TSTP Solution File: SWV686-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV686-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 : Wed Jul 20 21:14:26 EDT 2022
% Result : Timeout 300.02s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV686-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jun 15 05:26:03 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.02/1.35 ============================== Prover9 ===============================
% 1.02/1.35 Prover9 (32) version 2009-11A, November 2009.
% 1.02/1.35 Process 16113 was started by sandbox on n022.cluster.edu,
% 1.02/1.35 Wed Jun 15 05:26:03 2022
% 1.02/1.35 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15960_n022.cluster.edu".
% 1.02/1.35 ============================== end of head ===========================
% 1.02/1.35
% 1.02/1.35 ============================== INPUT =================================
% 1.02/1.35
% 1.02/1.35 % Reading from file /tmp/Prover9_15960_n022.cluster.edu
% 1.02/1.35
% 1.02/1.35 set(prolog_style_variables).
% 1.02/1.35 set(auto2).
% 1.02/1.35 % set(auto2) -> set(auto).
% 1.02/1.35 % set(auto) -> set(auto_inference).
% 1.02/1.35 % set(auto) -> set(auto_setup).
% 1.02/1.35 % set(auto_setup) -> set(predicate_elim).
% 1.02/1.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.02/1.35 % set(auto) -> set(auto_limits).
% 1.02/1.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.02/1.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.02/1.35 % set(auto) -> set(auto_denials).
% 1.02/1.35 % set(auto) -> set(auto_process).
% 1.02/1.35 % set(auto2) -> assign(new_constants, 1).
% 1.02/1.35 % set(auto2) -> assign(fold_denial_max, 3).
% 1.02/1.35 % set(auto2) -> assign(max_weight, "200.000").
% 1.02/1.35 % set(auto2) -> assign(max_hours, 1).
% 1.02/1.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.02/1.35 % set(auto2) -> assign(max_seconds, 0).
% 1.02/1.35 % set(auto2) -> assign(max_minutes, 5).
% 1.02/1.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.02/1.35 % set(auto2) -> set(sort_initial_sos).
% 1.02/1.35 % set(auto2) -> assign(sos_limit, -1).
% 1.02/1.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.02/1.35 % set(auto2) -> assign(max_megs, 400).
% 1.02/1.35 % set(auto2) -> assign(stats, some).
% 1.02/1.35 % set(auto2) -> clear(echo_input).
% 1.02/1.35 % set(auto2) -> set(quiet).
% 1.02/1.35 % set(auto2) -> clear(print_initial_clauses).
% 1.02/1.35 % set(auto2) -> clear(print_given).
% 1.02/1.35 assign(lrs_ticks,-1).
% 1.02/1.35 assign(sos_limit,10000).
% 1.02/1.35 assign(order,kbo).
% 1.02/1.35 set(lex_order_vars).
% 1.02/1.35 clear(print_given).
% 1.02/1.35
% 1.02/1.35 % formulas(sos). % not echoed (566 formulas)
% 1.02/1.35
% 1.02/1.35 ============================== end of input ==========================
% 1.02/1.35
% 1.02/1.35 % From the command line: assign(max_seconds, 300).
% 1.02/1.35
% 1.02/1.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.02/1.35
% 1.02/1.35 % Formulas that are not ordinary clauses:
% 1.02/1.35
% 1.02/1.35 ============================== end of process non-clausal formulas ===
% 1.02/1.35
% 1.02/1.35 ============================== PROCESS INITIAL CLAUSES ===============
% 1.02/1.35
% 1.02/1.35 ============================== PREDICATE ELIMINATION =================
% 1.02/1.35 1 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.02/1.35 2 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 1.02/1.35 3 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 1.02/1.35 4 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 1.02/1.35 5 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_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),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 1.02/1.35 6 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 1.02/1.35 7 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 1.02/1.35 8 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 1.02/1.35 9 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 1.02/1.35 10 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 1.02/1.35 11 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 1.02/1.35 12 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 1.02/1.35 13 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 1.02/1.35 14 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 1.02/1.35 15 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 1.02/1.35 16 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 1.02/1.35 17 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 1.02/1.35 18 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 1.02/1.35 19 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.02/1.35 20 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.02/1.35 21 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 1.02/1.35 22 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.02/1.35 23 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 1.02/1.35 24 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.02/1.35 25 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,2,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(1,a,3,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,4,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,5,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(1,a,6,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(1,a,8,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,10,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,11,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,12,a)].
% 1.02/1.35 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(1,a,13,a)].
% 1.02/1.38 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,14,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(1,a,15,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(1,a,16,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(1,a,17,a)].
% 1.02/1.38 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(1,a,18,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(1,a,19,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,20,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(1,a,21,a)].
% 1.02/1.38 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(1,a,22,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(1,a,23,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(1,a,24,a)].
% 1.02/1.38 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,25,a)].
% 1.02/1.38 26 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.02/1.38 27 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Otimes__class_Otimes(A)),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,D)),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(C,D))),A) | -c_Deriv_Oderiv(C,D,E,A) | -c_Deriv_Oderiv(B,D,F,A) # label(cls_DERIV__mult_H_0) # label(axiom). [assumption].
% 1.02/1.38 28 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Otimes__class_Otimes(A)),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(B,D))),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__mult_0) # label(axiom). [assumption].
% 1.02/1.38 29 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),B)),C),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),E),C),A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__cdivide_0) # label(axiom). [assumption].
% 1.02/1.38 30 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__diff_0) # label(axiom). [assumption].
% 1.02/1.38 31 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oplus__class_Oplus(A)),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__add_0) # label(axiom). [assumption].
% 1.02/1.38 32 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,B,A) # label(cls_DERIV__cmult__Id_0) # label(axiom). [assumption].
% 1.02/1.38 33 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBI(A),B,A) # label(cls_differentiable__ident_0) # label(axiom). [assumption].
% 1.02/1.38 34 -class_RealVector_Oreal__normed__field(A) | B = C | -c_Deriv_Oderiv(D,E,C,A) | -c_Deriv_Oderiv(D,E,B,A) # label(cls_DERIV__unique_0) # label(axiom). [assumption].
% 1.02/1.38 35 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(B,C,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_differentiable__def_1) # label(axiom). [assumption].
% 1.02/1.38 36 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(B,C,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_differentiableI_0) # label(axiom). [assumption].
% 1.02/1.38 37 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBI(A),B,c_HOL_Oone__class_Oone(A),A) # label(cls_DERIV__ident_0) # label(axiom). [assumption].
% 1.02/1.38 38 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(A,A,A),B),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,hAPP(C,D),E,A) # label(cls_DERIV__chain2_0) # label(axiom). [assumption].
% 1.02/1.38 39 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(A,A,A),B),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),A) | -c_Deriv_Oderiv(B,hAPP(C,D),E,A) | -c_Deriv_Oderiv(C,D,F,A) # label(cls_DERIV__chain_H_0) # label(axiom). [assumption].
% 1.02/1.38 40 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(A,A,A),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),A) | -c_Deriv_Oderiv(C,D,E,A) # label(cls_DERIV__cmult_0) # label(axiom). [assumption].
% 1.02/1.38 41 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(B,C,D,A) | -c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),hAPP(hAPP(c_COMBB(A,A,A),B),hAPP(c_HOL_Oplus__class_Oplus(A),C)))),hAPP(B,C))),c_COMBI(A),A,A,A),c_HOL_Ozero__class_Ozero(A),D,A,A) # label(cls_DERIV__iff_1) # label(axiom). [assumption].
% 1.02/1.38 42 -class_RealVector_Oreal__normed__field(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),hAPP(hAPP(c_COMBB(A,A,A),B),hAPP(c_HOL_Oplus__class_Oplus(A),C)))),hAPP(B,C))),c_COMBI(A),A,A,A),c_HOL_Ozero__class_Ozero(A),D,A,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_DERIV__D_0) # label(axiom). [assumption].
% 1.02/1.38 43 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(B,D)),F))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(C,D)),hAPP(C,D))),A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__divide_0) # label(axiom). [assumption].
% 1.02/1.38 44 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(B,C,D,A) | -c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),B)),hAPP(B,C))),hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Ominus__class_Ominus(A)),C),A,A,A),C,D,A,A) # label(cls_DERIV__iff2_1) # label(axiom). [assumption].
% 1.02/1.38 45 -class_RealVector_Oreal__normed__field(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),B)),hAPP(B,C))),hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Ominus__class_Ominus(A)),C),A,A,A),C,D,A,A) | -c_Deriv_Oderiv(B,C,D,A) # label(cls_DERIV__iff2_0) # label(axiom). [assumption].
% 1.02/1.38 46 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Series_Osuminf(B,A)),C) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_divide_Osuminf_0) # label(axiom). [assumption].
% 1.02/1.38 47 -class_RealVector_Oreal__normed__field(A) | c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Series_Osuminf(B,A)),C) | -c_Series_Osummable(B,A) # label(cls_suminf__divide_0) # label(axiom). [assumption].
% 1.02/1.38 48 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),B),C,A,A,A),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),hAPP(C,D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),hAPP(B,D)))),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(C,D)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Oderiv(C,D,F,A) | -c_Deriv_Oderiv(B,D,E,A) # label(cls_DERIV__quotient_0) # label(axiom). [assumption].
% 1.02/1.38 49 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 1.02/1.38 50 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_divide_Odiff_0) # label(axiom). [assumption].
% 1.02/1.38 51 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),B),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__diff_0) # label(axiom). [assumption].
% 1.02/1.38 52 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oplus__class_Oplus(A)),B),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__sum_0) # label(axiom). [assumption].
% 1.02/1.38 53 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBB(A,A,A),B),C),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,hAPP(C,D),A) # label(cls_differentiable__compose_0) # label(axiom). [assumption].
% 1.02/1.38 54 -class_RealVector_Oreal__normed__field(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Oinverse__class_Odivide(A)),B),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B),A,A) # label(cls_divide_Ocont_0) # label(axiom). [assumption].
% 1.02/1.38 55 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Otimes__class_Otimes(A)),B),C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__mult_0) # label(axiom). [assumption].
% 1.02/1.38 56 -class_RealVector_Oreal__normed__field(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oinverse__class_Odivide(A)),C)),D),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),E),D),F,B,A) | -c_Limits_Otendsto(C,E,F,B,A) # label(cls_divide_Otendsto_0) # label(axiom). [assumption].
% 1.02/1.38 57 -class_RealVector_Oreal__normed__field(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oinverse__class_Odivide(A)),C)),D),E,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_divide_OLIM_0) # label(axiom). [assumption].
% 1.02/1.38 58 -class_RealVector_Oreal__normed__field(A) | c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_divide_Osummable_0) # label(axiom). [assumption].
% 1.02/1.38 59 -class_RealVector_Oreal__normed__field(A) | c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_summable__divide_0) # label(axiom). [assumption].
% 1.02/1.38 60 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_divide_OLIMSEQ_0) # label(axiom). [assumption].
% 1.02/1.38 61 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),A) | -c_SEQ_OZseq(B,A) # label(cls_divide_OZseq_0) # label(axiom). [assumption].
% 1.02/1.38 62 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),A) | -c_SEQ_OCauchy(B,A) # label(cls_divide_OCauchy_0) # label(axiom). [assumption].
% 1.02/1.38 63 -class_RealVector_Oreal__normed__field(A) | c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_divide_Osums_0) # label(axiom). [assumption].
% 1.02/1.38 64 -class_RealVector_Oreal__normed__field(A) | c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B)),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_sums__divide_0) # label(axiom). [assumption].
% 1.02/1.38 65 -class_RealVector_Oreal__normed__field(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oinverse__class_Odivide(A)),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide_OLIM__zero_0) # label(axiom). [assumption].
% 1.02/1.38 66 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),B),C,A,A,A),D,A) | hAPP(C,D) = c_HOL_Ozero__class_Ozero(A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__divide_0) # label(axiom). [assumption].
% 1.02/1.38 67 -class_RealVector_Oreal__normed__field(A) | c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oinverse__class_Odivide(A)),C),D,B,A,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),E),F),V6,B,A) | F = c_HOL_Ozero__class_Ozero(A) | -c_Limits_Otendsto(D,F,V6,B,A) | -c_Limits_Otendsto(C,E,V6,B,A) # label(cls_tendsto__divide_0) # label(axiom). [assumption].
% 1.02/1.38 68 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oinverse__class_Odivide(A)),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E),A) | E = c_HOL_Ozero__class_Ozero(A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__divide_0) # label(axiom). [assumption].
% 1.02/1.38 69 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oinverse__class_Odivide(A)),C)),E)),D) # label(cls_divide_Osetsum_0) # label(axiom). [assumption].
% 1.02/1.38 70 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 1.02/1.38 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(A,C)),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(B,C))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,D,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,E,tc_Complex_Ocomplex). [resolve(26,a,27,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(A,C))),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(26,a,28,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A)),B),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),B),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(26,a,29,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(26,a,30,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(26,a,31,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,A,tc_Complex_Ocomplex). [resolve(26,a,32,a)].
% 1.02/1.38 Derived: c_Deriv_Odifferentiable(c_COMBI(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(26,a,33,a)].
% 1.02/1.38 Derived: A = B | -c_Deriv_Oderiv(C,D,B,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(C,D,A,tc_Complex_Ocomplex). [resolve(26,a,34,a)].
% 1.02/1.38 Derived: c_Deriv_Odifferentiable(A,B,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(26,a,35,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(c_COMBI(tc_Complex_Ocomplex),A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(26,a,37,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),E),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,hAPP(B,C),D,tc_Complex_Ocomplex). [resolve(26,a,38,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D),tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,D,tc_Complex_Ocomplex). [resolve(26,a,40,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex) | -c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B)))),hAPP(A,B))),c_COMBI(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(26,a,41,a)].
% 1.02/1.38 Derived: c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B)))),hAPP(A,B))),c_COMBI(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(26,a,42,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(A,C)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(B,C)),hAPP(B,C))),tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(26,a,43,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex) | -c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),hAPP(A,B))),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(26,a,44,a)].
% 1.02/1.38 Derived: c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),hAPP(A,B))),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,B,C,tc_Complex_Ocomplex). [resolve(26,a,45,a)].
% 1.02/1.38 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),B) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(26,a,46,a)].
% 1.02/1.38 Derived: c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),B) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(26,a,47,a)].
% 1.02/1.38 Derived: c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),hAPP(B,C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),hAPP(A,C)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(B,C)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Oderiv(B,C,E,tc_Complex_Ocomplex) | -c_Deriv_Oderiv(A,C,D,tc_Complex_Ocomplex). [resolve(26,a,48,a)].
% 1.02/1.38 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(26,a,49,a)].
% 1.02/1.38 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(26,a,50,a)].
% 1.02/1.38 Derived: c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(26,a,51,a)].
% 1.02/1.38 Derived: c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(26,a,52,a)].
% 1.02/1.38 Derived: c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,hAPP(B,C),tc_Complex_Ocomplex). [resolve(26,a,53,a)].
% 1.02/1.38 Derived: c_Lim_OLIM(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A),B,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(26,a,54,a)].
% 1.02/1.38 Derived: c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(26,a,55,a)].
% 1.02/1.38 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),B)),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),C),E,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,E,A,tc_Complex_Ocomplex). [resolve(26,a,56,a)].
% 1.02/1.38 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),B)),C),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(26,a,57,a)].
% 1.02/1.38 Derived: c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(26,a,58,a)].
% 1.02/1.38 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A)),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(26,a,60,a)].
% 1.02/1.38 Derived: c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(26,a,61,a)].
% 1.02/1.38 Derived: c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(A,tc_Complex_Ocomplex). [resolve(26,a,62,a)].
% 1.02/1.38 Derived: c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A)),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(26,a,63,a)].
% 1.02/1.38 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),B)),C),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(26,a,65,a)].
% 1.02/1.38 Derived: c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | hAPP(B,C) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(26,a,66,a)].
% 1.02/1.38 Derived: c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),D),E),F,A,tc_Complex_Ocomplex) | E = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,E,F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,F,A,tc_Complex_Ocomplex). [resolve(26,a,67,a)].
% 1.02/1.38 Derived: c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(26,a,68,a)].
% 1.02/1.41 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),B)),D)),C). [resolve(26,a,69,a)].
% 1.02/1.41 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(26,a,70,a)].
% 1.02/1.41 71 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.02/1.41 72 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.02/1.41 73 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 1.02/1.41 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(71,a,72,a)].
% 1.02/1.41 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(71,a,73,a)].
% 1.02/1.41 74 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.02/1.41 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)). [resolve(74,a,72,a)].
% 1.02/1.41 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(74,a,73,a)].
% 1.02/1.41 75 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.02/1.41 76 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 1.02/1.41 77 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Suc(B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 1.02/1.41 78 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),hAPP(hAPP(c_Finite__Set_Osetsum(E,A),F),V6)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(E,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(E,A),tc_fun(tc_fun(E,tc_bool),A),B),c_Finite__Set_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_HOL_Otimes__class_Otimes(A)),C))),F))),V6)),D) # label(cls_setsum__product_0) # label(axiom). [assumption].
% 1.02/1.41 79 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Finite__Set_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBB(A,A,C),hAPP(c_HOL_Otimes__class_Otimes(A),B)),D)),E) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 1.02/1.41 80 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),E)),D) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 1.02/1.41 81 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 1.02/1.41 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(75,a,76,a)].
% 1.02/1.41 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,77,a)].
% 1.02/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),hAPP(hAPP(c_Finite__Set_Osetsum(D,tc_nat),E),F)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(D,tc_nat),tc_fun(tc_fun(D,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(D,tc_nat)),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_nat),tc_fun(D,tc_nat)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_nat),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_nat)),A),c_COMBB(tc_nat,tc_nat,D)),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B))),E))),F)),C). [resolve(75,a,78,a)].
% 1.02/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,B),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A)),C)),D). [resolve(75,a,79,a)].
% 1.02/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B)),D)),C). [resolve(75,a,80,a)].
% 1.02/1.41 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(75,a,81,a)].
% 1.02/1.41 82 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.02/1.41 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(82,a,76,a)].
% 1.02/1.41 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(82,a,77,a)].
% 1.02/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C)),hAPP(hAPP(c_Finite__Set_Osetsum(D,tc_Complex_Ocomplex),E),F)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_bool),tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_fun(D,tc_Complex_Ocomplex),tc_fun(tc_fun(D,tc_bool),tc_Complex_Ocomplex),A),c_Finite__Set_Osetsum(D,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_Complex_Ocomplex),tc_fun(D,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_fun(tc_fun(D,tc_Complex_Ocomplex),tc_fun(D,tc_Complex_Ocomplex)),A),c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,D)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),B))),E))),F)),C). [resolve(82,a,78,a)].
% 1.02/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,B),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),C)),D). [resolve(82,a,79,a)].
% 1.02/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),B)),D)),C). [resolve(82,a,80,a)].
% 1.02/1.43 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(82,a,81,a)].
% 1.02/1.43 83 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.02/1.43 84 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_divide__1_0) # label(axiom). [assumption].
% 1.02/1.43 85 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom). [assumption].
% 1.02/1.43 86 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom). [assumption].
% 1.02/1.43 87 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom). [assumption].
% 1.02/1.43 88 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom). [assumption].
% 1.02/1.43 89 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B)),C) # label(cls_power__one__over_0) # label(axiom). [assumption].
% 1.02/1.43 90 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_HOL_Oone__class_Oone(A))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Oone__class_Oone(A))) | B = c_HOL_Oone__class_Oone(A) # label(cls_geometric__sum_0) # label(axiom). [assumption].
% 1.02/1.43 91 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 1.02/1.43 92 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_diff__divide__distrib_0) # label(axiom). [assumption].
% 1.02/1.43 93 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 1.02/1.43 94 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))),D) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 1.02/1.43 95 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 1.02/1.43 96 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom). [assumption].
% 1.02/1.43 97 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 1.02/1.43 98 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),E) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 1.02/1.43 99 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C) # label(cls_frac__eq__eq_0) # label(axiom). [assumption].
% 1.02/1.43 100 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 1.02/1.43 101 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom). [assumption].
% 1.02/1.43 102 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 1.02/1.43 103 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 1.02/1.43 104 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 1.02/1.43 105 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oinverse__class_Odivide(A)),C)),E)),D) # label(cls_setsum__divide__distrib_0) # label(axiom). [assumption].
% 1.02/1.43 106 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 1.02/1.43 107 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 1.02/1.43 108 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__divide_0) # label(axiom). [assumption].
% 1.02/1.43 109 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 1.02/1.43 110 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 1.02/1.43 111 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 1.02/1.43 112 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 1.02/1.43 113 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 1.02/1.43 114 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 1.02/1.43 115 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 1.02/1.43 116 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 1.02/1.43 117 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 1.02/1.43 118 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 1.02/1.43 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(83,a,84,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,85,a)].
% 1.02/1.43 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,86,a)].
% 1.02/1.43 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(83,a,88,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A)),B). [resolve(83,a,89,a)].
% 1.02/1.43 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(83,a,90,a)].
% 1.02/1.43 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,93,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C))),C) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,94,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B))),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,95,a)].
% 1.02/1.43 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,96,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,97,a)].
% 1.02/1.43 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B). [resolve(83,a,98,a)].
% 1.02/1.43 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B). [resolve(83,a,99,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(83,a,100,a)].
% 1.02/1.43 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,101,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,102,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,103,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A)),A). [resolve(83,a,104,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(83,a,107,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(83,a,108,a)].
% 1.02/1.43 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),A). [resolve(83,a,109,a)].
% 1.02/1.43 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),A) = B. [resolve(83,a,110,a)].
% 1.02/1.43 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,114,a)].
% 1.02/1.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,116,a)].
% 1.02/1.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(83,a,117,a)].
% 1.02/1.44 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(83,a,118,a)].
% 1.02/1.44 119 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.02/1.44 120 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oone__class_Oone(A)),B) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 1.02/1.44 121 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 1.02/1.44 122 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 1.02/1.44 123 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 1.02/1.44 124 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 1.02/1.44 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = c_HOL_Oone__class_Oone(tc_nat). [resolve(119,a,120,a)].
% 1.02/1.44 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(119,a,121,a)].
% 1.02/1.44 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(119,a,122,a)].
% 1.02/1.44 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A). [resolve(119,a,123,a)].
% 1.02/1.44 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(119,a,124,a)].
% 1.02/1.44 125 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.02/1.44 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(125,a,120,a)].
% 1.02/1.44 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(125,a,121,a)].
% 1.02/1.44 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(125,a,122,a)].
% 1.02/1.44 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A). [resolve(125,a,123,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(125,a,124,a)].
% 1.02/1.45 126 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.02/1.45 127 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 1.02/1.45 128 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 1.02/1.45 129 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 1.02/1.45 130 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 1.02/1.45 131 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A))),C) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 1.02/1.45 132 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 1.02/1.45 133 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 1.02/1.45 134 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 1.02/1.45 135 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 1.02/1.45 136 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 1.02/1.45 137 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 1.02/1.45 138 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 1.02/1.45 139 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 1.02/1.45 140 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 1.02/1.45 141 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.02/1.45 142 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_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_Suc(C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.02/1.45 143 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 1.02/1.45 144 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 1.02/1.45 145 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 1.02/1.45 146 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 1.02/1.45 147 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 1.02/1.45 148 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 1.02/1.45 149 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 1.02/1.45 150 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 1.02/1.45 151 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 1.02/1.45 152 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 1.02/1.45 153 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 1.02/1.45 154 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 1.02/1.45 155 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.02/1.45 156 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.02/1.45 157 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.02/1.45 158 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.02/1.45 159 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.02/1.45 160 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_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(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 1.02/1.45 161 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.02/1.45 162 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.02/1.45 163 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.02/1.45 164 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.02/1.45 165 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(126,a,130,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B). [resolve(126,a,131,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(126,a,132,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(126,a,133,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(126,a,134,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(126,a,135,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(126,a,136,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(126,a,137,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(126,a,138,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(126,a,140,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)). [resolve(126,a,141,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)). [resolve(126,a,142,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(126,a,143,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(126,a,145,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(126,a,146,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(126,a,147,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(126,a,149,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(126,a,150,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(126,a,152,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(126,a,153,a)].
% 1.02/1.45 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(126,a,155,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(126,a,156,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(126,a,158,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(126,a,159,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C)). [resolve(126,a,160,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(126,a,163,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(126,a,164,a)].
% 1.02/1.46 166 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(166,a,130,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),B). [resolve(166,a,131,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(166,a,132,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(166,a,133,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(166,a,134,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(166,a,135,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(166,a,136,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(166,a,137,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(166,a,138,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(166,a,140,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)). [resolve(166,a,141,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)). [resolve(166,a,142,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(166,a,143,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)). [resolve(166,a,145,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(166,a,146,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C). [resolve(166,a,147,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D)). [resolve(166,a,149,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),A). [resolve(166,a,150,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(166,a,152,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(166,a,153,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C). [resolve(166,a,155,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(166,a,156,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(166,a,158,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(166,a,159,a)].
% 1.02/1.46 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(166,a,160,a)].
% 1.02/1.48 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(166,a,163,a)].
% 1.02/1.48 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A). [resolve(166,a,164,a)].
% 1.02/1.48 167 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.02/1.48 168 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 1.02/1.48 169 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_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(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 1.02/1.48 170 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.02/1.48 171 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.02/1.48 172 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 1.02/1.48 173 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 1.02/1.48 174 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 1.02/1.48 175 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 1.02/1.48 176 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 1.02/1.48 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(171,a,172,a)].
% 1.02/1.48 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(171,a,173,a)].
% 1.02/1.48 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(171,a,175,a)].
% 1.02/1.48 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(171,a,176,a)].
% 1.02/1.48 177 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.02/1.48 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(177,a,172,a)].
% 1.02/1.48 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(177,a,173,a)].
% 1.02/1.48 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(177,a,175,a)].
% 1.02/1.48 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(177,a,176,a)].
% 1.02/1.48 178 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 1.02/1.48 179 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,C,A) | -c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),A,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,A),B)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),C,A) # label(cls_sums__def_1) # label(axiom). [assumption].
% 1.02/1.48 180 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),A,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,A),B)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),C,A) | -c_Series_Osums(B,C,A) # label(cls_sums__def_0) # label(axiom). [assumption].
% 1.02/1.48 181 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),D),B,tc_nat,A,A),c_HOL_Ozero__class_Ozero(A),A) | -c_SEQ_OLIMSEQ(D,C,A) # label(cls_LIMSEQ__diff__approach__zero2_0) # label(axiom). [assumption].
% 1.02/1.48 182 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B),D,tc_nat,A,A),c_HOL_Ozero__class_Ozero(A),A) | -c_SEQ_OLIMSEQ(D,C,A) # label(cls_LIMSEQ__diff__approach__zero_0) # label(axiom). [assumption].
% 1.02/1.48 183 -class_RealVector_Oreal__normed__vector(A) | -class_HOL_Oinverse(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),B)),hAPP(B,C))),hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Ominus__class_Ominus(A)),C),A,A,A),C,D,A,A) | -c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),hAPP(hAPP(c_COMBB(A,A,A),B),hAPP(c_HOL_Oplus__class_Oplus(A),C)))),hAPP(B,C))),c_COMBI(A),A,A,A),c_HOL_Ozero__class_Ozero(A),D,A,A) # label(cls_DERIV__LIM__iff_0) # label(axiom). [assumption].
% 1.02/1.48 184 -class_RealVector_Oreal__normed__vector(A) | -class_HOL_Oinverse(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),hAPP(hAPP(c_COMBB(A,A,A),B),hAPP(c_HOL_Oplus__class_Oplus(A),C)))),hAPP(B,C))),c_COMBI(A),A,A,A),c_HOL_Ozero__class_Ozero(A),D,A,A) | -c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),hAPP(hAPP(c_COMBC(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),B)),hAPP(B,C))),hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Ominus__class_Ominus(A)),C),A,A,A),C,D,A,A) # label(cls_DERIV__LIM__iff_1) # label(axiom). [assumption].
% 1.02/1.48 185 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),A,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,A),B)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),c_Series_Osuminf(B,A),A) | -c_Series_Osummable(B,A) # label(cls_summable__sumr__LIMSEQ__suminf_0) # label(axiom). [assumption].
% 1.02/1.48 186 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C),D,B,A,A),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__add__zero_0) # label(axiom). [assumption].
% 1.02/1.48 187 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C)),E),D,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__zero__iff_0) # label(axiom). [assumption].
% 1.02/1.48 188 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,D,B,A) # label(cls_LIM__zero_0) # label(axiom). [assumption].
% 1.02/1.48 189 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B)),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__diff__const_0) # label(axiom). [assumption].
% 1.02/1.48 190 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oplus__class_Oplus(A)),B)),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add__const_0) # label(axiom). [assumption].
% 1.02/1.48 191 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oplus__class_Oplus(A)),B),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__add_0) # label(axiom). [assumption].
% 1.02/1.48 192 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E),A) | -c_Series_Osums(C,E,A) | -c_Series_Osums(B,D,A) # label(cls_sums__diff_0) # label(axiom). [assumption].
% 1.02/1.48 193 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__diff_0) # label(axiom). [assumption].
% 1.02/1.48 194 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B),C,tc_nat,A,A),A) | -c_Series_Osummable(C,A) | -c_Series_Osummable(B,A) # label(cls_summable__diff_0) # label(axiom). [assumption].
% 1.02/1.48 195 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oplus__class_Oplus(A)),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add_0) # label(axiom). [assumption].
% 1.02/1.48 196 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oplus__class_Oplus(A)),B),C,tc_nat,A,A),A) | -c_Series_Osummable(C,A) | -c_Series_Osummable(B,A) # label(cls_summable__add_0) # label(axiom). [assumption].
% 1.02/1.48 197 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__diff_0) # label(axiom). [assumption].
% 1.02/1.48 198 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oplus__class_Oplus(A)),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_Series_Osums(C,E,A) | -c_Series_Osums(B,D,A) # label(cls_sums__add_0) # label(axiom). [assumption].
% 1.02/1.48 199 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C),D,B,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),F),V6,B,A) | -c_Limits_Otendsto(D,F,V6,B,A) | -c_Limits_Otendsto(C,E,V6,B,A) # label(cls_tendsto__add_0) # label(axiom). [assumption].
% 1.02/1.48 200 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C),D,B,A,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),F),V6,B,A) | -c_Limits_Otendsto(D,F,V6,B,A) | -c_Limits_Otendsto(C,E,V6,B,A) # label(cls_tendsto__diff_0) # label(axiom). [assumption].
% 1.02/1.48 201 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C),D,B,A,A),E,hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),F),V6),B,A) | -c_Lim_OLIM(D,E,V6,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__diff_0) # label(axiom). [assumption].
% 1.02/1.48 202 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C),D,B,A,A),E,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),V6),B,A) | -c_Lim_OLIM(D,E,V6,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__add_0) # label(axiom). [assumption].
% 1.02/1.48 203 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(hAPP(hAPP(c_COMBB(B,A,B),C),hAPP(c_HOL_Oplus__class_Oplus(B),D)),c_HOL_Ozero__class_Ozero(B),E,B,A) # label(cls_LIM__offset__zero__cancel_0) # label(axiom). [assumption].
% 1.02/1.48 204 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(B,A,B),C),hAPP(c_HOL_Oplus__class_Oplus(B),D)),c_HOL_Ozero__class_Ozero(B),E,B,A) | -c_Lim_OLIM(C,D,E,B,A) # label(cls_LIM__offset__zero_0) # label(axiom). [assumption].
% 1.02/1.48 205 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,hAPP(C,D),A,B) | -c_Lim_OLIM(hAPP(hAPP(c_COMBB(A,B,A),C),hAPP(c_HOL_Oplus__class_Oplus(A),D)),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) # label(cls_LIM__isCont__iff_1) # label(axiom). [assumption].
% 1.02/1.48 206 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(A,B,A),C),hAPP(c_HOL_Oplus__class_Oplus(A),D)),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) | -c_Lim_OLIM(C,D,hAPP(C,D),A,B) # label(cls_LIM__isCont__iff_0) # label(axiom). [assumption].
% 1.02/1.48 207 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B)),C),A) # label(cls_LIMSEQ__Zseq__iff_1) # label(axiom). [assumption].
% 1.02/1.48 208 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B)),C),A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__Zseq__iff_0) # label(axiom). [assumption].
% 1.02/1.48 209 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(B,A,B),C),hAPP(hAPP(c_COMBC(B,B,B),c_HOL_Oplus__class_Oplus(B)),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(B),E),D),F,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__offset_0) # label(axiom). [assumption].
% 1.02/1.48 210 -class_RealVector_Oreal__normed__vector(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Series_Osuminf(B,A)),c_Series_Osuminf(C,A)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Oplus__class_Oplus(A)),B),C,tc_nat,A,A),A) | -c_Series_Osummable(C,A) | -c_Series_Osummable(B,A) # label(cls_suminf__add_0) # label(axiom). [assumption].
% 1.02/1.48 211 -class_RealVector_Oreal__normed__vector(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Series_Osuminf(B,A)),c_Series_Osuminf(C,A)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B),C,tc_nat,A,A),A) | -c_Series_Osummable(C,A) | -c_Series_Osummable(B,A) # label(cls_suminf__diff_0) # label(axiom). [assumption].
% 1.02/1.49 212 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_Series_Osums(B,C,A) # label(cls_sums__summable_0) # label(axiom). [assumption].
% 1.02/1.49 213 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_Series_Osums(B,C,A) # label(cls_sums__iff_0) # label(axiom). [assumption].
% 1.02/1.49 214 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,c_HOL_Ozero__class_Ozero(A),A) | -c_Series_Osummable(B,A) # label(cls_summable__LIMSEQ__zero_0) # label(axiom). [assumption].
% 1.02/1.49 215 -class_RealVector_Oreal__normed__vector(A) | B = c_Series_Osuminf(C,A) | -c_Series_Osums(C,B,A) # label(cls_sums__unique_0) # label(axiom). [assumption].
% 1.02/1.49 216 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osuminf(B,A) = C | -c_Series_Osums(B,C,A) # label(cls_sums__iff_1) # label(axiom). [assumption].
% 1.02/1.49 217 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,c_Series_Osuminf(B,A),A) | -c_Series_Osummable(B,A) # label(cls_summable__sums_0) # label(axiom). [assumption].
% 1.02/1.49 218 -class_RealVector_Oreal__normed__vector(A) | -c_Series_Osummable(B,A) | c_Series_Osums(B,c_Series_Osuminf(B,A),A) # label(cls_sums__iff_2) # label(axiom). [assumption].
% 1.02/1.49 Derived: c_Series_Osums(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),B,tc_Complex_Ocomplex). [resolve(178,a,179,a)].
% 1.02/1.49 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),B,tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(178,a,180,a)].
% 1.02/1.49 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),C),A,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex). [resolve(178,a,181,a)].
% 1.02/1.49 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A),C,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex). [resolve(178,a,182,a)].
% 1.02/1.49 Derived: -class_HOL_Oinverse(tc_Complex_Ocomplex) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),hAPP(A,B))),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex) | -c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B)))),hAPP(A,B))),c_COMBI(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(178,a,183,a)].
% 1.02/1.49 Derived: -class_HOL_Oinverse(tc_Complex_Ocomplex) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B)))),hAPP(A,B))),c_COMBI(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex) | -c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),hAPP(A,B))),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(178,a,184,a)].
% 1.02/1.49 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),c_Series_Osuminf(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(178,a,185,a)].
% 1.02/1.49 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(178,a,186,a)].
% 1.02/1.49 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B)),D),C,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(178,a,187,a)].
% 1.02/1.49 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B)),C),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,C,A,tc_Complex_Ocomplex). [resolve(178,a,188,a)].
% 1.02/1.49 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(178,a,189,a)].
% 1.02/1.49 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),A)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(178,a,190,a)].
% 1.02/1.49 Derived: c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(178,a,191,a)].
% 1.02/1.49 Derived: c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_Series_Osums(B,D,tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(178,a,192,a)].
% 1.02/1.49 Derived: c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(178,a,193,a)].
% 1.02/1.49 Derived: c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(178,a,194,a)].
% 1.02/1.49 Derived: c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(178,a,195,a)].
% 1.02/1.49 Derived: c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(178,a,196,a)].
% 1.02/1.49 Derived: c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(178,a,197,a)].
% 1.02/1.49 Derived: c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_Series_Osums(B,D,tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(178,a,198,a)].
% 1.02/1.49 Derived: c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),D),E),F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,E,F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,F,A,tc_Complex_Ocomplex). [resolve(178,a,199,a)].
% 1.02/1.49 Derived: c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),E),F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,E,F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,F,A,tc_Complex_Ocomplex). [resolve(178,a,200,a)].
% 1.02/1.49 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),E),F),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,F,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(178,a,201,a)].
% 1.02/1.50 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),E),F),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,F,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(178,a,202,a)].
% 1.02/1.50 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),D,tc_Complex_Ocomplex,A). [resolve(178,a,203,b)].
% 1.02/1.50 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),B),hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),D,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,C,D,tc_Complex_Ocomplex,A). [resolve(178,a,204,b)].
% 1.02/1.50 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex). [resolve(178,a,207,a)].
% 1.02/1.50 Derived: c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex). [resolve(178,a,208,a)].
% 1.02/1.50 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),B),hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),C),E,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,D,E,tc_Complex_Ocomplex,A). [resolve(178,a,209,b)].
% 1.02/1.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),c_Series_Osuminf(B,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(178,a,210,a)].
% 1.02/1.50 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),c_Series_Osuminf(B,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(178,a,211,a)].
% 1.02/1.50 Derived: c_Series_Osummable(A,tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(178,a,212,a)].
% 1.02/1.50 Derived: c_SEQ_OLIMSEQ(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(178,a,214,a)].
% 1.02/1.50 Derived: A = c_Series_Osuminf(B,tc_Complex_Ocomplex) | -c_Series_Osums(B,A,tc_Complex_Ocomplex). [resolve(178,a,215,a)].
% 1.02/1.50 Derived: c_Series_Osuminf(A,tc_Complex_Ocomplex) = B | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(178,a,216,a)].
% 1.02/1.50 Derived: c_Series_Osums(A,c_Series_Osuminf(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(178,a,217,a)].
% 1.02/1.50 219 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.02/1.50 220 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Series_Osuminf(B,A)),C) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_suminf__mult2_0) # label(axiom). [assumption].
% 1.02/1.50 221 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Series_Osuminf(B,A)),C) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_mult__left_Osuminf_0) # label(axiom). [assumption].
% 1.02/1.50 222 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Series_Osuminf(C,A)) = c_Series_Osuminf(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osuminf_0) # label(axiom). [assumption].
% 1.02/1.50 223 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osuminf(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Series_Osuminf(C,A)) | -c_Series_Osummable(C,A) # label(cls_suminf__mult_0) # label(axiom). [assumption].
% 1.02/1.50 224 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult__left_Odiff_0) # label(axiom). [assumption].
% 1.02/1.50 225 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 1.02/1.50 226 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 1.02/1.50 227 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__right_Odiff_0) # label(axiom). [assumption].
% 1.02/1.50 228 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A,A) # label(cls_mult__right_Ocont_0) # label(axiom). [assumption].
% 1.02/1.50 229 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 1.02/1.50 230 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 1.02/1.50 231 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 1.02/1.50 232 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 1.02/1.50 233 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 1.02/1.50 234 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(A,A,B),hAPP(c_HOL_Otimes__class_Otimes(A),C)),D),E,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),F),B,A) | -c_Lim_OLIM(D,E,F,B,A) # label(cls_mult__right_OLIM_0) # label(axiom). [assumption].
% 1.02/1.50 235 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBB(A,A,B),hAPP(c_HOL_Otimes__class_Otimes(A),C)),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),F,B,A) | -c_Limits_Otendsto(D,E,F,B,A) # label(cls_mult__right_Otendsto_0) # label(axiom). [assumption].
% 1.02/1.50 236 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Otimes__class_Otimes(A)),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A,A) # label(cls_mult__left_Ocont_0) # label(axiom). [assumption].
% 1.02/1.50 237 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_Series_Osums(C,D,A) # label(cls_sums__mult_0) # label(axiom). [assumption].
% 1.02/1.50 238 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_Series_Osums(C,D,A) # label(cls_mult__right_Osums_0) # label(axiom). [assumption].
% 1.02/1.50 239 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osummable_0) # label(axiom). [assumption].
% 1.02/1.50 240 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),A) | -c_Series_Osummable(C,A) # label(cls_summable__mult_0) # label(axiom). [assumption].
% 1.02/1.50 241 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),A) | -c_SEQ_OZseq(C,A) # label(cls_Zseq__mult__right_0) # label(axiom). [assumption].
% 1.02/1.50 242 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),A) | -c_SEQ_OZseq(C,A) # label(cls_mult__right_OZseq_0) # label(axiom). [assumption].
% 1.02/1.50 243 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_SEQ_OLIMSEQ(C,D,A) # label(cls_mult__right_OLIMSEQ_0) # label(axiom). [assumption].
% 1.02/1.50 244 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OCauchy(hAPP(hAPP(c_COMBB(A,A,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),A) | -c_SEQ_OCauchy(C,A) # label(cls_mult__right_OCauchy_0) # label(axiom). [assumption].
% 1.02/1.50 245 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(A,A,B),hAPP(c_HOL_Otimes__class_Otimes(A),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__right__zero_0) # label(axiom). [assumption].
% 1.02/1.50 246 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(A,A,B),hAPP(c_HOL_Otimes__class_Otimes(A),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right_OLIM__zero_0) # label(axiom). [assumption].
% 1.02/1.50 247 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),D),F,B,A) | -c_Limits_Otendsto(C,E,F,B,A) # label(cls_mult__left_Otendsto_0) # label(axiom). [assumption].
% 1.02/1.50 248 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),D),E,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_mult__left_OLIM_0) # label(axiom). [assumption].
% 1.02/1.50 249 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C),D,B,A,A),E,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),V6),B,A) | -c_Lim_OLIM(D,E,V6,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__mult_0) # label(axiom). [assumption].
% 1.02/1.50 250 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C),D,B,A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),F),V6,B,A) | -c_Limits_Otendsto(D,F,V6,B,A) | -c_Limits_Otendsto(C,E,V6,B,A) # label(cls_mult_Otendsto_0) # label(axiom). [assumption].
% 1.02/1.50 251 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__mult_0) # label(axiom). [assumption].
% 1.02/1.50 252 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B),C,tc_nat,A,A),A) | -c_SEQ_OZseq(C,A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__mult_0) # label(axiom). [assumption].
% 1.02/1.50 253 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_sums__mult2_0) # label(axiom). [assumption].
% 1.02/1.50 254 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_mult__left_Osums_0) # label(axiom). [assumption].
% 1.02/1.50 255 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_summable__mult2_0) # label(axiom). [assumption].
% 1.02/1.50 256 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),A) | -c_Series_Osummable(B,A) # label(cls_mult__left_Osummable_0) # label(axiom). [assumption].
% 1.02/1.50 257 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),A) | -c_SEQ_OCauchy(B,A) # label(cls_mult__left_OCauchy_0) # label(axiom). [assumption].
% 1.02/1.50 258 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_mult__left_OLIMSEQ_0) # label(axiom). [assumption].
% 1.02/1.50 259 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__mult__left_0) # label(axiom). [assumption].
% 1.02/1.50 260 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B)),C),A) | -c_SEQ_OZseq(B,A) # label(cls_mult__left_OZseq_0) # label(axiom). [assumption].
% 1.02/1.50 261 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__left__zero_0) # label(axiom). [assumption].
% 1.02/1.50 262 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),D),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__left_OLIM__zero_0) # label(axiom). [assumption].
% 1.02/1.50 263 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C),D,B,A,A),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__zero_0) # label(axiom). [assumption].
% 1.02/1.50 264 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 1.02/1.50 265 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 1.02/1.50 266 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 1.02/1.50 267 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 1.02/1.50 268 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Finite__Set_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBB(A,A,C),hAPP(c_HOL_Otimes__class_Otimes(A),B)),D)),E) # label(cls_mult__right_Osetsum_0) # label(axiom). [assumption].
% 1.02/1.50 269 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),E)),D) # label(cls_mult__left_Osetsum_0) # label(axiom). [assumption].
% 1.02/1.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Series_Osuminf(A,tc_Complex_Ocomplex)),B) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(219,a,220,a)].
% 1.02/1.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Series_Osuminf(B,tc_Complex_Ocomplex)) = c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(219,a,222,a)].
% 1.02/1.50 Derived: c_Series_Osuminf(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Series_Osuminf(B,tc_Complex_Ocomplex)) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(219,a,223,a)].
% 1.02/1.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(219,a,224,a)].
% 1.02/1.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(219,a,226,a)].
% 1.02/1.50 Derived: c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(219,a,228,a)].
% 1.02/1.50 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D))). [resolve(219,a,233,a)].
% 1.02/1.50 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B)),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),E),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,E,A,tc_Complex_Ocomplex). [resolve(219,a,234,a)].
% 1.02/1.50 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D),E,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,D,E,A,tc_Complex_Ocomplex). [resolve(219,a,235,a)].
% 1.02/1.50 Derived: c_Lim_OLIM(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(219,a,236,a)].
% 1.02/1.50 Derived: c_Series_Osums(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_Series_Osums(B,C,tc_Complex_Ocomplex). [resolve(219,a,237,a)].
% 1.02/1.50 Derived: c_Series_Osummable(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(219,a,239,a)].
% 1.02/1.50 Derived: c_SEQ_OZseq(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex). [resolve(219,a,241,a)].
% 1.02/1.50 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,C,tc_Complex_Ocomplex). [resolve(219,a,243,a)].
% 1.02/1.50 Derived: c_SEQ_OCauchy(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(B,tc_Complex_Ocomplex). [resolve(219,a,244,a)].
% 1.02/1.50 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B)),C),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(219,a,245,a)].
% 1.02/1.50 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),B)),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),C),E,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,E,A,tc_Complex_Ocomplex). [resolve(219,a,247,a)].
% 1.02/1.50 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),B)),C),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(219,a,248,a)].
% 1.02/1.50 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),F),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,F,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(219,a,249,a)].
% 1.02/1.50 Derived: c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),E),F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(C,E,F,A,tc_Complex_Ocomplex) | -c_Limits_Otendsto(B,D,F,A,tc_Complex_Ocomplex). [resolve(219,a,250,a)].
% 1.02/1.50 Derived: c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(219,a,251,a)].
% 1.02/1.50 Derived: c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(219,a,252,a)].
% 1.02/1.50 Derived: c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(219,a,253,a)].
% 1.02/1.50 Derived: c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(219,a,255,a)].
% 1.02/1.50 Derived: c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(A,tc_Complex_Ocomplex). [resolve(219,a,257,a)].
% 1.02/1.50 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(219,a,258,a)].
% 1.02/1.50 Derived: c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A)),B),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(219,a,259,a)].
% 1.02/1.51 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),B)),C),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(219,a,261,a)].
% 1.02/1.51 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(219,a,263,a)].
% 1.02/1.51 270 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.02/1.51 271 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),c_Suc(D))) = c_HOL_Ozero__class_Ozero(A) | -c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_setsum__op__ivl__Suc_0) # label(axiom). [assumption].
% 1.02/1.51 272 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 1.02/1.51 273 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 1.02/1.51 274 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 1.02/1.51 275 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 1.02/1.51 276 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),c_Suc(D))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D))),hAPP(B,D)) | c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_setsum__op__ivl__Suc_1) # label(axiom). [assumption].
% 1.02/1.51 277 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(C),tc_nat),D))) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_setsum__head__upt__Suc_0) # label(axiom). [assumption].
% 1.02/1.51 278 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 1.02/1.51 279 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C),D,B,A,A)),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),E)),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),D),E)) # label(cls_setsum__addf_0) # label(axiom). [assumption].
% 1.02/1.51 280 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) # label(cls_setsum__shift__lb__Suc0__0__upt_0) # label(axiom). [assumption].
% 1.02/1.51 281 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(C,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(C,A),tc_fun(tc_fun(C,tc_bool),A),B),c_Finite__Set_Osetsum(C,A)),D)),E)),F) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBC(C,tc_fun(B,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(B,A),tc_fun(tc_fun(B,tc_bool),A),C),c_Finite__Set_Osetsum(B,A)),hAPP(c_COMBC(B,C,A),D))),F)),E) # label(cls_setsum__commute_0) # label(axiom). [assumption].
% 1.02/1.51 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),c_Suc(C))) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(270,a,271,a)].
% 1.02/1.51 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),c_Suc(C))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C))),hAPP(A,C)) | c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(270,a,276,a)].
% 1.02/1.51 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(B),tc_nat),C))) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(270,a,277,a)].
% 1.02/1.51 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Oplus__class_Oplus(tc_nat)),B),C,A,tc_nat,tc_nat)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),C),D)). [resolve(270,a,279,a)].
% 1.02/1.51 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),B)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(270,a,280,a)].
% 1.02/1.51 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(B,tc_nat),tc_fun(tc_fun(B,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(B,tc_nat)),C)),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_nat),tc_fun(tc_fun(A,tc_bool),tc_nat),B),c_Finite__Set_Osetsum(A,tc_nat)),hAPP(c_COMBC(A,B,tc_nat),C))),E)),D). [resolve(270,a,281,a)].
% 1.02/1.51 282 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.02/1.51 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),c_Suc(C))) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(282,a,271,a)].
% 1.02/1.51 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),c_Suc(C))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C))),hAPP(A,C)) | c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(282,a,276,a)].
% 1.02/1.51 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(A,B)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(B),tc_nat),C))) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(282,a,277,a)].
% 1.02/1.52 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),C),D)). [resolve(282,a,279,a)].
% 1.02/1.52 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),B)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(282,a,280,a)].
% 1.02/1.52 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_bool),tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_fun(B,tc_Complex_Ocomplex),tc_fun(tc_fun(B,tc_bool),tc_Complex_Ocomplex),A),c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex)),C)),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_bool),tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_fun(A,tc_Complex_Ocomplex),tc_fun(tc_fun(A,tc_bool),tc_Complex_Ocomplex),B),c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex)),hAPP(c_COMBC(A,B,tc_Complex_Ocomplex),C))),E)),D). [resolve(282,a,281,a)].
% 1.02/1.52 283 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.02/1.52 284 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 1.02/1.52 285 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 1.02/1.52 286 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 1.02/1.52 287 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 1.02/1.52 288 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 1.02/1.52 289 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 1.02/1.53 290 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 1.02/1.53 291 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 1.02/1.53 292 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 1.02/1.53 293 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 1.02/1.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(283,a,284,a)].
% 1.02/1.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | B = D | A = C. [resolve(283,a,287,a)].
% 1.02/1.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(283,a,289,a)].
% 1.02/1.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(283,a,290,a)].
% 1.02/1.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(283,a,291,a)].
% 1.02/1.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(283,a,292,a)].
% 1.02/1.53 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(283,a,293,a)].
% 1.02/1.53 294 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 1.02/1.53 295 -class_RealVector_Oreal__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))),F) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)),F))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),F)),E)) # label(cls_DERIV__mult__lemma_0) # label(axiom). [assumption].
% 1.02/1.53 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D))),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),E)),D)). [resolve(294,a,295,a)].
% 1.02/1.56 296 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.02/1.56 297 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B)),D). [resolve(296,a,297,a)].
% 1.02/1.56 298 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B)),D). [resolve(298,a,297,a)].
% 1.02/1.56 299 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.02/1.56 300 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 1.02/1.56 301 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.02/1.56 302 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.02/1.56 303 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 1.02/1.56 304 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 1.02/1.56 305 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.02/1.56 306 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.02/1.56 307 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 1.02/1.56 308 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 1.02/1.56 309 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 1.02/1.56 310 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 1.02/1.56 311 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),C) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 1.02/1.56 312 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(306,a,307,a)].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(306,a,308,a)].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(306,a,309,a)].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(306,a,311,a)].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(306,a,312,a)].
% 1.02/1.56 313 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 1.02/1.56 314 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 1.02/1.56 315 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 1.02/1.56 316 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom). [assumption].
% 1.02/1.56 317 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),D) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 1.02/1.56 318 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 1.02/1.56 319 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_add__cancel__21_1) # label(axiom). [assumption].
% 1.02/1.56 320 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 1.02/1.56 321 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C),D,B,A,A)),E) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),E)),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),D),E)) # label(cls_setsum__subtractf_0) # label(axiom). [assumption].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)). [resolve(313,a,316,a)].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),C) | A = B. [resolve(313,a,317,a)].
% 1.02/1.56 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C) | B = C. [resolve(313,a,318,a)].
% 1.02/1.58 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) = D. [resolve(313,a,320,a)].
% 1.02/1.58 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),B),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),C),D)). [resolve(313,a,321,a)].
% 1.02/1.58 322 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.02/1.58 323 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 1.02/1.58 324 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 1.02/1.58 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(322,a,323,a)].
% 1.02/1.58 325 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.02/1.58 326 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.02/1.58 327 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.02/1.58 328 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.02/1.58 329 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.02/1.58 330 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.02/1.58 331 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.02/1.60 332 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.02/1.60 333 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.02/1.60 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(325,a,326,a)].
% 1.02/1.60 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(325,a,327,a)].
% 1.02/1.60 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat). [resolve(325,a,329,a)].
% 1.02/1.60 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat). [resolve(325,a,330,a)].
% 1.02/1.60 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(325,a,331,a)].
% 1.02/1.60 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(325,a,332,a)].
% 1.02/1.60 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(325,a,333,a)].
% 1.02/1.60 334 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.02/1.60 335 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 1.02/1.60 336 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.60 337 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 1.02/1.60 338 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.60 339 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.02/1.60 340 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 1.02/1.61 341 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 1.02/1.61 342 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 1.02/1.61 343 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | D = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 1.02/1.61 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),A)),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D). [resolve(339,a,340,a)].
% 1.02/1.61 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C)). [resolve(339,a,341,a)].
% 1.02/1.61 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C) = E. [resolve(339,a,342,a)].
% 1.02/1.61 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),D),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),A)),B)),E). [resolve(339,a,343,a)].
% 1.02/1.61 344 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.02/1.61 345 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.02/1.61 346 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.02/1.61 347 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.02/1.61 348 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.02/1.65 349 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.02/1.65 350 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.02/1.65 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(B,A,tc_nat) | B = A. [resolve(344,a,345,a)].
% 1.02/1.65 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(344,a,349,a)].
% 1.02/1.65 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(344,a,350,a)].
% 1.02/1.65 351 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.02/1.65 352 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__algebra__1(B) | C = D | -c_Lim_OLIM(E,F,D,B,A) | -c_Lim_OLIM(E,F,C,B,A) # label(cls_LIM__unique_0) # label(axiom). [assumption].
% 1.02/1.65 353 -class_RealVector_Oreal__normed__algebra__1(A) | c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),B),hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),tc_nat,A,A),A) = hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) # label(cls_powser__zero_0) # label(axiom). [assumption].
% 1.02/1.65 Derived: -class_RealVector_Ometric__space(A) | B = C | -c_Lim_OLIM(D,E,C,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(D,E,B,tc_Complex_Ocomplex,A). [resolve(351,a,352,b)].
% 1.02/1.65 Derived: c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex)),A),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)). [resolve(351,a,353,a)].
% 1.02/1.65 354 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.65 355 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 1.02/1.65 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(354,a,355,a)].
% 1.02/1.65 356 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.65 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(356,a,355,a)].
% 1.02/1.65 357 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.02/1.65 358 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 1.02/1.65 359 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 1.02/1.65 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(357,a,359,a)].
% 1.02/1.65 360 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.02/1.65 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A = C. [resolve(360,a,359,a)].
% 1.02/1.65 361 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.02/1.66 362 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 1.02/1.66 363 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 1.02/1.66 364 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 1.02/1.66 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(361,a,362,a)].
% 1.02/1.66 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(361,a,363,a)].
% 1.02/1.66 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(361,a,364,a)].
% 1.02/1.66 365 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.02/1.66 366 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 1.02/1.66 367 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 1.02/1.66 368 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 1.02/1.66 369 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 1.02/1.66 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(365,a,366,a)].
% 1.02/1.66 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(365,a,368,a)].
% 1.02/1.66 370 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 1.02/1.66 371 -class_Ring__and__Field_Oring__1(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(C,A)),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBC(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B)),D)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) # label(cls_sumr__diff__mult__const2_0) # label(axiom). [assumption].
% 1.02/1.68 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)),C)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex)),A)),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(370,a,371,a)].
% 1.02/1.68 372 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.02/1.68 373 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 1.02/1.68 374 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 1.02/1.68 375 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 1.02/1.68 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(372,a,375,a)].
% 1.02/1.68 376 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.02/1.68 377 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 1.02/1.68 378 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.02/1.68 379 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 1.02/1.68 380 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 1.02/1.68 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(379,a,380,a)].
% 1.02/1.68 381 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.02/1.68 382 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 1.02/1.68 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(381,a,382,a)].
% 1.02/1.68 383 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.02/1.68 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex) | A = B. [resolve(383,a,382,a)].
% 1.02/1.68 384 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.02/1.68 385 c_fequal(A,A,B) # label(cls_ATP_Cputime limit exceeded (core dumped)
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