TSTP Solution File: ALG406-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG406-1 : 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 : n021.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 : Wed Aug 30 16:43:12 EDT 2023
% Result : Unsatisfiable 92.91s 12.44s
% Output : Proof 93.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG406-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.18/0.35 % Computer : n021.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Mon Aug 28 02:44:28 EDT 2023
% 0.18/0.35 % CPUTime :
% 92.91/12.44 Command-line arguments: --flatten
% 92.91/12.44
% 92.91/12.44 % SZS status Unsatisfiable
% 92.91/12.44
% 93.80/12.50 % SZS output start Proof
% 93.80/12.50 Take the following subset of the input axioms:
% 93.80/12.50 fof(cls_conjecture_0, negated_conjecture, ~c_lessequals(c_HOL_Otimes__class_Otimes(v_t____, c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 93.80/12.50 fof(cls_mult__right__mono_0, axiom, ![T_a, V_a, V_b, V_c]: (~class_Ring__and__Field_Omult__mono(T_a) | (c_lessequals(c_HOL_Otimes__class_Otimes(V_a, V_c, T_a), c_HOL_Otimes__class_Otimes(V_b, V_c, T_a), T_a) | (~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_c, T_a) | ~c_lessequals(V_a, V_b, T_a))))).
% 93.80/12.50 fof(cls_norm__ge__zero_0, axiom, ![V_x, T_a2]: (~class_RealVector_Oreal__normed__vector(T_a2) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(V_x, T_a2), tc_RealDef_Oreal))).
% 93.80/12.50 fof(cls_real__less__def_0, axiom, ![V_y, V_x2]: (c_lessequals(V_x2, V_y, tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(V_x2, V_y, tc_RealDef_Oreal))).
% 93.80/12.50 fof(cls_real__mult__1_0, axiom, ![V_z]: c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), V_z, tc_RealDef_Oreal)=V_z).
% 93.80/12.50 fof(cls_t_I2_J_0, axiom, c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 93.80/12.50 fof(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, axiom, class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)).
% 93.80/12.50 fof(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add, axiom, class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)).
% 93.80/12.50 fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)).
% 93.80/12.50 fof(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, axiom, class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)).
% 93.80/12.50 fof(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, axiom, class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)).
% 93.80/12.50 fof(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs, axiom, class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)).
% 93.80/12.50 fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add, axiom, class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal)).
% 93.80/12.50 fof(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if, axiom, class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)).
% 93.80/12.50 fof(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, axiom, class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal)).
% 93.80/12.50 fof(clsarity_nat__OrderedGroup_Oab__semigroup__add, axiom, class_OrderedGroup_Oab__semigroup__add(tc_nat)).
% 93.80/12.50 fof(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, axiom, class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)).
% 93.80/12.50
% 93.80/12.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 93.80/12.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 93.80/12.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 93.80/12.51 fresh(y, y, x1...xn) = u
% 93.80/12.51 C => fresh(s, t, x1...xn) = v
% 93.80/12.51 where fresh is a fresh function symbol and x1..xn are the free
% 93.80/12.51 variables of u and v.
% 93.80/12.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 93.80/12.51 input problem has no model of domain size 1).
% 93.80/12.51
% 93.80/12.51 The encoding turns the above axioms into the following unit equations and goals:
% 93.80/12.51
% 93.80/12.51 Axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if): class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) = true2.
% 93.80/12.51 Axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs): class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) = true2.
% 93.80/12.51 Axiom 3 (clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono): class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) = true2.
% 93.80/12.51 Axiom 4 (clsarity_nat__OrderedGroup_Oab__semigroup__add): class_OrderedGroup_Oab__semigroup__add(tc_nat) = true2.
% 93.80/12.51 Axiom 5 (clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add): class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) = true2.
% 93.80/12.51 Axiom 6 (clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add): class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) = true2.
% 93.80/12.51 Axiom 7 (clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add): class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) = true2.
% 93.80/12.51 Axiom 8 (clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add): class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) = true2.
% 93.80/12.51 Axiom 9 (clsarity_nat__OrderedGroup_Opordered__comm__monoid__add): class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) = true2.
% 93.80/12.51 Axiom 10 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add): class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) = true2.
% 93.80/12.51 Axiom 11 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector): class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) = true2.
% 93.80/12.51 Axiom 12 (cls_norm__ge__zero_0): fresh206(X, X, Y, Z) = true2.
% 93.80/12.51 Axiom 13 (cls_real__less__def_0): fresh153(X, X, Y, Z) = true2.
% 93.80/12.51 Axiom 14 (cls_t_I2_J_0): c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 93.80/12.51 Axiom 15 (cls_real__mult__1_0): c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), X, tc_RealDef_Oreal) = X.
% 93.80/12.51 Axiom 16 (cls_inverse__nonnegative__iff__nonnegative_0): fresh375(X, X, Y, Z) = c_lessequals(c_HOL_Ozero__class_Ozero(Y), Z, Y).
% 93.80/12.51 Axiom 17 (cls_mult__right__mono_0): fresh567(X, X, Y, Z, W, V) = true2.
% 93.80/12.51 Axiom 18 (cls_norm__ge__zero_0): fresh206(class_RealVector_Oreal__normed__vector(X), true2, X, Y) = c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(Y, X), tc_RealDef_Oreal).
% 93.80/12.51 Axiom 19 (cls_real__less__def_0): fresh153(c_HOL_Oord__class_Oless(X, Y, tc_RealDef_Oreal), true2, X, Y) = c_lessequals(X, Y, tc_RealDef_Oreal).
% 93.80/12.51 Axiom 20 (cls_mult__right__mono_0): fresh566(X, X, Y, Z, W, V) = fresh567(c_lessequals(Z, V, Y), true2, Y, Z, W, V).
% 93.80/12.51 Axiom 21 (cls_real__mult__le__cancel__iff1_1): fresh150(X, X, Y, Z, W) = c_lessequals(c_HOL_Otimes__class_Otimes(Y, Z, tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(W, Z, tc_RealDef_Oreal), tc_RealDef_Oreal).
% 93.80/12.51 Axiom 22 (cls_mult__right__mono_0): fresh249(X, X, Y, Z, W, V) = c_lessequals(c_HOL_Otimes__class_Otimes(Z, W, Y), c_HOL_Otimes__class_Otimes(V, W, Y), Y).
% 93.80/12.51 Axiom 23 (cls_mult__right__mono_0): fresh566(class_Ring__and__Field_Omult__mono(X), true2, X, Y, Z, W) = fresh249(c_lessequals(c_HOL_Ozero__class_Ozero(X), Z, X), true2, X, Y, Z, W).
% 93.80/12.51
% 93.80/12.51 Lemma 24: class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) = class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal).
% 93.80/12.51 Proof:
% 93.80/12.51 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 93.80/12.51 = { by axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) }
% 93.80/12.51 true2
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.51 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 93.80/12.51
% 93.80/12.51 Lemma 25: class_OrderedGroup_Oab__semigroup__add(tc_nat) = class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal).
% 93.80/12.51 Proof:
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 93.80/12.51 = { by axiom 4 (clsarity_nat__OrderedGroup_Oab__semigroup__add) }
% 93.80/12.51 true2
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.51 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 24 R->L }
% 93.80/12.51 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 93.80/12.51
% 93.80/12.51 Lemma 26: class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) = class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 93.80/12.51 Proof:
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)
% 93.80/12.51 = { by axiom 5 (clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) }
% 93.80/12.51 true2
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.51 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 24 R->L }
% 93.80/12.51 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 25 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 93.80/12.51
% 93.80/12.51 Lemma 27: class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) = class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex).
% 93.80/12.51 Proof:
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
% 93.80/12.51 = { by axiom 6 (clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) }
% 93.80/12.51 true2
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.51 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 24 R->L }
% 93.80/12.51 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 25 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 93.80/12.51 = { by lemma 26 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)
% 93.80/12.51
% 93.80/12.51 Lemma 28: class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) = class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal).
% 93.80/12.51 Proof:
% 93.80/12.51 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
% 93.80/12.51 = { by axiom 7 (clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) }
% 93.80/12.51 true2
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.51 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 24 R->L }
% 93.80/12.51 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 25 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 93.80/12.51 = { by lemma 26 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)
% 93.80/12.51 = { by lemma 27 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
% 93.80/12.51
% 93.80/12.51 Lemma 29: class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) = class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex).
% 93.80/12.51 Proof:
% 93.80/12.51 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
% 93.80/12.51 = { by axiom 8 (clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) }
% 93.80/12.51 true2
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.51 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 24 R->L }
% 93.80/12.51 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 25 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 93.80/12.51 = { by lemma 26 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)
% 93.80/12.51 = { by lemma 27 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 28 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
% 93.80/12.51
% 93.80/12.51 Lemma 30: class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) = class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal).
% 93.80/12.51 Proof:
% 93.80/12.51 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 93.80/12.51 = { by axiom 9 (clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) }
% 93.80/12.51 true2
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.51 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 24 R->L }
% 93.80/12.51 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 25 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 93.80/12.51 = { by lemma 26 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)
% 93.80/12.51 = { by lemma 27 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 28 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
% 93.80/12.51 = { by lemma 29 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
% 93.80/12.51
% 93.80/12.51 Lemma 31: class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) = class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 93.80/12.51 Proof:
% 93.80/12.51 class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal)
% 93.80/12.51 = { by axiom 10 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) }
% 93.80/12.51 true2
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.51 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 24 R->L }
% 93.80/12.51 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 25 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_nat)
% 93.80/12.51 = { by lemma 26 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex)
% 93.80/12.51 = { by lemma 27 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 28 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
% 93.80/12.51 = { by lemma 29 R->L }
% 93.80/12.51 class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
% 93.80/12.51 = { by lemma 30 R->L }
% 93.80/12.51 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat)
% 93.80/12.51
% 93.80/12.51 Goal 1 (cls_conjecture_0): c_lessequals(c_HOL_Otimes__class_Otimes(v_t____, c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 93.80/12.51 Proof:
% 93.80/12.51 c_lessequals(c_HOL_Otimes__class_Otimes(v_t____, c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 93.80/12.51 = { by axiom 21 (cls_real__mult__le__cancel__iff1_1) R->L }
% 93.80/12.51 fresh150(X, X, v_t____, c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by axiom 15 (cls_real__mult__1_0) R->L }
% 93.80/12.51 fresh150(X, X, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by axiom 21 (cls_real__mult__le__cancel__iff1_1) }
% 93.80/12.51 c_lessequals(c_HOL_Otimes__class_Otimes(v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 93.80/12.51 = { by axiom 22 (cls_mult__right__mono_0) R->L }
% 93.80/12.51 fresh249(class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 31 }
% 93.80/12.51 fresh249(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 30 }
% 93.80/12.51 fresh249(class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 29 }
% 93.80/12.51 fresh249(class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 28 }
% 93.80/12.51 fresh249(class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 27 }
% 93.80/12.51 fresh249(class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 26 }
% 93.80/12.51 fresh249(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 25 }
% 93.80/12.51 fresh249(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 24 }
% 93.80/12.51 fresh249(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) }
% 93.80/12.51 fresh249(true2, class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by axiom 12 (cls_norm__ge__zero_0) R->L }
% 93.80/12.51 fresh249(fresh206(class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 31 }
% 93.80/12.51 fresh249(fresh206(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 30 }
% 93.80/12.51 fresh249(fresh206(class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 29 }
% 93.80/12.51 fresh249(fresh206(class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 28 }
% 93.80/12.51 fresh249(fresh206(class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 27 }
% 93.80/12.51 fresh249(fresh206(class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 26 }
% 93.80/12.51 fresh249(fresh206(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 25 }
% 93.80/12.51 fresh249(fresh206(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 24 }
% 93.80/12.51 fresh249(fresh206(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) }
% 93.80/12.51 fresh249(fresh206(true2, class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by axiom 11 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) R->L }
% 93.80/12.51 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 31 }
% 93.80/12.51 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 30 }
% 93.80/12.51 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 29 }
% 93.80/12.51 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 28 }
% 93.80/12.51 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.51 = { by lemma 27 }
% 93.80/12.51 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 26 }
% 93.80/12.52 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Oab__semigroup__add(tc_nat), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 25 }
% 93.80/12.52 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 24 }
% 93.80/12.52 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) }
% 93.80/12.52 fresh249(fresh206(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_w____), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 18 (cls_norm__ge__zero_0) }
% 93.80/12.52 fresh249(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 16 (cls_inverse__nonnegative__iff__nonnegative_0) R->L }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 15 (cls_real__mult__1_0) R->L }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 31 }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 30 }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 29 }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 28 }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 27 }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 26 }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_OrderedGroup_Oab__semigroup__add(tc_nat), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 25 }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 24 }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) }
% 93.80/12.52 fresh249(fresh375(Y, Y, tc_RealDef_Oreal, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal)), true2, tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 16 (cls_inverse__nonnegative__iff__nonnegative_0) }
% 93.80/12.52 fresh249(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 23 (cls_mult__right__mono_0) R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 24 R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 25 R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_nat), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 26 R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 27 R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 28 R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 29 R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 30 R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 31 R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 3 (clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) }
% 93.80/12.52 fresh566(true2, class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.52 fresh566(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 24 R->L }
% 93.80/12.52 fresh566(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 25 R->L }
% 93.80/12.52 fresh566(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 26 R->L }
% 93.80/12.52 fresh566(class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 27 R->L }
% 93.80/12.52 fresh566(class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 28 R->L }
% 93.80/12.52 fresh566(class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 29 R->L }
% 93.80/12.52 fresh566(class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 30 R->L }
% 93.80/12.52 fresh566(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 31 R->L }
% 93.80/12.52 fresh566(class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 20 (cls_mult__right__mono_0) }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 24 R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 25 R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_nat), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 26 R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 27 R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 28 R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 29 R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 30 R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 31 R->L }
% 93.80/12.52 fresh567(c_lessequals(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 19 (cls_real__less__def_0) R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), true2, v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 24 R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 25 R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_nat), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 26 R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 27 R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 28 R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 29 R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 30 R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 31 R->L }
% 93.80/12.52 fresh567(fresh153(c_HOL_Oord__class_Oless(v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 14 (cls_t_I2_J_0) }
% 93.80/12.52 fresh567(fresh153(true2, class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.52 fresh567(fresh153(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 24 R->L }
% 93.80/12.52 fresh567(fresh153(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 25 R->L }
% 93.80/12.52 fresh567(fresh153(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 26 R->L }
% 93.80/12.52 fresh567(fresh153(class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 27 R->L }
% 93.80/12.52 fresh567(fresh153(class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 28 R->L }
% 93.80/12.52 fresh567(fresh153(class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 29 R->L }
% 93.80/12.52 fresh567(fresh153(class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 30 R->L }
% 93.80/12.52 fresh567(fresh153(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 31 R->L }
% 93.80/12.52 fresh567(fresh153(class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), v_t____, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 13 (cls_real__less__def_0) }
% 93.80/12.52 fresh567(true2, class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 93.80/12.52 fresh567(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 24 R->L }
% 93.80/12.52 fresh567(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 25 R->L }
% 93.80/12.52 fresh567(class_OrderedGroup_Oab__semigroup__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 26 R->L }
% 93.80/12.52 fresh567(class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 27 R->L }
% 93.80/12.52 fresh567(class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 28 R->L }
% 93.80/12.52 fresh567(class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 29 R->L }
% 93.80/12.52 fresh567(class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 30 R->L }
% 93.80/12.52 fresh567(class_OrderedGroup_Opordered__comm__monoid__add(tc_nat), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by lemma 31 R->L }
% 93.80/12.52 fresh567(class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_t____, c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(v_w____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal))
% 93.80/12.52 = { by axiom 17 (cls_mult__right__mono_0) }
% 93.80/12.52 true2
% 93.80/12.52 % SZS output end Proof
% 93.80/12.52
% 93.80/12.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------