TSTP Solution File: ALG362-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG362-1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:43:04 EDT 2023
% Result : Unsatisfiable 230.03s 29.62s
% Output : Proof 230.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG362-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 04:41:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 230.03/29.62 Command-line arguments: --flatten
% 230.03/29.62
% 230.03/29.62 % SZS status Unsatisfiable
% 230.03/29.62
% 230.23/29.73 % SZS output start Proof
% 230.23/29.73 Take the following subset of the input axioms:
% 230.23/29.74 fof(cls_abs__Re__le__cmod_0, axiom, ![V_x]: c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(V_x, tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 230.23/29.74 fof(cls_conjecture_0, negated_conjecture, ~c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 230.23/29.74 fof(cls_less__add__one_0, axiom, ![T_a, V_a]: (~class_Ring__and__Field_Oordered__semidom(T_a) | c_HOL_Oord__class_Oless(V_a, c_HOL_Oplus__class_Oplus(V_a, c_HOL_Oone__class_Oone(T_a), T_a), T_a))).
% 230.23/29.74 fof(cls_order__le__less__trans_0, axiom, ![V_y, V_z, T_a2, V_x2]: (~class_Orderings_Opreorder(T_a2) | (c_HOL_Oord__class_Oless(V_x2, V_z, T_a2) | (~c_HOL_Oord__class_Oless(V_y, V_z, T_a2) | ~c_lessequals(V_x2, V_y, T_a2))))).
% 230.23/29.74 fof(cls_r_0, axiom, ![V_n]: c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s, V_n), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal)).
% 230.23/29.74 fof(cls_real__less__def_0, axiom, ![V_x2, V_y2]: (c_lessequals(V_x2, V_y2, tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(V_x2, V_y2, tc_RealDef_Oreal))).
% 230.23/29.74 fof(cls_xt1_I7_J_0, axiom, ![T_a2, V_x2, V_y2, V_z2]: (~class_Orderings_Oorder(T_a2) | (c_HOL_Oord__class_Oless(V_z2, V_x2, T_a2) | (~c_lessequals(V_z2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2))))).
% 230.23/29.74 fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, axiom, class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)).
% 230.23/29.74 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, axiom, class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)).
% 230.23/29.74 fof(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add, axiom, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)).
% 230.23/29.74 fof(clsarity_RealDef__Oreal__Orderings_Oorder, axiom, class_Orderings_Oorder(tc_RealDef_Oreal)).
% 230.23/29.74 fof(clsarity_RealDef__Oreal__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_RealDef_Oreal)).
% 230.23/29.74 fof(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if, axiom, class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)).
% 230.23/29.74 fof(clsarity_RealDef__Oreal__Ring__and__Field_Oidom, axiom, class_Ring__and__Field_Oidom(tc_RealDef_Oreal)).
% 230.23/29.74 fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom, axiom, class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal)).
% 230.23/29.74
% 230.23/29.74 Now clausify the problem and encode Horn clauses using encoding 3 of
% 230.23/29.74 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 230.23/29.74 We repeatedly replace C & s=t => u=v by the two clauses:
% 230.23/29.74 fresh(y, y, x1...xn) = u
% 230.23/29.74 C => fresh(s, t, x1...xn) = v
% 230.23/29.74 where fresh is a fresh function symbol and x1..xn are the free
% 230.23/29.74 variables of u and v.
% 230.23/29.74 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 230.23/29.74 input problem has no model of domain size 1).
% 230.23/29.74
% 230.23/29.74 The encoding turns the above axioms into the following unit equations and goals:
% 230.23/29.74
% 230.23/29.74 Axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if): class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) = true2.
% 230.23/29.74 Axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Oidom): class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) = true2.
% 230.23/29.74 Axiom 3 (clsarity_RealDef__Oreal__Ring__and__Field_Oidom): class_Ring__and__Field_Oidom(tc_RealDef_Oreal) = true2.
% 230.23/29.74 Axiom 4 (clsarity_RealDef__Oreal__Orderings_Opreorder): class_Orderings_Opreorder(tc_RealDef_Oreal) = true2.
% 230.23/29.74 Axiom 5 (clsarity_RealDef__Oreal__Orderings_Oorder): class_Orderings_Oorder(tc_RealDef_Oreal) = true2.
% 230.23/29.74 Axiom 6 (clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom): class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) = true2.
% 230.23/29.74 Axiom 7 (clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add): class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) = true2.
% 230.23/29.74 Axiom 8 (clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add): class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) = true2.
% 230.23/29.74 Axiom 9 (cls_less__add__one_0): fresh410(X, X, Y, Z) = true2.
% 230.23/29.74 Axiom 10 (cls_real__less__def_0): fresh191(X, X, Y, Z) = true2.
% 230.23/29.74 Axiom 11 (cls_xt1_I7_J_0): fresh849(X, X, Y, Z, W) = true2.
% 230.23/29.74 Axiom 12 (cls_order__le__less__trans_0): fresh843(X, X, Y, Z, W) = true2.
% 230.23/29.74 Axiom 13 (cls_order__le__less__trans_0): fresh225(X, X, Y, Z, W, V) = c_HOL_Oord__class_Oless(Z, W, Y).
% 230.23/29.74 Axiom 14 (cls_xt1_I7_J_0): fresh121(X, X, Y, Z, W, V) = c_HOL_Oord__class_Oless(Z, W, Y).
% 230.23/29.74 Axiom 15 (cls_real__less__def_0): fresh191(c_HOL_Oord__class_Oless(X, Y, tc_RealDef_Oreal), true2, X, Y) = c_lessequals(X, Y, tc_RealDef_Oreal).
% 230.23/29.74 Axiom 16 (cls_less__add__one_0): fresh410(class_Ring__and__Field_Oordered__semidom(X), true2, X, Y) = c_HOL_Oord__class_Oless(Y, c_HOL_Oplus__class_Oplus(Y, c_HOL_Oone__class_Oone(X), X), X).
% 230.23/29.74 Axiom 17 (cls_r_0): c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s, X), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal) = true2.
% 230.23/29.74 Axiom 18 (cls_xt1_I7_J_0): fresh848(X, X, Y, Z, W, V) = fresh849(c_HOL_Oord__class_Oless(V, W, Y), true2, Y, Z, W).
% 230.23/29.74 Axiom 19 (cls_order__le__less__trans_0): fresh842(X, X, Y, Z, W, V) = fresh843(c_HOL_Oord__class_Oless(V, W, Y), true2, Y, Z, W).
% 230.23/29.74 Axiom 20 (cls_abs__Re__le__cmod_0): c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(X, tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 230.23/29.74 Axiom 21 (cls_order__le__less__trans_0): fresh842(class_Orderings_Opreorder(X), true2, X, Y, Z, W) = fresh225(c_lessequals(Y, W, X), true2, X, Y, Z, W).
% 230.23/29.74 Axiom 22 (cls_xt1_I7_J_0): fresh848(class_Orderings_Oorder(X), true2, X, Y, Z, W) = fresh121(c_lessequals(Y, W, X), true2, X, Y, Z, W).
% 230.23/29.74
% 230.23/29.74 Lemma 23: class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) = class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal).
% 230.23/29.74 Proof:
% 230.23/29.74 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
% 230.23/29.74 = { by axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) }
% 230.23/29.74 true2
% 230.23/29.74 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.74 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 230.23/29.74
% 230.23/29.74 Lemma 24: class_Ring__and__Field_Oidom(tc_RealDef_Oreal) = class_Ring__and__Field_Oidom(tc_Complex_Ocomplex).
% 230.23/29.74 Proof:
% 230.23/29.74 class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
% 230.23/29.74 = { by axiom 3 (clsarity_RealDef__Oreal__Ring__and__Field_Oidom) }
% 230.23/29.74 true2
% 230.23/29.74 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.74 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 230.23/29.74 = { by lemma 23 R->L }
% 230.23/29.74 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
% 230.23/29.74
% 230.23/29.74 Lemma 25: class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) = class_Ring__and__Field_Oidom(tc_RealDef_Oreal).
% 230.23/29.74 Proof:
% 230.23/29.74 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
% 230.23/29.74 = { by axiom 7 (clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) }
% 230.23/29.74 true2
% 230.23/29.74 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.74 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 230.23/29.74 = { by lemma 23 R->L }
% 230.23/29.74 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
% 230.23/29.74 = { by lemma 24 R->L }
% 230.23/29.74 class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
% 230.23/29.74
% 230.23/29.74 Lemma 26: class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) = class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex).
% 230.23/29.74 Proof:
% 230.23/29.74 class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
% 230.23/29.74 = { by axiom 8 (clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) }
% 230.23/29.74 true2
% 230.23/29.74 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.74 class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal)
% 230.23/29.74 = { by lemma 23 R->L }
% 230.23/29.74 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
% 230.23/29.74 = { by lemma 24 R->L }
% 230.23/29.74 class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
% 230.23/29.74 = { by lemma 25 R->L }
% 230.23/29.74 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
% 230.23/29.74
% 230.23/29.74 Goal 1 (cls_conjecture_0): c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 230.23/29.74 Proof:
% 230.23/29.74 c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 230.23/29.74 = { by axiom 15 (cls_real__less__def_0) R->L }
% 230.23/29.74 fresh191(c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), true2, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.74 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.74 fresh191(c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.74 = { by lemma 23 R->L }
% 230.23/29.74 fresh191(c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.74 = { by lemma 24 R->L }
% 230.23/29.75 fresh191(c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 25 R->L }
% 230.23/29.75 fresh191(c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 26 R->L }
% 230.23/29.75 fresh191(c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 14 (cls_xt1_I7_J_0) R->L }
% 230.23/29.75 fresh191(fresh121(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 26 }
% 230.23/29.75 fresh191(fresh121(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 25 }
% 230.23/29.75 fresh191(fresh121(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 24 }
% 230.23/29.75 fresh191(fresh121(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 23 }
% 230.23/29.75 fresh191(fresh121(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) }
% 230.23/29.75 fresh191(fresh121(true2, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 20 (cls_abs__Re__le__cmod_0) R->L }
% 230.23/29.75 fresh191(fresh121(c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 26 }
% 230.23/29.75 fresh191(fresh121(c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 25 }
% 230.23/29.75 fresh191(fresh121(c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 24 }
% 230.23/29.75 fresh191(fresh121(c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 23 }
% 230.23/29.75 fresh191(fresh121(c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) }
% 230.23/29.75 fresh191(fresh121(c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 22 (cls_xt1_I7_J_0) R->L }
% 230.23/29.75 fresh191(fresh848(class_Orderings_Oorder(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.75 fresh191(fresh848(class_Orderings_Oorder(tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 23 R->L }
% 230.23/29.75 fresh191(fresh848(class_Orderings_Oorder(tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 24 R->L }
% 230.23/29.75 fresh191(fresh848(class_Orderings_Oorder(tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 25 R->L }
% 230.23/29.75 fresh191(fresh848(class_Orderings_Oorder(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 26 R->L }
% 230.23/29.75 fresh191(fresh848(class_Orderings_Oorder(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 5 (clsarity_RealDef__Oreal__Orderings_Oorder) }
% 230.23/29.75 fresh191(fresh848(true2, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.75 fresh191(fresh848(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 23 R->L }
% 230.23/29.75 fresh191(fresh848(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 24 R->L }
% 230.23/29.75 fresh191(fresh848(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 25 R->L }
% 230.23/29.75 fresh191(fresh848(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 26 R->L }
% 230.23/29.75 fresh191(fresh848(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 18 (cls_xt1_I7_J_0) }
% 230.23/29.75 fresh191(fresh849(c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.75 fresh191(fresh849(c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 23 R->L }
% 230.23/29.75 fresh191(fresh849(c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 24 R->L }
% 230.23/29.75 fresh191(fresh849(c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.75 = { by lemma 25 R->L }
% 230.23/29.75 fresh191(fresh849(c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 26 R->L }
% 230.23/29.76 fresh191(fresh849(c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 13 (cls_order__le__less__trans_0) R->L }
% 230.23/29.76 fresh191(fresh849(fresh225(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 26 }
% 230.23/29.76 fresh191(fresh849(fresh225(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 25 }
% 230.23/29.76 fresh191(fresh849(fresh225(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 24 }
% 230.23/29.76 fresh191(fresh849(fresh225(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 23 }
% 230.23/29.76 fresh191(fresh849(fresh225(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) }
% 230.23/29.76 fresh191(fresh849(fresh225(true2, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 17 (cls_r_0) R->L }
% 230.23/29.76 fresh191(fresh849(fresh225(c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 26 }
% 230.23/29.76 fresh191(fresh849(fresh225(c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 25 }
% 230.23/29.76 fresh191(fresh849(fresh225(c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 24 }
% 230.23/29.76 fresh191(fresh849(fresh225(c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 23 }
% 230.23/29.76 fresh191(fresh849(fresh225(c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) }
% 230.23/29.76 fresh191(fresh849(fresh225(c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), v_r, tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 21 (cls_order__le__less__trans_0) R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Orderings_Opreorder(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Orderings_Opreorder(tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 23 R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Orderings_Opreorder(tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 24 R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Orderings_Opreorder(tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 25 R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Orderings_Opreorder(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 26 R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Orderings_Opreorder(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 4 (clsarity_RealDef__Oreal__Orderings_Opreorder) }
% 230.23/29.76 fresh191(fresh849(fresh842(true2, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 23 R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 24 R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 25 R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 26 R->L }
% 230.23/29.76 fresh191(fresh849(fresh842(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 19 (cls_order__le__less__trans_0) }
% 230.23/29.76 fresh191(fresh849(fresh843(c_HOL_Oord__class_Oless(v_r, c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.76 fresh191(fresh849(fresh843(c_HOL_Oord__class_Oless(v_r, c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 23 R->L }
% 230.23/29.76 fresh191(fresh849(fresh843(c_HOL_Oord__class_Oless(v_r, c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 24 R->L }
% 230.23/29.76 fresh191(fresh849(fresh843(c_HOL_Oord__class_Oless(v_r, c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.76 = { by lemma 25 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(c_HOL_Oord__class_Oless(v_r, c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 26 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(c_HOL_Oord__class_Oless(v_r, c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 16 (cls_less__add__one_0) R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal), class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 23 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 24 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal), class_Ring__and__Field_Oidom(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 25 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 26 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 6 (clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(true2, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 23 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 24 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 25 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 26 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(fresh410(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, v_r), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 9 (cls_less__add__one_0) }
% 230.23/29.77 fresh191(fresh849(fresh843(true2, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 23 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 24 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 25 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 26 R->L }
% 230.23/29.77 fresh191(fresh849(fresh843(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(hAPP(v_s, v_n____), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 12 (cls_order__le__less__trans_0) }
% 230.23/29.77 fresh191(fresh849(true2, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.77 fresh191(fresh849(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 23 R->L }
% 230.23/29.77 fresh191(fresh849(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 24 R->L }
% 230.23/29.77 fresh191(fresh849(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 25 R->L }
% 230.23/29.77 fresh191(fresh849(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 26 R->L }
% 230.23/29.77 fresh191(fresh849(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), tc_RealDef_Oreal, c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal)), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 11 (cls_xt1_I7_J_0) }
% 230.23/29.77 fresh191(true2, class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) R->L }
% 230.23/29.77 fresh191(class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 23 R->L }
% 230.23/29.77 fresh191(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 24 R->L }
% 230.23/29.77 fresh191(class_Ring__and__Field_Oidom(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 25 R->L }
% 230.23/29.77 fresh191(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by lemma 26 R->L }
% 230.23/29.77 fresh191(class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal), c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s, v_n____)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))
% 230.23/29.77 = { by axiom 10 (cls_real__less__def_0) }
% 230.23/29.77 true2
% 230.23/29.77 % SZS output end Proof
% 230.23/29.77
% 230.23/29.77 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------