TSTP Solution File: SWV685-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV685-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 21:14:25 EDT 2022
% Result : Unsatisfiable 23.27s 23.60s
% Output : Refutation 23.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV685-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 06:15:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.06/1.33 ============================== Prover9 ===============================
% 1.06/1.33 Prover9 (32) version 2009-11A, November 2009.
% 1.06/1.33 Process 28122 was started by sandbox on n003.cluster.edu,
% 1.06/1.33 Thu Jun 16 06:15:27 2022
% 1.06/1.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27969_n003.cluster.edu".
% 1.06/1.33 ============================== end of head ===========================
% 1.06/1.33
% 1.06/1.33 ============================== INPUT =================================
% 1.06/1.33
% 1.06/1.33 % Reading from file /tmp/Prover9_27969_n003.cluster.edu
% 1.06/1.33
% 1.06/1.33 set(prolog_style_variables).
% 1.06/1.33 set(auto2).
% 1.06/1.33 % set(auto2) -> set(auto).
% 1.06/1.33 % set(auto) -> set(auto_inference).
% 1.06/1.33 % set(auto) -> set(auto_setup).
% 1.06/1.33 % set(auto_setup) -> set(predicate_elim).
% 1.06/1.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.06/1.33 % set(auto) -> set(auto_limits).
% 1.06/1.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.06/1.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.06/1.33 % set(auto) -> set(auto_denials).
% 1.06/1.33 % set(auto) -> set(auto_process).
% 1.06/1.33 % set(auto2) -> assign(new_constants, 1).
% 1.06/1.33 % set(auto2) -> assign(fold_denial_max, 3).
% 1.06/1.33 % set(auto2) -> assign(max_weight, "200.000").
% 1.06/1.33 % set(auto2) -> assign(max_hours, 1).
% 1.06/1.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.06/1.33 % set(auto2) -> assign(max_seconds, 0).
% 1.06/1.33 % set(auto2) -> assign(max_minutes, 5).
% 1.06/1.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.06/1.33 % set(auto2) -> set(sort_initial_sos).
% 1.06/1.33 % set(auto2) -> assign(sos_limit, -1).
% 1.06/1.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.06/1.33 % set(auto2) -> assign(max_megs, 400).
% 1.06/1.33 % set(auto2) -> assign(stats, some).
% 1.06/1.33 % set(auto2) -> clear(echo_input).
% 1.06/1.33 % set(auto2) -> set(quiet).
% 1.06/1.33 % set(auto2) -> clear(print_initial_clauses).
% 1.06/1.33 % set(auto2) -> clear(print_given).
% 1.06/1.33 assign(lrs_ticks,-1).
% 1.06/1.33 assign(sos_limit,10000).
% 1.06/1.33 assign(order,kbo).
% 1.06/1.33 set(lex_order_vars).
% 1.06/1.33 clear(print_given).
% 1.06/1.33
% 1.06/1.33 % formulas(sos). % not echoed (590 formulas)
% 1.06/1.33
% 1.06/1.33 ============================== end of input ==========================
% 1.06/1.33
% 1.06/1.33 % From the command line: assign(max_seconds, 300).
% 1.06/1.33
% 1.06/1.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.06/1.33
% 1.06/1.33 % Formulas that are not ordinary clauses:
% 1.06/1.33
% 1.06/1.33 ============================== end of process non-clausal formulas ===
% 1.06/1.33
% 1.06/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 1.06/1.33
% 1.06/1.33 ============================== PREDICATE ELIMINATION =================
% 1.06/1.33 1 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.06/1.33 2 -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].
% 1.06/1.33 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(1,a,2,a)].
% 1.06/1.33 3 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.06/1.33 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(3,a,2,a)].
% 1.06/1.33 4 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 1.06/1.33 5 -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].
% 1.06/1.33 6 -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].
% 1.06/1.33 7 -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].
% 1.06/1.33 8 -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].
% 1.06/1.33 9 -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].
% 1.06/1.33 10 -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].
% 1.06/1.33 11 -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].
% 1.06/1.33 12 -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].
% 1.06/1.33 13 -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].
% 1.06/1.33 14 -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].
% 1.06/1.33 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),A),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),A),B)). [resolve(4,a,5,a)].
% 1.06/1.33 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(4,a,7,a)].
% 1.06/1.33 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(4,a,9,a)].
% 1.10/1.36 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(4,a,10,a)].
% 1.10/1.36 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(4,a,11,a)].
% 1.10/1.36 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(4,a,12,a)].
% 1.10/1.36 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(4,a,13,a)].
% 1.10/1.36 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(4,a,14,a)].
% 1.10/1.36 15 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 1.10/1.36 16 -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].
% 1.10/1.36 17 -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].
% 1.10/1.36 18 -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].
% 1.10/1.36 19 -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].
% 1.10/1.36 20 -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].
% 1.10/1.36 21 -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].
% 1.10/1.36 22 -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].
% 1.10/1.36 23 -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].
% 1.10/1.36 24 -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].
% 1.10/1.36 25 -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].
% 1.10/1.36 26 -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].
% 1.10/1.36 27 -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].
% 1.10/1.36 28 -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].
% 1.10/1.36 29 -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].
% 1.10/1.36 30 -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].
% 1.10/1.36 31 -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].
% 1.10/1.36 32 -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].
% 1.10/1.36 33 -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].
% 1.10/1.36 34 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(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),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].
% 1.10/1.36 35 -class_RealVector_Oreal__normed__algebra(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBS(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),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].
% 1.10/1.36 36 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__mult_0) # label(axiom). [assumption].
% 1.10/1.36 37 -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].
% 1.10/1.36 38 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(B,tc_nat,A),hAPP(hAPP(c_COMBB(A,tc_fun(tc_nat,A),B),c_Power_Opower__class_Opower(A)),C)),D),E,hAPP(hAPP(c_Power_Opower__class_Opower(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__power_0) # label(axiom). [assumption].
% 1.10/1.36 39 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_nat,A),hAPP(hAPP(c_COMBB(A,tc_fun(tc_nat,A),tc_nat),c_Power_Opower__class_Opower(A)),B)),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__pow_0) # label(axiom). [assumption].
% 1.10/1.36 40 -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].
% 1.10/1.36 41 -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].
% 1.10/1.36 42 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(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(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].
% 1.10/1.36 43 -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].
% 1.10/1.36 44 -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].
% 1.10/1.36 45 -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].
% 1.10/1.36 46 -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].
% 1.10/1.36 47 -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].
% 1.10/1.36 48 -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].
% 1.10/1.36 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(15,a,16,a)].
% 1.10/1.36 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(15,a,17,a)].
% 1.10/1.36 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(15,a,19,a)].
% 1.10/1.36 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(15,a,21,a)].
% 1.10/1.36 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(15,a,23,a)].
% 1.10/1.36 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(15,a,25,a)].
% 1.10/1.36 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(15,a,26,a)].
% 1.10/1.36 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(15,a,27,a)].
% 1.10/1.36 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(15,a,28,a)].
% 1.10/1.36 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(15,a,29,a)].
% 1.10/1.36 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(15,a,30,a)].
% 1.10/1.36 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(15,a,32,a)].
% 1.10/1.36 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(15,a,33,a)].
% 1.10/1.36 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(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),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(15,a,34,a)].
% 1.10/1.36 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBS(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),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(15,a,35,a)].
% 1.10/1.36 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(15,a,36,a)].
% 1.10/1.36 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(15,a,37,a)].
% 1.10/1.36 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBC(A,tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),A),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),B)),C),D,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(15,a,38,a)].
% 1.10/1.36 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),A)),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(15,a,39,a)].
% 1.10/1.36 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(15,a,40,a)].
% 1.10/1.36 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(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(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(15,a,42,a)].
% 1.10/1.36 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(15,a,43,a)].
% 1.10/1.37 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(15,a,45,a)].
% 1.10/1.37 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(15,a,47,a)].
% 1.10/1.37 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(15,a,48,a)].
% 1.10/1.37 49 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.10/1.37 50 -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].
% 1.10/1.37 51 -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].
% 1.10/1.37 52 -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].
% 1.10/1.37 53 -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].
% 1.10/1.37 54 -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].
% 1.10/1.37 55 -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].
% 1.10/1.37 56 -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].
% 1.10/1.37 57 -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].
% 1.10/1.37 58 -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].
% 1.10/1.37 59 -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].
% 1.10/1.37 60 -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].
% 1.10/1.37 61 -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),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 1.10/1.37 62 -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),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 1.10/1.37 63 -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)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 1.10/1.37 64 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 1.10/1.37 65 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 1.10/1.37 66 -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].
% 1.10/1.37 67 -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].
% 1.10/1.37 68 -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].
% 1.10/1.37 69 -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].
% 1.10/1.37 70 -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].
% 1.10/1.37 71 -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].
% 1.10/1.37 72 -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].
% 1.10/1.37 73 -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].
% 1.10/1.37 74 -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].
% 1.10/1.37 75 -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].
% 1.10/1.37 76 -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].
% 1.10/1.37 77 -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].
% 1.10/1.37 78 -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].
% 1.10/1.37 79 -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].
% 1.10/1.37 80 -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].
% 1.10/1.37 81 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 1.10/1.37 82 -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].
% 1.10/1.37 83 -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].
% 1.10/1.37 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(49,a,50,a)].
% 1.10/1.37 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(49,a,51,a)].
% 1.10/1.37 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(49,a,52,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(49,a,53,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(49,a,54,a)].
% 1.10/1.37 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(49,a,56,a)].
% 1.10/1.37 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(49,a,57,a)].
% 1.10/1.37 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(49,a,58,a)].
% 1.10/1.37 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(49,a,59,a)].
% 1.10/1.37 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),hAPP(c_Suc,B)). [resolve(49,a,61,a)].
% 1.10/1.37 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),hAPP(c_Suc,B)). [resolve(49,a,62,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(49,a,63,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(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(49,a,64,a)].
% 1.10/1.37 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(49,a,66,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(49,a,67,a)].
% 1.10/1.37 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(49,a,69,a)].
% 1.10/1.37 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(49,a,70,a)].
% 1.10/1.37 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(49,a,72,a)].
% 1.10/1.37 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(49,a,73,a)].
% 1.10/1.37 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(49,a,75,a)].
% 1.10/1.37 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(49,a,76,a)].
% 1.10/1.37 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(49,a,77,a)].
% 1.10/1.37 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(49,a,80,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(49,a,81,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(49,a,82,a)].
% 1.10/1.37 84 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.10/1.37 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(84,a,52,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(84,a,53,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(84,a,54,a)].
% 1.10/1.37 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(84,a,56,a)].
% 1.10/1.37 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(84,a,57,a)].
% 1.10/1.37 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(84,a,58,a)].
% 1.10/1.37 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(84,a,59,a)].
% 1.10/1.37 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),hAPP(c_Suc,B)). [resolve(84,a,61,a)].
% 1.10/1.37 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),hAPP(c_Suc,B)). [resolve(84,a,62,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(84,a,63,a)].
% 1.10/1.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(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(84,a,64,a)].
% 1.10/1.37 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(84,a,66,a)].
% 1.10/1.37 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(84,a,67,a)].
% 1.10/1.37 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(84,a,72,a)].
% 1.10/1.41 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(84,a,73,a)].
% 1.10/1.41 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(84,a,75,a)].
% 1.10/1.41 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(84,a,76,a)].
% 1.10/1.41 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(84,a,77,a)].
% 1.10/1.41 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(84,a,80,a)].
% 1.10/1.41 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(84,a,81,a)].
% 1.10/1.41 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(84,a,82,a)].
% 1.10/1.41 85 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.10/1.41 86 -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].
% 1.10/1.41 87 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 1.10/1.41 88 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 1.10/1.41 89 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBS(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oplus__class_Oplus(A)),B)),C),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__sum_0) # label(axiom). [assumption].
% 1.10/1.41 90 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBS(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Ominus__class_Ominus(A)),B)),C),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__diff_0) # label(axiom). [assumption].
% 1.10/1.41 91 -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].
% 1.10/1.41 92 -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].
% 1.10/1.41 93 -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].
% 1.10/1.41 94 -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].
% 1.10/1.41 95 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBS(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Otimes__class_Otimes(A)),B)),C),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__mult_0) # label(axiom). [assumption].
% 1.10/1.41 96 -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].
% 1.10/1.41 97 -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].
% 1.10/1.41 98 -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].
% 1.10/1.41 99 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBC(A,tc_nat,A),hAPP(hAPP(c_COMBB(A,tc_fun(tc_nat,A),A),c_Power_Opower__class_Opower(A)),B)),C),D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__power_0) # label(axiom). [assumption].
% 1.10/1.41 100 -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].
% 1.10/1.41 101 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBS(A,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),A),c_HOL_Oinverse__class_Odivide(A)),B)),C),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].
% 1.10/1.41 102 -class_RealVector_Oreal__normed__field(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBS(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),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].
% 1.10/1.41 103 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),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].
% 1.10/1.41 104 -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].
% 1.10/1.41 105 -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].
% 1.10/1.41 Derived: c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBS(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_Oplus__class_Oplus(tc_Complex_Ocomplex)),A)),B),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(88,a,89,a)].
% 1.10/1.41 Derived: c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBS(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)),B),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(88,a,90,a)].
% 1.10/1.41 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(88,a,91,a)].
% 1.10/1.41 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(88,a,92,a)].
% 1.10/1.41 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(88,a,93,a)].
% 1.10/1.41 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(88,a,94,a)].
% 1.10/1.41 Derived: c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBS(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_Otimes__class_Otimes(tc_Complex_Ocomplex)),A)),B),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(88,a,95,a)].
% 1.10/1.41 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(88,a,96,a)].
% 1.10/1.41 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(88,a,97,a)].
% 1.10/1.41 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(88,a,98,a)].
% 1.10/1.41 Derived: c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBC(tc_Complex_Ocomplex,tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),A)),B),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(88,a,99,a)].
% 1.10/1.42 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(88,a,100,a)].
% 1.10/1.42 Derived: c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBS(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,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(88,a,101,a)].
% 1.10/1.42 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBS(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),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(88,a,102,a)].
% 1.10/1.42 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),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(88,a,103,a)].
% 1.10/1.42 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(88,a,104,a)].
% 1.10/1.42 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(88,a,105,a)].
% 1.10/1.42 106 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 1.10/1.42 107 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C)),D),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].
% 1.10/1.42 108 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C)),D),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].
% 1.10/1.42 109 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C)),D),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].
% 1.10/1.42 110 -class_RealVector_Oreal__normed__vector(A) | c_Limits_Otendsto(hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C)),D),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].
% 1.10/1.42 111 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__diff_0) # label(axiom). [assumption].
% 1.10/1.42 112 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),E),A) | -c_SEQ_OLIMSEQ(C,E,A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add_0) # label(axiom). [assumption].
% 1.10/1.42 113 -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].
% 1.10/1.42 114 -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].
% 1.10/1.42 115 -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].
% 1.10/1.42 116 -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].
% 1.10/1.42 117 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(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) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__add__zero_0) # label(axiom). [assumption].
% 1.10/1.42 118 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),D)),B),c_HOL_Ozero__class_Ozero(A),A) | -c_SEQ_OLIMSEQ(D,C,A) # label(cls_LIMSEQ__diff__approach__zero2_0) # label(axiom). [assumption].
% 1.10/1.42 119 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),B)),D),c_HOL_Ozero__class_Ozero(A),A) | -c_SEQ_OLIMSEQ(D,C,A) # label(cls_LIMSEQ__diff__approach__zero_0) # label(axiom). [assumption].
% 1.10/1.42 120 -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].
% 1.10/1.42 121 -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].
% 1.10/1.42 122 -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].
% 1.10/1.42 123 -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].
% 1.10/1.42 124 -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].
% 1.10/1.42 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(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_Oplus__class_Oplus(tc_Complex_Ocomplex)),B)),C),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(106,a,107,a)].
% 1.10/1.42 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(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,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(106,a,108,a)].
% 1.10/1.42 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBS(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),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(106,a,109,a)].
% 1.10/1.42 Derived: c_Limits_Otendsto(hAPP(hAPP(c_COMBS(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_Oplus__class_Oplus(tc_Complex_Ocomplex)),B)),C),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(106,a,110,a)].
% 1.10/1.42 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(106,a,111,a)].
% 1.10/1.42 Derived: c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),D),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,D,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(106,a,112,a)].
% 1.10/1.42 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(106,a,113,a)].
% 1.10/1.42 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(106,a,114,a)].
% 1.18/1.43 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(106,a,115,a)].
% 1.18/1.43 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(106,a,116,a)].
% 1.18/1.43 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(hAPP(hAPP(c_COMBS(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_Oplus__class_Oplus(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) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(106,a,117,a)].
% 1.18/1.43 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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)),C)),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex). [resolve(106,a,118,a)].
% 1.18/1.43 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBS(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),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(C,B,tc_Complex_Ocomplex). [resolve(106,a,119,a)].
% 1.18/1.43 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(106,a,120,b)].
% 1.18/1.43 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(106,a,121,b)].
% 1.18/1.43 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(106,a,124,b)].
% 1.18/1.43 125 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 1.18/1.43 126 -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].
% 1.18/1.43 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(125,a,126,a)].
% 1.18/1.44 127 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.18/1.44 128 -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].
% 1.18/1.44 129 -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].
% 1.18/1.44 130 -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].
% 1.18/1.44 131 -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].
% 1.18/1.44 132 -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].
% 1.18/1.44 133 -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].
% 1.18/1.44 134 -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].
% 1.18/1.44 135 -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].
% 1.18/1.44 136 -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].
% 1.18/1.44 137 -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].
% 1.18/1.44 138 -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].
% 1.18/1.44 139 -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].
% 1.18/1.44 140 -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].
% 1.18/1.44 141 -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].
% 1.18/1.44 142 -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].
% 1.18/1.44 143 -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].
% 1.18/1.44 144 -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].
% 1.18/1.44 145 -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].
% 1.18/1.44 146 -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].
% 1.18/1.44 147 -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].
% 1.18/1.44 148 -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].
% 1.18/1.44 149 -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].
% 1.18/1.44 150 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C))) = hAPP(hAPP(c_Power_Opower__class_Opower(A),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),B),E))),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__divides__special_0) # label(axiom). [assumption].
% 1.18/1.44 151 -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].
% 1.18/1.44 152 -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].
% 1.18/1.44 153 -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].
% 1.18/1.44 154 -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].
% 1.18/1.44 155 -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].
% 1.18/1.44 156 -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].
% 1.18/1.44 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(127,a,130,a)].
% 1.18/1.44 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(127,a,131,a)].
% 1.18/1.44 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(127,a,132,a)].
% 1.18/1.45 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(127,a,133,a)].
% 1.18/1.45 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(127,a,134,a)].
% 1.18/1.45 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(127,a,135,a)].
% 1.18/1.45 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(127,a,136,a)].
% 1.18/1.45 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(127,a,137,a)].
% 1.18/1.45 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(127,a,138,a)].
% 1.18/1.45 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(127,a,139,a)].
% 1.18/1.45 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(127,a,140,a)].
% 1.18/1.45 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(127,a,141,a)].
% 1.18/1.45 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(127,a,144,a)].
% 1.18/1.45 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(127,a,145,a)].
% 1.18/1.46 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(127,a,146,a)].
% 1.18/1.46 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(127,a,147,a)].
% 1.18/1.46 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),B))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),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),A),D))),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(127,a,150,a)].
% 1.18/1.46 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(127,a,152,a)].
% 1.18/1.46 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(127,a,154,a)].
% 1.18/1.46 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(127,a,155,a)].
% 1.18/1.46 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(127,a,156,a)].
% 1.18/1.46 157 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.18/1.46 158 -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].
% 1.18/1.46 159 -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].
% 1.18/1.46 160 -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].
% 1.18/1.46 161 -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].
% 1.18/1.46 162 -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].
% 1.18/1.47 163 -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].
% 1.18/1.47 164 -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].
% 1.18/1.47 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(157,a,158,a)].
% 1.18/1.47 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(157,a,159,a)].
% 1.18/1.47 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(157,a,160,a)].
% 1.18/1.47 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(157,a,161,a)].
% 1.18/1.47 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(157,a,162,a)].
% 1.18/1.47 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(157,a,163,a)].
% 1.18/1.47 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(157,a,164,a)].
% 1.18/1.47 165 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.18/1.47 166 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat)) = 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].
% 1.18/1.47 167 -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].
% 1.18/1.47 168 -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].
% 1.18/1.47 169 -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].
% 1.18/1.47 170 -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].
% 1.18/1.47 171 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),B),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),D))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat))) # label(cls_sumr__offset3_0) # label(axiom). [assumption].
% 1.18/1.47 172 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C)),D)),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].
% 1.18/1.47 173 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),B),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat)) # label(cls_setsum__shift__bounds__Suc__ivl_0) # label(axiom). [assumption].
% 1.18/1.47 174 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat))),hAPP(B,D)) | c_HOL_Oord__class_Oless(D,C,tc_nat) # label(cls_setsum__op__ivl__Suc_1) # label(axiom). [assumption].
% 1.18/1.47 175 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),D,tc_nat))) | -c_HOL_Oord__class_Oless(C,D,tc_nat) # label(cls_setsum__head__upt__Suc_0) # label(axiom). [assumption].
% 1.18/1.47 176 -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].
% 1.18/1.47 177 -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),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) # label(cls_setsum__shift__lb__Suc0__0__upt_0) # label(axiom). [assumption].
% 1.18/1.47 178 -class_Power_Opower(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B))),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)))),hAPP(c_Power_Opower__class_Opower(A),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) # label(cls_lemma__realpow__rev__sumr_0) # label(axiom). [assumption].
% 1.18/1.47 179 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),D),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),B),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),D))),c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat)) # label(cls_setsum__shift__bounds__nat__ivl_0) # label(axiom). [assumption].
% 1.18/1.47 180 -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].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(165,a,166,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),A),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))). [resolve(165,a,171,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBS(A,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Oplus__class_Oplus(tc_nat)),B)),C)),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(165,a,172,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),A),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)). [resolve(165,a,173,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(A,C)) | c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(165,a,174,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat))) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(165,a,175,a)].
% 1.18/1.47 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),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(165,a,177,a)].
% 1.18/1.47 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBS(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A))),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBS(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),hAPP(c_Power_Opower__class_Opower(tc_nat),B))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)). [resolve(165,a,178,b)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),A),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)). [resolve(165,a,179,a)].
% 1.18/1.47 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(165,a,180,a)].
% 1.18/1.47 181 class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(181,a,166,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),A),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))). [resolve(181,a,171,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBS(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_Oplus__class_Oplus(tc_Complex_Ocomplex)),B)),C)),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(181,a,172,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),A),c_Suc)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)). [resolve(181,a,173,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat))),hAPP(A,C)) | c_HOL_Oord__class_Oless(C,B,tc_nat). [resolve(181,a,174,a)].
% 1.18/1.47 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = 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),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat))) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(181,a,175,a)].
% 1.18/1.47 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),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(181,a,177,a)].
% 1.18/1.47 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBS(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)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A))),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBS(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)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)). [resolve(181,a,178,b)].
% 1.18/1.48 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),A),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat)). [resolve(181,a,179,a)].
% 1.18/1.48 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(181,a,180,a)].
% 1.18/1.48 182 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.18/1.48 183 -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].
% 1.18/1.48 184 -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].
% 1.18/1.48 185 -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].
% 1.18/1.48 186 -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].
% 1.18/1.48 187 -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].
% 1.23/1.50 188 -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].
% 1.23/1.50 189 -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].
% 1.23/1.50 190 -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].
% 1.23/1.50 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(182,a,183,a)].
% 1.23/1.50 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(182,a,184,a)].
% 1.23/1.50 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(182,a,186,a)].
% 1.23/1.50 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(182,a,187,a)].
% 1.23/1.50 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(182,a,188,a)].
% 1.23/1.50 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(182,a,189,a)].
% 1.23/1.50 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(182,a,190,a)].
% 1.23/1.50 191 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.23/1.50 192 -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].
% 1.23/1.50 193 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.23/1.50 194 -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)),hAPP(c_Suc,B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 1.23/1.50 195 -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].
% 1.23/1.50 196 -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].
% 1.23/1.50 197 -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].
% 1.23/1.50 198 -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].
% 1.23/1.50 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(193,a,194,a)].
% 1.23/1.50 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(193,a,195,a)].
% 1.23/1.50 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(193,a,196,a)].
% 1.23/1.50 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(193,a,197,a)].
% 1.23/1.50 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(193,a,198,a)].
% 1.23/1.50 199 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.23/1.50 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)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(199,a,194,a)].
% 1.23/1.50 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(199,a,197,a)].
% 1.23/1.50 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(199,a,198,a)].
% 1.23/1.54 200 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.23/1.54 201 -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].
% 1.23/1.54 202 -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].
% 1.23/1.54 203 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.23/1.54 204 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.23/1.54 205 -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].
% 1.23/1.54 206 -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].
% 1.23/1.54 207 -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].
% 1.23/1.54 208 -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].
% 1.23/1.54 209 -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].
% 1.23/1.54 210 -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].
% 1.23/1.54 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(204,a,205,a)].
% 1.23/1.54 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(204,a,206,a)].
% 1.23/1.54 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(204,a,207,a)].
% 1.23/1.54 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(204,a,209,a)].
% 1.23/1.54 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(204,a,210,a)].
% 1.23/1.54 211 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 1.23/1.54 212 -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].
% 1.23/1.54 213 -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].
% 1.23/1.54 214 -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].
% 1.23/1.54 215 -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].
% 1.23/1.54 216 -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].
% 1.23/1.54 217 -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].
% 1.23/1.54 218 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),B),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))) # label(cls_sumr__offset_0) # label(axiom). [assumption].
% 1.23/1.54 219 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C)),D)),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].
% 1.23/1.54 220 -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].
% 1.23/1.54 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(211,a,214,a)].
% 1.23/1.54 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(211,a,215,a)].
% 1.23/1.54 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(211,a,216,a)].
% 1.23/1.54 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),A),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),c_HOL_Oplus__class_Oplus(tc_nat)),B))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat))),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))). [resolve(211,a,218,a)].
% 1.23/1.54 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBS(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) = 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(211,a,219,a)].
% 1.31/1.57 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(211,a,220,a)].
% 1.31/1.57 221 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.31/1.57 222 -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].
% 1.31/1.57 223 -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].
% 1.31/1.57 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(221,a,222,a)].
% 1.31/1.57 224 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.31/1.57 225 -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].
% 1.31/1.57 226 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.31/1.57 227 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 1.31/1.57 228 -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].
% 1.31/1.57 229 -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].
% 1.31/1.57 230 -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].
% 1.31/1.57 231 -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].
% 1.31/1.57 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(227,a,228,a)].
% 1.31/1.59 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(227,a,229,a)].
% 1.31/1.59 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(227,a,230,a)].
% 1.31/1.59 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(227,a,231,a)].
% 1.31/1.59 232 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.31/1.59 233 -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].
% 1.31/1.59 234 -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].
% 1.31/1.59 235 -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].
% 1.31/1.59 236 -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].
% 1.31/1.59 237 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.31/1.59 238 -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].
% 1.31/1.59 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(B,A,tc_nat) | B = A. [resolve(232,a,233,a)].
% 1.31/1.59 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(232,a,237,a)].
% 1.31/1.59 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(232,a,238,a)].
% 1.31/1.59 239 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.31/1.59 240 -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].
% 1.31/1.59 241 -class_RealVector_Oreal__normed__algebra__1(A) | c_Series_Osuminf(hAPP(hAPP(c_COMBS(tc_nat,A,A),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))),A) = hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) # label(cls_powser__zero_0) # label(axiom). [assumption].
% 1.31/1.59 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(239,a,240,b)].
% 1.31/1.59 Derived: c_Series_Osuminf(hAPP(hAPP(c_COMBS(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)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))),tc_Complex_Ocomplex) = hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)). [resolve(239,a,241,a)].
% 1.31/1.61 242 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.31/1.61 243 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 1.31/1.61 244 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(cls_power__add_0) # label(axiom). [assumption].
% 1.31/1.61 245 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Suc,C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B))),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),D)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))) # label(cls_lemma__realpow__diff__sumr2_0) # label(axiom). [assumption].
% 1.31/1.61 246 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | 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)),hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)))),hAPP(c_Power_Opower__class_Opower(A),B)))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B))),hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)))),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat)) # label(cls_lemma__termdiff1_0) # label(axiom). [assumption].
% 1.31/1.61 247 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B))),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,D))))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,A),hAPP(hAPP(c_COMBS(tc_nat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B))),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat))) # label(cls_lemma__realpow__diff__sumr_0) # label(axiom). [assumption].
% 1.31/1.61 248 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) # label(cls_power__mult_0) # label(axiom). [assumption].
% 1.31/1.61 249 -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].
% 1.31/1.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(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(242,a,243,a)].
% 1.31/1.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)). [resolve(242,a,244,a)].
% 1.31/1.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),hAPP(c_Suc,B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBS(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A))),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,B),tc_nat))). [resolve(242,a,245,b)].
% 1.31/1.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBC(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(tc_nat)),hAPP(hAPP(c_COMBS(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),hAPP(c_Power_Opower__class_Opower(tc_nat),A)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBS(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A))),hAPP(hAPP(c_COMBS(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)). [resolve(242,a,246,b)].
% 1.31/1.61 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_nat) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBS(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A))),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C))))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),hAPP(hAPP(c_COMBS(tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A))),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))). [resolve(242,a,247,b)].
% 1.31/1.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C). [resolve(242,a,248,a)].
% 1.31/1.61 250 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.31/1.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(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(250,a,243,a)].
% 1.31/1.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),A),C)). [resolve(250,a,244,a)].
% 1.31/1.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(c_Suc,B))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),hAPP(c_Suc,B))) = 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_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBS(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)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A))),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,B),tc_nat))). [resolve(250,a,245,b)].
% 1.31/1.61 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) | 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)),hAPP(hAPP(c_COMBS(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)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBS(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)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A))),hAPP(hAPP(c_COMBS(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)),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)). [resolve(250,a,246,b)].
% 1.36/1.61 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) | hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBS(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)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A))),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C))))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBS(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)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A))),hAPP(hAPP(c_COMBB(tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat))). [resolve(250,a,247,b)].
% 1.36/1.61 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C). [resolve(250,a,248,a)].
% 1.36/1.61 251 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.36/1.61 252 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 1.36/1.61 253 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 1.36/1.61 254 -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].
% 1.36/1.61 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(251,a,252,a)].
% 1.36/1.61 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(251,a,253,a)].
% 1.36/1.61 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(251,a,254,a)].
% 1.36/1.61 255 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.36/1.61 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(255,a,252,a)].
% 1.36/1.65 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(255,a,253,a)].
% 1.36/1.65 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(255,a,254,a)].
% 1.36/1.65 256 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.36/1.65 257 -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].
% 1.36/1.65 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(256,a,257,a)].
% 1.36/1.65 258 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.36/1.65 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(258,a,257,a)].
% 1.36/1.65 259 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.36/1.65 260 -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].
% 1.36/1.65 261 -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].
% 1.36/1.65 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(259,a,261,a)].
% 1.36/1.65 262 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.36/1.65 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(262,a,261,a)].
% 1.36/1.65 263 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.36/1.65 264 -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].
% 1.36/1.65 265 -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].
% 1.36/1.65 266 -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].
% 1.36/1.65 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(263,a,264,a)].
% 1.36/1.65 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(263,a,265,a)].
% 1.36/1.65 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(263,a,266,a)].
% 1.40/1.66 267 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 1.40/1.66 268 -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].
% 1.40/1.66 269 -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].
% 1.40/1.66 270 -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].
% 1.40/1.66 271 -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].
% 1.40/1.66 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(267,a,268,a)].
% 1.40/1.66 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(267,a,270,a)].
% 1.40/1.66 272 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 1.40/1.66 273 -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),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat))),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)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)) # label(cls_sumr__diff__mult__const2_0) # label(axiom). [assumption].
% 1.40/1.66 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat))),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)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)). [resolve(272,a,273,a)].
% 1.40/1.66 274 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].
% 1.40/1.66 275 -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].
% 1.40/1.66 276 -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].
% 1.40/1.66 277 -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].
% 1.40/1.67 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(274,a,277,a)].
% 1.40/1.67 278 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.40/1.67 279 -class_Ring__and__Field_Omult__zero(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__zero__right_0) # label(axiom). [assumption].
% 1.40/1.67 280 -class_Ring__and__Field_Omult__zero(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__zero__left_0) # label(axiom). [assumption].
% 1.40/1.67 281 -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].
% 1.40/1.67 282 -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].
% 1.40/1.67 283 -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].
% 1.40/1.68 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(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(278,a,282,c)].
% 1.40/1.68 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(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(278,a,283,c)].
% 1.40/1.68 284 class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.40/1.68 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Ono__zero__divisors(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(284,a,282,c)].
% 1.40/1.68 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Ono__zero__divisors(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(284,a,283,c)].
% 1.40/1.68 285 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.40/1.68 286 -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].
% 1.40/1.68 287 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.99/2.31 288 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.99/2.31 289 -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].
% 1.99/2.31 290 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.99/2.31 291 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].
% 1.99/2.31 292 -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].
% 1.99/2.31 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(291,a,292,a)].
% 1.99/2.31 293 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.99/2.31 294 -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].
% 1.99/2.31 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(293,a,294,a)].
% 1.99/2.31 295 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.99/2.31 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(295,a,294,a)].
% 1.99/2.31 296 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.99/2.31 297 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.99/2.31 Derived: A = A. [resolve(296,b,297,a)].
% 1.99/2.31
% 1.99/2.31 ============================== end predicate elimination =============
% 1.99/2.31
% 1.99/2.31 Auto_denials: (non-Horn, no changes).
% 1.99/2.31
% 1.99/2.31 Term ordering decisions:
% 1.99/2.31 Function symbol KB weights: tc_nat=1. tc_Complex_Ocomplex=1. c_Suc=1. tc_bool=1. v_i=1. v_n=1. v_a=1. hAPP=1. tc_fun=1. c_Finite__Set_Osetsum=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Series_Osuminf=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ominus__class_Ominus=1. c_Power_Opower__class_Opower=1. c_HOL_Oinverse__class_Odivide=1. c_FFT__Mirabelle_Oroot=1. c_COMBB=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_COMBC=1. c_COMBS=1. c_FFT__Mirabelle_ODFT=1. c_FFT__Mirabelle_OIDFT=1.
% 1.99/2.31
% 1.99/2.31 ============================== end of process initial clauses ========
% 1.99/2.31
% 1.99/2.31 ============================== CLAUSES FOR SEARCH ====================
% 1.99/2.31
% 1.99/2.31 ============================== end of clauses for search =============
% 1.99/2.31
% 1.99/2.31 ============================== SEARCH ================================
% 1.99/2.31
% 1.99/2.31 % Starting search at 0.50 seconds.
% 1.99/2.31
% 1.99/2.31 Low Water (keep): wt=109.000, iters=3584
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% 1.99/2.31 Low Water (keep): wt=70.000, iters=3347
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% 1.99/2.31 Low Water (keep): wt=69.000, iters=3334
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% 1.99/2.31 Low Water (keep): wt=68.000, iters=3413
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% 1.99/2.31 Low Water (keep): wt=67.000, iters=3826
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% 1.99/2.31 Low Water (keep): wt=47.000, iters=3427
% 23.27/23.60
% 23.27/23.60 Low Water (keep): wt=46.000, iters=3378
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% 23.27/23.60 Low Water (keep): wt=43.000, iters=3400
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% 23.27/23.60 Low Water (keep): wt=40.000, iters=3343
% 23.27/23.60
% 23.27/23.60 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 77 (0.00 of 1.15 sec).
% 23.27/23.60
% 23.27/23.60 Low Water (keep): wt=38.000, iters=3349
% 23.27/23.60
% 23.27/23.60 Low Water (keep): wt=37.000, iters=3358
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% 23.27/23.60 Low Water (keep): wt=36.000, iters=3421
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% 23.27/23.60 Low Water (keep): wt=35.000, iters=3343
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% 23.27/23.60 Low Water (keep): wt=34.000, iters=3358
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% 23.27/23.60 Low Water (keep): wt=33.000, iters=3342
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% 23.27/23.60 Low Water (keep): wt=32.000, iters=3394
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% 23.27/23.60 Low Water (keep): wt=31.000, iters=3385
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% 23.27/23.60 Low Water (keep): wt=30.000, iters=3341
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% 23.27/23.60 Low Water (keep): wt=28.000, iters=3335
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% 23.27/23.60 Low Water (keep): wt=27.000, iters=3337
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% 23.27/23.60 Low Water (keep): wt=26.000, iters=3345
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% 23.27/23.60 Low Water (keep): wt=25.000, iters=3517
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% 23.27/23.60 Low Water (keep): wt=24.000, iters=3358
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% 23.27/23.60 Low Water (keep): wt=23.000, iters=3361
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% 23.27/23.60 Low Water (keep): wt=22.000, iters=3342
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% 23.27/23.60 Low Water (keep): wt=21.000, iters=3346
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% 23.27/23.60 Low Water (keep): wt=20.000, iters=3344
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% 23.27/23.60 Low Water (displace): id=4080, wt=199.000
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% 23.27/23.60 Low Water (displace): id=4098, wt=197.000
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% 23.27/23.60 Low Water (displace): id=4099, wt=195.000
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% 23.27/23.60 Low Water (displace): id=4094, wt=181.000
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% 23.27/23.60 Low Water (displace): id=4089, wt=170.000
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% 23.27/23.60 Low Water (displace): id=4328, wt=163.000
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% 23.27/23.60 Low Water (displace): id=4083, wt=159.000
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% 23.27/23.60 Low Water (displace): id=3948, wt=157.000
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% 23.27/23.60 Low Water (displace): id=3967, wt=155.000
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% 23.27/23.60 Low Water (displace): id=3968, wt=153.000
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% 23.27/23.60 Low Water (displace): id=4088, wt=150.000
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% 23.27/23.60 Low Water (displace): id=4043, wt=143.000
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% 23.27/23.60 Low Water (displace): id=4303, wt=137.000
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% 23.27/23.60 Low Water (displace): id=4335, wt=135.000
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% 23.27/23.60 Low Water (displace): id=4336, wt=133.000
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% 23.27/23.60 Low Water (displace): id=4378, wt=127.000
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% 23.27/23.60 Low Water (displace): id=3962, wt=126.000
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% 23.27/23.60 Low Water (displace): id=3080, wt=125.000
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% 23.27/23.60 Low Water (displace): id=4086, wt=124.000
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% 23.27/23.60 Low Water (displace): id=4312, wt=123.000
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% 23.27/23.60 Low Water (displace): id=3321, wt=122.000
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% 23.27/23.60 Low Water (displace): id=3180, wt=121.000
% 23.27/23.60
% 23.27/23.60 Low Water (displace): id=4095, wt=120.000
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% 23.27/23.60 Low Water (displace): id=3879, wt=119.000
% 23.27/23.60
% 23.27/23.60 Low Water (displace): id=3895, wt=118.000
% 23.27/23.60
% 23.27/23.60 Low Water (displace): id=4387, wt=117.000
% 23.27/23.60
% 23.27/23.60 Low Water (displace): id=3942, wt=116.000
% 23.27/23.60
% 23.27/23.60 Low Water (displace): id=3957, wt=115.000
% 23.27/23.60
% 23.27/23.60 Low Water (displace): id=11983, wt=18.000
% 23.27/23.60
% 23.27/23.60 Low Water (displace): id=12174, wt=17.000
% 23.27/23.60
% 23.27/23.60 Low Water (keep): wt=19.000, iters=3346
% 23.27/23.60
% 23.27/23.60 Low Water (keep): wt=18.000, iters=3333
% 23.27/23.60
% 23.27/23.60 ============================== PROOF =================================
% 23.27/23.60 % SZS status Unsatisfiable
% 23.27/23.60 % SZS output start Refutation
% 23.27/23.60
% 23.27/23.60 % Proof 1 at 21.71 (+ 0.67) seconds.
% 23.27/23.60 % Length of proof is 16.
% 23.27/23.60 % Level of proof is 6.
% 23.27/23.60 % Maximum clause weight is 30.000.
% 23.27/23.60 % Given clauses 6549.
% 23.27/23.60
% 23.27/23.60 301 hAPP(c_Suc,A) != c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_nat_Osimps_I3_J_0) # label(axiom). [assumption].
% 23.27/23.60 310 A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_natgb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 23.27/23.60 311 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != A | c_HOL_Ozero__class_Ozero(tc_nat) = B. [copy(310),flip(a),flip(b)].
% 23.27/23.60 320 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A # label(cls_plus__nat_Oadd__0_0) # label(axiom). [assumption].
% 23.27/23.60 420 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)) # label(cls_add__Suc__shift_0) # label(axiom). [assumption].
% 23.27/23.60 427 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) # label(cls_add__Suc_0) # label(axiom). [assumption].
% 23.27/23.60 428 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)). [copy(427),rewrite([420(6)])].
% 23.27/23.60 431 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A) # label(cls_nat__add__commute_0) # label(axiom). [assumption].
% 23.27/23.60 480 hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)) # label(cls_COMBB__def_0) # label(axiom). [assumption].
% 23.27/23.60 482 hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)) # label(cls_COMBS__def_0) # label(axiom). [assumption].
% 23.27/23.60 1356 hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != A. [para(428(a,1),311(a,1)),flip(b),unit_del(b,301)].
% 23.27/23.60 1721 hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))),E) = hAPP(hAPP(D,E),E). [para(320(a,1),482(a,2,2))].
% 23.27/23.60 4868 hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != B. [para(431(a,1),1356(a,1,2))].
% 23.27/23.60 4901 hAPP(c_Suc,hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_HOL_Oplus__class_Oplus(tc_nat)),D),E)) != hAPP(D,E). [para(482(a,2),4868(a,1,2))].
% 23.27/23.60 70600 hAPP(hAPP(A,B),B) != hAPP(c_Suc,hAPP(hAPP(hAPP(c_COMBS(C,D,E),c_HOL_Oplus__class_Oplus(tc_nat)),hAPP(hAPP(c_COMBS(F,V6,V7),A),hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))),B)). [para(1721(a,1),4901(a,2)),flip(a)].
% 23.27/23.60 70601 $F. [resolve(70600,a,480,a)].
% 23.27/23.60
% 23.27/23.60 % SZS output end Refutation
% 23.27/23.60 ============================== end of proof ==========================
% 23.27/23.60
% 23.27/23.60 ============================== STATISTICS ============================
% 23.27/23.60
% 23.27/23.60 Given=6549. Generated=1130461. Kept=70122. proofs=1.
% 23.27/23.60 Usable=6534. Sos=9999. Demods=1166. Limbo=46, Disabled=54368. Hints=0.
% 23.27/23.60 Megabytes=71.77.
% 23.27/23.60 User_CPU=21.71, System_CPU=0.67, Wall_clock=22.
% 23.27/23.60
% 23.27/23.60 ============================== end of statistics =====================
% 23.27/23.60
% 23.27/23.60 ============================== end of search =========================
% 23.27/23.60
% 23.27/23.60 THEOREM PROVED
% 23.27/23.60 % SZS status Unsatisfiable
% 23.27/23.60
% 23.27/23.60 Exiting with 1 proof.
% 23.27/23.60
% 23.27/23.60 Process 28122 exit (max_proofs) Thu Jun 16 06:15:49 2022
% 23.27/23.60 Prover9 interrupted
%------------------------------------------------------------------------------