case=1. c_Big__Operators_Olattice_OInf__fin=1. c_Big__Operators_Olattice_OSup__fin=1. c_List_Olinorder__class_Oinsort__key=1. c_Relation_OImage=1. c_Finite__Set_Ofold=1. c_Finite__Set_Ofold__image=1. c_Relation_Orel__comp=1. c_Set_Ovimage=1. c_List_Oreplicate=1. c_SetInterval_Oord__class_OgreaterThanAtMost=1. c_SetInterval_Oord__class_OgreaterThanLessThan=1. c_List_OtakeWhile=1. c_List_Oremove1=1. c_List_OdropWhile=1. c_Predicate_Oconversep=1. c_List_Osublist=1. c_Lazy__Sequence_Olazy__sequence_OInsert=1. c_List_Olist_Olist__size=1. c_Com_Ocom_OCond=1. c_Com_Ocom_OLocal=1. c_Enum_On__lists=1. c_Finite__Set_Ofold1Set=1. c_Hoare__Mirabelle_Opeek__and=1. c_List_Oinsert=1. c_Lazy__Sequence_Oappend=1. c_List_Opartition=1. c_Nat_Onat_Onat__rec=1. c_Lazy__Sequence_Obind=1. c_List_Osplice=1. c_Predicate_ODomainP=1. c_Predicate_ORangeP=1. c_FunDef_OTHE__default=1. c_Lazy__Sequence_Oanamorph=1. c_List_Oset__Cons=1. c_Power_Opower_Opower=1. c_Wellfounded_Omlex__prod=1. c_FunDef_Oin__rel=1. c_New__DSequence_Opos__union=1. c_Partial__Function_Oflat__lub=1. c_Product__Type_Ointernal__split=1. c_Random_Ominus__shift=1. c_SetInterval_Oord_OatLeast=1. c_SetInterval_Oord_OatMost=1. c_SetInterval_Oord_OgreaterThan=1. c_SetInterval_Oord_OlessThan=1. c_Hoare__Mirabelle_Otriple_Otriple__size=1. c_Nitpick_Oof__frac=1. c_Nitpick_Oplus__frac=1. c_Nitpick_Otimes__frac=1. c_Random__Sequence_Oempty=1. f20=1. f23=1. f24=1. f33=1. f34=1. f37=1. f43=1. f44=1. f45=1. f46=1. f47=1. f48=1. f51=1. f64=1. f65=1. f66=1. f68=1. f69=1. f70=1. f71=1. f72=1. f77=1. f78=1. f79=1. f80=1. f82=1. f84=1. f86=1. f90=1. f91=1. f97=1. f102=1. f105=1. f116=1. f117=1. f119=1. f120=1. f121=1. f122=1. f126=1. f127=1. f128=1. f129=1. f131=1. f132=1. f138=1. f139=1. f140=1. f141=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f148=1. f150=1. f151=1. f152=1. f153=1. f154=1. f155=1. f157=1. f158=1. f159=1. f160=1. f161=1. f162=1. f163=1. f164=1. f165=1. f166=1. f167=1. f170=1. f172=1. f173=1. f174=1. f183=1. f224=1. f225=1. f226=1. f227=1. f240=1. f258=1. f269=1. f270=1. f271=1. f272=1. f273=1. f274=1. f275=1. f276=1. f277=1. f278=1. f279=1. f280=1. f289=1. f303=1. f305=1. f320=1. f329=1. f330=1. f331=1. f337=1. f338=1. f339=1. f350=1. f351=1. f355=1. f356=1. f361=1. f362=1. f363=1. f364=1. f365=1. f367=1. f368=1. f383=1. f386=1. f395=1. f403=1. f405=1. f406=1. f407=1. f408=1. f410=1. f418=1. f419=1. f429=1. f430=1. f431=1. f432=1. f435=1. f442=1. f443=1. f444=1. f445=1. f447=1. f448=1. f449=1. f450=1. f451=1. f454=1. f455=1. f459=1. f485=1. f486=1. f487=1. f488=1. f489=1. f490=1. f491=1. f492=1. f493=1. f494=1. f495=1. f496=1. f497=1. f498=1. f502=1. f503=1. f505=1. f512=1. f516=1. f525=1. f526=1. f540=1. f555=1. f556=1. f559=1. f560=1. f579=1. f581=1. f582=1. c_Fun_Ocomp=1. c_List_Ofoldl=1. c_Hilbert__Choice_Oinv__into=1. c_List_Olinorder__class_Osort__key=1. c_SetInterval_Oord_OatLeastAtMost=1. c_Product__Type_Oapsnd=1. c_Nat_Onat_Onat__case=1. c_Product__Type_Oapfst=1. c_Product__Type_Oscomp=1. c_Sum__Type_OPlus=1. c_Fun_Othe__inv__into=1. c_List_Olist_Olist__case=1. c_Nat_Osemiring__1__class_Oof__nat__aux=1. c_Nitpick_Opair__box_OPairBox=1. c_Wellfounded_Olex__prod=1. c_Product__Type_Ocurry=1. c_Nitpick_Osetsum_H=1. c_Enum_Oproduct=1. c_Lazy__Sequence_Omap=1. c_List_Omaps=1. c_SetInterval_Oord_OgreaterThanLessThan=1. c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec=1. c_Lazy__Sequence_Oproduct=1. c_New__DSequence_Oneg__decr__bind=1. c_New__DSequence_Opos__decr__bind=1. c_Random_Oiterate=1. c_Random__Sequence_ORandom=1. c_Recdef_Osame__fst=1. c_Code__Numeral_Ocode__numeral_Ocode__numeral__case=1. c_Lazy__Sequence_Ohb__bind=1. c_New__DSequence_Oneg__bind=1. c_New__DSequence_Opos__bind=1. c_New__Random__Sequence_Oneg__bind=1. c_New__Random__Sequence_Opos__bind=1. c_Quotient_OBabs=1. c_Hoare__Mirabelle_Otriple_Otriple__case=1. c_Hoare__Mirabelle_Otriple_Otriple__rec=1. c_New__Random__Sequence_Oneg__map=1. c_New__Random__Sequence_Opos__empty=1. c_New__Random__Sequence_Opos__map=1. c_New__Random__Sequence_Opos__not__random__dseq=1. c_Nitpick_Oprod=1. c_Random__Sequence_Obind=1. c_Random__Sequence_Omap=1. f9=1. f10=1. f11=1. f12=1. f13=1. f14=1. f15=1. f25=1. f26=1. f73=1. f74=1. f81=1. f83=1. f98=1. f100=1. f103=1. f104=1. f106=1. f107=1. f123=1. f124=1. f168=1. f188=1. f189=1. f190=1. f195=1. f196=1. f212=1. f213=1. f214=1. f215=1. f216=1. f217=1. f218=1. f219=1. f220=1. f221=1. f222=1. f223=1. f228=1. f229=1. f230=1. f231=1. f236=1. f237=1. f238=1. f239=1. f242=1. f254=1. f255=1. f256=1. f257=1. f261=1. f263=1. f264=1. f265=1. f288=1. f290=1. f293=1. f295=1. f298=1. f311=1. f315=1. f316=1. f317=1. f322=1. f323=1. f324=1. f325=1. f326=1. f328=1. f332=1. f335=1. f353=1. f354=1. f380=1. f381=1. f392=1. f393=1. f400=1. f401=1. f402=1. f404=1. f409=1. f412=1. f413=1. f414=1. f417=1. f423=1. f424=1. f425=1. f426=1. f439=1. f460=1. f461=1. f464=1. f471=1. f474=1. f484=1. f499=1. f500=1. f501=1. f506=1. f507=1. f508=1. f509=1. f510=1. f511=1. f522=1. f527=1. f529=1. f549=1. f557=1. f558=1. f577=1. f578=1. c_Finite__Set_Ofold__graph=1. c_List_Ofoldr=1. c_List_Olinorder__class_Oinsort__insert__key=1. c_Fun_Ofun__upd=1. c_Predicate_Opred__comp=1. c_SetInterval_Oord_OatLeastLessThan=1. c_SetInterval_Oord_OgreaterThanAtMost=1. c_Option_Ooption_Ooption__case=1. c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case=1. c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec=1. c_New__DSequence_Opos__map=1. c_Nitpick_Opair__box_Opair__box__case=1. c_Nitpick_Opair__box_Opair__box__rec=1. c_Nitpick_Opair__box_Opair__box__size=1. c_Product__Type_Oprod_Oprod__rec=1. c_Product__Type_Oprod_Oprod__size=1. f29=1. f30=1. f31=1. f32=1. f35=1. f57=1. f58=1. f59=1. f60=1. f62=1. f85=1. f87=1. f88=1. f89=1. f94=1. f95=1. f115=1. f169=1. f181=1. f191=1. f192=1. f193=1. f194=1. f197=1. f198=1. f199=1. f200=1. f207=1. f208=1. f209=1. f210=1. f211=1. f241=1. f259=1. f260=1. f262=1. f283=1. f284=1. f285=1. f286=1. f287=1. f299=1. f300=1. f352=1. f360=1. f369=1. f370=1. f371=1. f372=1. f373=1. f374=1. f375=1. f376=1. f377=1. f378=1. f379=1. f388=1. f396=1. f397=1. f398=1. f399=1. f420=1. f421=1. f422=1. f427=1. f433=1. f434=1. f436=1. f437=1. f438=1. f456=1. f472=1. f475=1. f476=1. f477=1. f479=1. f480=1. f504=1. f528=1. f541=1. f554=1. f562=1. c_Product__Type_Omap__pair=1. c_New__Random__Sequence_Opos__union=1. c_Partial__Function_Ofun__lub=1. f2=1. f3=1. f4=1. f5=1. f101=1. f182=1. f294=1. f296=1. f297=1. f307=1. f310=1. f312=1. f340=1. f341=1. f342=1. f343=1. f344=1. f345=1. f349=1. f389=1. f390=1. f391=1. f542=1. f543=1. f544=1. f551=1. f561=1. f573=1. f574=1. f575=1. f576=1. c_New__Random__Sequence_Oneg__decr__bind=1. c_New__Random__Sequence_Opos__decr__bind=1. f6=1. f7=1. f8=1. f49=1. f50=1. f52=1. f63=1. f205=1. f206=1. f245=1. f246=1. f249=1. f318=1. f478=1. f481=1. f513=1. f514=1. f517=1. f518=1. f567=1. f568=1. f266=1. f301=1. f302=1. f346=1. f357=1. f358=1. f468=1. f563=1. f564=1. f565=1. f566=1. f569=1. f570=1. f571=1. f572=1. f267=1. f247=1. f248=1.
% 192.14/192.08
% 192.14/192.08 ============================== PROOF =================================
% 192.14/192.08 % SZS status Theorem
% 192.14/192.08 % SZS output start Refutation
% 192.14/192.08
% 192.14/192.08 % Proof 1 at 186.59 (+ 0.10) seconds.
% 192.14/192.08 % Length of proof is 18.
% 192.14/192.08 % Level of proof is 5.
% 192.14/192.08 % Maximum clause weight is 31.000.
% 192.14/192.08 % Given clauses 0.
% 192.14/192.08
% 192.14/192.08 2327 (all V_Q_2 all V_ca_2 all V_Ga_2 all T_b c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))) # label(fact_falseE) # label(axiom) # label(non_clause). [assumption].
% 192.14/192.08 3178 (all V_Pa_2 all T_b hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2) # label(fact_Collect__def) # label(axiom) # label(non_clause). [assumption].
% 192.14/192.08 3179 (all T_b c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) # label(fact_empty__def) # label(axiom) # label(non_clause). [assumption].
% 192.14/192.08 3195 (all V_a_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_singleton__conv) # label(axiom) # label(non_clause). [assumption].
% 192.14/192.08 3196 (all V_a_2 all T_b hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) # label(fact_singleton__conv2) # label(axiom) # label(non_clause). [assumption].
% 192.14/192.08 4906 -((exists B_Z exists B_x1 v_P(B_Z,B_x1)) -> (exists B_P_H exists B_Q_H c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B_P_H),v_c),B_Q_H)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))) # label(conj_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 192.14/192.08 9364 c_Hoare__Mirabelle_Ohoare__derivs(A,B,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(A)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(A),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),A),hAPP(c_COMBK(tc_HOL_Obool,tc_Com_Ostate),c_fFalse))),C),D)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(A),tc_HOL_Obool)))) # label(fact_falseE) # label(axiom). [clausify(2327)].
% 192.14/192.08 10585 hAPP(c_Set_OCollect(A),B) = B # label(fact_Collect__def) # label(axiom). [clausify(3178)].
% 192.14/192.08 10586 c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)) = hAPP(c_Set_OCollect(A),hAPP(c_COMBK(tc_HOL_Obool,A),c_fFalse)) # label(fact_empty__def) # label(axiom). [clausify(3179)].
% 192.14/192.08 10587 hAPP(c_COMBK(tc_HOL_Obool,A),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)). [copy(10586),rewrite([10585(9)]),flip(a)].
% 192.14/192.08 10625 hAPP(c_Set_OCollect(A),hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),B)) = hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))) # label(fact_singleton__conv) # label(axiom). [clausify(3195)].
% 192.14/192.08 10626 hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))) = hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),B). [copy(10625),rewrite([10585(7)]),flip(a)].
% 192.14/192.08 10627 hAPP(c_Set_OCollect(A),hAPP(c_fequal,B)) = hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))) # label(fact_singleton__conv2) # label(axiom). [clausify(3196)].
% 192.14/192.08 10628 hAPP(hAPP(c_COMBC(A,A,tc_HOL_Obool),c_fequal),B) = hAPP(c_fequal,B). [copy(10627),rewrite([10585(4),10626(8)]),flip(a)].
% 192.14/192.08 13327 -c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),A),v_c),B)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) # label(conj_0) # label(negated_conjecture). [clausify(4906)].
% 192.14/192.08 13328 -c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),A),v_c),B))). [copy(13327),rewrite([10626(18),10628(17)])].
% 192.14/192.08 17402 c_Hoare__Mirabelle_Ohoare__derivs(A,B,hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(A),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),A),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_HOL_Obool)))),C),D))). [back_rewrite(9364),rewrite([10587(12),10626(21),10628(20)])].
% 192.14/192.08 17403 $F. [resolve(17402,a,13328,a)].
% 192.14/192.08
% 192.14/192.08 % SZS output end Refutation
% 192.14/192.08 ============================== end of proof ==========================
% 192.14/192.08
% 192.14/192.08 ============================== STATISTICS ============================
% 192.14/192.08
% 192.14/192.08 Given=0. Generated=8940. Kept=7633. proofs=1.
% 192.14/192.08 Usable=0. Sos=2604. Demods=1386. Limbo=4731, Disabled=10374. Hints=0.
% 192.14/192.08 Megabytes=233.84.
% 192.14/192.08 User_CPU=186.59, System_CPU=0.10, Wall_clock=187.
% 192.14/192.08
% 192.14/192.08 ============================== end of statistics =====================
% 192.14/192.08
% 192.14/192.08 ============================== end of search =========================
% 192.14/192.08
% 192.14/192.08 THEOREM PROVED
% 192.14/192.08 % SZS status Theorem
% 192.14/192.08
% 192.14/192.08 Exiting with 1 proof.
% 192.14/192.08
% 192.14/192.08 Process 19349 exit (max_proofs) Sun Jun 5 02:59:42 2022
% 192.14/192.08 Prover9 interrupted
%------------------------------------------------------------------------------