TSTP Solution File: SWV601-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV601-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n025.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 : 300s
% DateTime : Thu Aug 31 23:05:34 EDT 2023
% Result : Unsatisfiable 133.97s 17.51s
% Output : Proof 133.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV601-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31 % Computer : n025.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Aug 29 09:14:40 EDT 2023
% 0.11/0.32 % CPUTime :
% 133.97/17.51 Command-line arguments: --flatten
% 133.97/17.51
% 133.97/17.51 % SZS status Unsatisfiable
% 133.97/17.51
% 133.97/17.57 % SZS output start Proof
% 133.97/17.57 Take the following subset of the input axioms:
% 133.97/17.57 fof(cls_Complex__eq__0_0, axiom, ![V_a, V_b]: (c_Complex_Ocomplex_OComplex(V_a, V_b)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | V_a=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 133.97/17.57 fof(cls_Complex__eq__0_1, axiom, ![V_a2, V_b2]: (c_Complex_Ocomplex_OComplex(V_a2, V_b2)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | V_b2=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 133.97/17.57 fof(cls_add__0__left_0, axiom, ![T_a, V_a2]: (~class_OrderedGroup_Omonoid__add(T_a) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a), V_a2, T_a)=V_a2)).
% 133.97/17.57 fof(cls_add__diff__cancel_0, axiom, ![T_a2, V_a2, V_b2]: (~class_OrderedGroup_Ogroup__add(T_a2) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a2, V_b2, T_a2), V_b2, T_a2)=V_a2)).
% 133.97/17.57 fof(cls_conjecture_0, negated_conjecture, c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 133.97/17.57 fof(cls_cos__minus_0, axiom, ![V_x]: c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(V_x, tc_RealDef_Oreal))=c_Transcendental_Ocos(V_x)).
% 133.97/17.57 fof(cls_mult__eq__0__iff_1, axiom, ![T_a2, V_b2]: (~class_Ring__and__Field_Oring__no__zero__divisors(T_a2) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), V_b2, T_a2)=c_HOL_Ozero__class_Ozero(T_a2))).
% 133.97/17.57 fof(cls_mult__zero__left_0, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Omult__zero(T_a2) | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), V_a2, T_a2)=c_HOL_Ozero__class_Ozero(T_a2))).
% 133.97/17.57 fof(cls_neg__equal__zero_1, axiom, ![T_a2]: (~class_OrderedGroup_Oordered__ab__group__add(T_a2) | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a2), T_a2)=c_HOL_Ozero__class_Ozero(T_a2))).
% 133.97/17.57 fof(cls_real__diff__def_0, axiom, ![V_r, V_s]: c_HOL_Ominus__class_Ominus(V_r, V_s, tc_RealDef_Oreal)=c_HOL_Oplus__class_Oplus(V_r, c_HOL_Ouminus__class_Ouminus(V_s, tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 133.97/17.57 fof(cls_real__mult__commute_0, axiom, ![V_w, V_z]: c_HOL_Otimes__class_Otimes(V_z, V_w, tc_RealDef_Oreal)=c_HOL_Otimes__class_Otimes(V_w, V_z, tc_RealDef_Oreal)).
% 133.97/17.57 fof(cls_real__zero__not__eq__one_0, axiom, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_HOL_Oone__class_Oone(tc_RealDef_Oreal)).
% 133.97/17.57 fof(cls_sin__add_0, axiom, ![V_y, V_x2]: c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x2, V_y, tc_RealDef_Oreal))=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x2), c_Transcendental_Ocos(V_y), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x2), c_Transcendental_Osin(V_y), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 133.97/17.57 fof(cls_sin__minus_0, axiom, ![V_x2]: c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(V_x2, tc_RealDef_Oreal))=c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x2), tc_RealDef_Oreal)).
% 133.97/17.57 fof(cls_sin__pi__half_0, axiom, c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal))=c_HOL_Oone__class_Oone(tc_RealDef_Oreal)).
% 133.97/17.57 fof(clsarity_Complex__Ocomplex__RealVector_Oreal__field, axiom, class_RealVector_Oreal__field(tc_Complex_Ocomplex)).
% 133.97/17.57 fof(clsarity_Int__Oint__Ring__and__Field_Opordered__ring, axiom, class_Ring__and__Field_Opordered__ring(tc_Int_Oint)).
% 133.97/17.57 fof(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add, axiom, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)).
% 133.97/17.57 fof(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, axiom, class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)).
% 133.97/17.57 fof(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add, axiom, class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)).
% 133.97/17.57 fof(clsarity_RealDef__Oreal__RealVector_Oreal__field, axiom, class_RealVector_Oreal__field(tc_RealDef_Oreal)).
% 133.97/17.57 fof(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, axiom, class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal)).
% 133.97/17.57 fof(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, axiom, class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal)).
% 133.97/17.57 fof(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors, axiom, class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal)).
% 133.97/17.57 fof(clsarity_nat__Ring__and__Field_Omult__mono, axiom, class_Ring__and__Field_Omult__mono(tc_nat)).
% 133.97/17.57 fof(clsarity_nat__Ring__and__Field_Omult__mono1, axiom, class_Ring__and__Field_Omult__mono1(tc_nat)).
% 133.97/17.57
% 133.97/17.57 Now clausify the problem and encode Horn clauses using encoding 3 of
% 133.97/17.57 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 133.97/17.57 We repeatedly replace C & s=t => u=v by the two clauses:
% 133.97/17.57 fresh(y, y, x1...xn) = u
% 133.97/17.57 C => fresh(s, t, x1...xn) = v
% 133.97/17.57 where fresh is a fresh function symbol and x1..xn are the free
% 133.97/17.57 variables of u and v.
% 133.97/17.57 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 133.97/17.57 input problem has no model of domain size 1).
% 133.97/17.57
% 133.97/17.57 The encoding turns the above axioms into the following unit equations and goals:
% 133.97/17.57
% 133.97/17.57 Axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field): class_RealVector_Oreal__field(tc_Complex_Ocomplex) = true2.
% 133.97/17.57 Axiom 2 (clsarity_RealDef__Oreal__RealVector_Oreal__field): class_RealVector_Oreal__field(tc_RealDef_Oreal) = true2.
% 133.97/17.57 Axiom 3 (clsarity_nat__Ring__and__Field_Omult__mono1): class_Ring__and__Field_Omult__mono1(tc_nat) = true2.
% 133.97/17.57 Axiom 4 (clsarity_nat__Ring__and__Field_Omult__mono): class_Ring__and__Field_Omult__mono(tc_nat) = true2.
% 133.97/17.57 Axiom 5 (clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors): class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) = true2.
% 133.97/17.57 Axiom 6 (clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add): class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) = true2.
% 133.97/17.57 Axiom 7 (clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add): class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) = true2.
% 133.97/17.57 Axiom 8 (clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero): class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) = true2.
% 133.97/17.57 Axiom 9 (clsarity_Int__Oint__Ring__and__Field_Opordered__ring): class_Ring__and__Field_Opordered__ring(tc_Int_Oint) = true2.
% 133.97/17.57 Axiom 10 (clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring): class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) = true2.
% 133.97/17.57 Axiom 11 (clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add): class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) = true2.
% 133.97/17.57 Axiom 12 (cls_neg__equal__zero_1): fresh248(X, X, Y) = c_HOL_Ozero__class_Ozero(Y).
% 133.97/17.57 Axiom 13 (cls_Complex__eq__0_1): fresh34(X, X, Y) = Y.
% 133.97/17.58 Axiom 14 (cls_Complex__eq__0_0): fresh33(X, X, Y) = Y.
% 133.97/17.58 Axiom 15 (cls_cos__minus_0): c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(X, tc_RealDef_Oreal)) = c_Transcendental_Ocos(X).
% 133.97/17.58 Axiom 16 (cls_sin__minus_0): c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(X, tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(X), tc_RealDef_Oreal).
% 133.97/17.58 Axiom 17 (cls_real__mult__commute_0): c_HOL_Otimes__class_Otimes(X, Y, tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(Y, X, tc_RealDef_Oreal).
% 133.97/17.58 Axiom 18 (cls_mult__eq__0__iff_1): fresh323(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 133.97/17.58 Axiom 19 (cls_mult__zero__left_0): fresh262(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 133.97/17.58 Axiom 20 (cls_neg__equal__zero_1): fresh248(class_OrderedGroup_Oordered__ab__group__add(X), true2, X) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X), X).
% 133.97/17.58 Axiom 21 (cls_add__0__left_0): fresh43(X, X, Y, Z) = Z.
% 133.97/17.58 Axiom 22 (cls_mult__eq__0__iff_1): fresh323(class_Ring__and__Field_Oring__no__zero__divisors(X), true2, X, Y) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X), Y, X).
% 133.97/17.58 Axiom 23 (cls_mult__zero__left_0): fresh262(class_Ring__and__Field_Omult__zero(X), true2, X, Y) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X), Y, X).
% 133.97/17.58 Axiom 24 (cls_add__diff__cancel_0): fresh55(X, X, Y, Z, W) = Z.
% 133.97/17.58 Axiom 25 (cls_add__0__left_0): fresh43(class_OrderedGroup_Omonoid__add(X), true2, X, Y) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X), Y, X).
% 133.97/17.58 Axiom 26 (cls_real__diff__def_0): c_HOL_Ominus__class_Ominus(X, Y, tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X, c_HOL_Ouminus__class_Ouminus(Y, tc_RealDef_Oreal), tc_RealDef_Oreal).
% 133.97/17.58 Axiom 27 (cls_Complex__eq__0_1): fresh34(c_Complex_Ocomplex_OComplex(X, Y), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), Y) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 133.97/17.58 Axiom 28 (cls_Complex__eq__0_0): fresh33(c_Complex_Ocomplex_OComplex(X, Y), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), X) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 133.97/17.58 Axiom 29 (cls_add__diff__cancel_0): fresh55(class_OrderedGroup_Ogroup__add(X), true2, X, Y, Z) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(Y, Z, X), Z, X).
% 133.97/17.58 Axiom 30 (cls_sin__pi__half_0): c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal).
% 133.97/17.58 Axiom 31 (cls_sin__add_0): c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(X, Y, tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(X), c_Transcendental_Ocos(Y), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(X), c_Transcendental_Osin(Y), tc_RealDef_Oreal), tc_RealDef_Oreal).
% 133.97/17.58 Axiom 32 (cls_conjecture_0): c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal))) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 133.97/17.58
% 133.97/17.58 Lemma 33: class_RealVector_Oreal__field(tc_RealDef_Oreal) = class_RealVector_Oreal__field(tc_Complex_Ocomplex).
% 133.97/17.58 Proof:
% 133.97/17.58 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 133.97/17.58 = { by axiom 2 (clsarity_RealDef__Oreal__RealVector_Oreal__field) }
% 133.97/17.58 true2
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 133.97/17.58
% 133.97/17.58 Lemma 34: class_Ring__and__Field_Omult__mono1(tc_nat) = class_RealVector_Oreal__field(tc_RealDef_Oreal).
% 133.97/17.58 Proof:
% 133.97/17.58 class_Ring__and__Field_Omult__mono1(tc_nat)
% 133.97/17.58 = { by axiom 3 (clsarity_nat__Ring__and__Field_Omult__mono1) }
% 133.97/17.58 true2
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 133.97/17.58 = { by lemma 33 R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 133.97/17.58
% 133.97/17.58 Lemma 35: class_Ring__and__Field_Omult__mono(tc_nat) = class_Ring__and__Field_Omult__mono1(tc_nat).
% 133.97/17.58 Proof:
% 133.97/17.58 class_Ring__and__Field_Omult__mono(tc_nat)
% 133.97/17.58 = { by axiom 4 (clsarity_nat__Ring__and__Field_Omult__mono) }
% 133.97/17.58 true2
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 133.97/17.58 = { by lemma 33 R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 133.97/17.58 = { by lemma 34 R->L }
% 133.97/17.58 class_Ring__and__Field_Omult__mono1(tc_nat)
% 133.97/17.58
% 133.97/17.58 Lemma 36: class_Ring__and__Field_Opordered__ring(tc_Int_Oint) = class_Ring__and__Field_Omult__mono(tc_nat).
% 133.97/17.58 Proof:
% 133.97/17.58 class_Ring__and__Field_Opordered__ring(tc_Int_Oint)
% 133.97/17.58 = { by axiom 9 (clsarity_Int__Oint__Ring__and__Field_Opordered__ring) }
% 133.97/17.58 true2
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 133.97/17.58 = { by lemma 33 R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 133.97/17.58 = { by lemma 34 R->L }
% 133.97/17.58 class_Ring__and__Field_Omult__mono1(tc_nat)
% 133.97/17.58 = { by lemma 35 R->L }
% 133.97/17.58 class_Ring__and__Field_Omult__mono(tc_nat)
% 133.97/17.58
% 133.97/17.58 Lemma 37: class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) = class_Ring__and__Field_Opordered__ring(tc_Int_Oint).
% 133.97/17.58 Proof:
% 133.97/17.58 class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal)
% 133.97/17.58 = { by axiom 10 (clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) }
% 133.97/17.58 true2
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 133.97/17.58 = { by lemma 33 R->L }
% 133.97/17.58 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 133.97/17.58 = { by lemma 34 R->L }
% 133.97/17.58 class_Ring__and__Field_Omult__mono1(tc_nat)
% 133.97/17.58 = { by lemma 35 R->L }
% 133.97/17.58 class_Ring__and__Field_Omult__mono(tc_nat)
% 133.97/17.58 = { by lemma 36 R->L }
% 133.97/17.58 class_Ring__and__Field_Opordered__ring(tc_Int_Oint)
% 133.97/17.58
% 133.97/17.58 Lemma 38: c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 133.97/17.58 Proof:
% 133.97/17.58 c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.58 = { by axiom 17 (cls_real__mult__commute_0) R->L }
% 133.97/17.58 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), X, tc_RealDef_Oreal)
% 133.97/17.58 = { by axiom 22 (cls_mult__eq__0__iff_1) R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, X)
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 33 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 34 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono1(tc_nat), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 35 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono(tc_nat), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 36 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_Int_Oint), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 37 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by axiom 5 (clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) }
% 133.97/17.58 fresh323(true2, class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.58 fresh323(class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 33 R->L }
% 133.97/17.58 fresh323(class_RealVector_Oreal__field(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 34 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Omult__mono1(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 35 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Omult__mono(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 36 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Opordered__ring(tc_Int_Oint), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by lemma 37 R->L }
% 133.97/17.58 fresh323(class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, X)
% 133.97/17.58 = { by axiom 18 (cls_mult__eq__0__iff_1) }
% 133.97/17.58 c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
% 133.97/17.58
% 133.97/17.58 Goal 1 (cls_real__zero__not__eq__one_0): c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal).
% 133.97/17.58 Proof:
% 133.97/17.58 c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
% 133.97/17.58 = { by axiom 19 (cls_mult__zero__left_0) R->L }
% 133.97/17.58 fresh262(class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 37 }
% 133.97/17.58 fresh262(class_Ring__and__Field_Opordered__ring(tc_Int_Oint), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 36 }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__mono(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 35 }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__mono1(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 34 }
% 133.97/17.58 fresh262(class_RealVector_Oreal__field(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 33 }
% 133.97/17.58 fresh262(class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) }
% 133.97/17.58 fresh262(true2, class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by axiom 8 (clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) R->L }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 37 }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_Int_Oint), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 36 }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono(tc_nat), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 35 }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono1(tc_nat), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 34 }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by lemma 33 }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) }
% 133.97/17.58 fresh262(class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)))
% 133.97/17.58 = { by axiom 23 (cls_mult__zero__left_0) }
% 133.97/17.58 c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal)
% 133.97/17.59 = { by lemma 38 R->L }
% 133.97/17.59 c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal)
% 133.97/17.59 = { by axiom 17 (cls_real__mult__commute_0) }
% 133.97/17.59 c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.59 = { by axiom 21 (cls_add__0__left_0) R->L }
% 133.97/17.59 fresh43(class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 37 }
% 133.97/17.59 fresh43(class_Ring__and__Field_Opordered__ring(tc_Int_Oint), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 36 }
% 133.97/17.59 fresh43(class_Ring__and__Field_Omult__mono(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 35 }
% 133.97/17.59 fresh43(class_Ring__and__Field_Omult__mono1(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 34 }
% 133.97/17.59 fresh43(class_RealVector_Oreal__field(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 33 }
% 133.97/17.59 fresh43(class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) }
% 133.97/17.59 fresh43(true2, class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by axiom 7 (clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) R->L }
% 133.97/17.59 fresh43(class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 37 }
% 133.97/17.59 fresh43(class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_Int_Oint), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 36 }
% 133.97/17.59 fresh43(class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono(tc_nat), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 35 }
% 133.97/17.59 fresh43(class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono1(tc_nat), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 34 }
% 133.97/17.59 fresh43(class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by lemma 33 }
% 133.97/17.59 fresh43(class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) }
% 133.97/17.59 fresh43(class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.59 = { by axiom 25 (cls_add__0__left_0) }
% 133.97/17.59 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.59 = { by lemma 38 R->L }
% 133.97/17.59 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.59 = { by axiom 28 (cls_Complex__eq__0_0) R->L }
% 133.97/17.59 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh33(c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal))), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal))), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.59 = { by axiom 32 (cls_conjecture_0) }
% 133.97/17.59 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh33(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal))), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.59 = { by axiom 14 (cls_Complex__eq__0_0) }
% 133.97/17.59 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.59 = { by axiom 15 (cls_cos__minus_0) R->L }
% 133.97/17.59 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Otimes__class_Otimes(X, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.59 = { by lemma 38 }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by axiom 12 (cls_neg__equal__zero_1) R->L }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by lemma 37 }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_Ring__and__Field_Opordered__ring(tc_Int_Oint), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by lemma 36 }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_Ring__and__Field_Omult__mono(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by lemma 35 }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_Ring__and__Field_Omult__mono1(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by lemma 34 }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_RealVector_Oreal__field(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by lemma 33 }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(true2, class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by axiom 6 (clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) R->L }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by lemma 37 }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_Int_Oint), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by lemma 36 }
% 133.97/17.60 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono(tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.60 = { by lemma 35 }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono1(tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by lemma 34 }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by lemma 33 }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), fresh248(class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal), true2, tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by axiom 20 (cls_neg__equal__zero_1) }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by axiom 27 (cls_Complex__eq__0_1) R->L }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ouminus__class_Ouminus(fresh34(c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal))), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal))), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by axiom 32 (cls_conjecture_0) }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ouminus__class_Ouminus(fresh34(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal))), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by axiom 13 (cls_Complex__eq__0_1) }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by axiom 16 (cls_sin__minus_0) R->L }
% 133.97/17.61 c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 133.97/17.61 = { by axiom 31 (cls_sin__add_0) R->L }
% 133.97/17.61 c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.61 = { by axiom 26 (cls_real__diff__def_0) R->L }
% 133.97/17.61 c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.61 = { by axiom 29 (cls_add__diff__cancel_0) R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 33 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 34 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono1(tc_nat), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 35 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_Ring__and__Field_Omult__mono(tc_nat), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 36 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_Int_Oint), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 37 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by axiom 11 (clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) }
% 133.97/17.61 c_Transcendental_Osin(fresh55(true2, class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by axiom 1 (clsarity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 33 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_RealVector_Oreal__field(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 34 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_Ring__and__Field_Omult__mono1(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 35 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_Ring__and__Field_Omult__mono(tc_nat), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 36 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_Ring__and__Field_Opordered__ring(tc_Int_Oint), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by lemma 37 R->L }
% 133.97/17.61 c_Transcendental_Osin(fresh55(class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), c_Transcendental_Opi, tc_RealDef_Oreal), c_RealDef_Oreal(v_n, tc_nat), tc_RealDef_Oreal)))
% 133.97/17.61 = { by axiom 24 (cls_add__diff__cancel_0) }
% 133.97/17.61 c_Transcendental_Osin(c_HOL_Oinverse__class_Odivide(c_Transcendental_Opi, c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 133.97/17.61 = { by axiom 30 (cls_sin__pi__half_0) }
% 133.97/17.61 c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
% 133.97/17.61 % SZS output end Proof
% 133.97/17.61
% 133.97/17.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------