TPTP Problem File: SWV686-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV686-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Software Verification
% Problem : Fast Fourier Transform 431_3
% Version : Especial.
% English : Formalization of a functional implementation of the FFT algorithm
% over the complex numbers, and its inverse. Both are shown
% equivalent to the usual definitions of these operations through
% Vandermonde matrices. They are also shown to be inverse to each
% other, more precisely, that composition of the inverse and the
% transformation yield the identity up to a scalar.
% Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : FFT-431_3 [Nip10]
% Status : Unsatisfiable
% Rating : 0.85 v8.2.0, 0.81 v8.1.0, 0.74 v7.5.0, 0.89 v7.4.0, 0.82 v7.3.0, 0.92 v7.0.0, 0.93 v6.4.0, 1.00 v6.2.0, 0.90 v6.1.0, 1.00 v6.0.0, 0.90 v5.5.0, 1.00 v5.4.0, 0.95 v5.3.0, 0.94 v5.0.0, 0.93 v4.1.0
% Syntax : Number of clauses : 566 ( 93 unt; 81 nHn; 326 RR)
% Number of literals : 1622 ( 308 equ; 987 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 64 ( 63 usr; 0 prp; 1-5 aty)
% Number of functors : 25 ( 25 usr; 6 con; 0-5 aty)
% Number of variables : 1695 ( 103 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_one__less__power_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_power__strict__decreasing_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ).
cnf(cls_power__Suc__less__one_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_DERIV__mult_H_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Otimes__class_Otimes(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(V_f,V_x)),V_E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_D),hAPP(V_g,V_x))),T_a)
| ~ c_Deriv_Oderiv(V_g,V_x,V_E,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_DERIV__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Otimes__class_Otimes(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_Da),hAPP(V_g,V_x))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_Db),hAPP(V_f,V_x))),T_a)
| ~ c_Deriv_Oderiv(V_g,V_x,V_Db,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_Da,T_a) ) ).
cnf(cls_power__Suc__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_of__nat__Suc_0,axiom,
( ~ class_Ring__and__Field_Osemiring__1(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)) ) ).
cnf(cls_DERIV__cdivide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),V_f)),V_c),V_x,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_D),V_c),T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_power__strict__increasing_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_n,V_N,tc_nat) ) ).
cnf(cls_power__strict__increasing__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_y),T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ).
cnf(cls_power__less__imp__less__exp_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_power__strict__increasing__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_y),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a) ) ).
cnf(cls_power__gt1_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_DERIV__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_D),V_E),T_a)
| ~ c_Deriv_Oderiv(V_g,V_x,V_E,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_power__0__left_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_DERIV__add_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oplus__class_Oplus(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_D),V_E),T_a)
| ~ c_Deriv_Oderiv(V_g,V_x,V_E,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_gt__half__sum_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a))),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_less__half__sum_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a))),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_power__gt1__lemma_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_power__less__power__Suc_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_divide__less__0__1__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__1__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__less__divide__1__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_b),T_a) ) ).
cnf(cls_zero__less__divide__1__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ).
cnf(cls_zero__less__two_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a) ) ).
cnf(cls_root__unity_0,axiom,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(V_n)),V_n) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ).
cnf(cls_divide__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),c_HOL_Oone__class_Oone(T_a)) = V_a ) ).
cnf(cls_power__one_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Oone__class_Oone(T_a)),V_n) = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_DERIV__cmult__Id_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_x,V_c,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Oone__class_Oone(T_a)),V_a) = V_a ) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Oone__class_Oone(T_a)) = V_a ) ).
cnf(cls_class__semiring_Omul__1_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Oone__class_Oone(T_a)),V_x) = V_x ) ).
cnf(cls_mult__1_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Oone__class_Oone(T_a)),V_a) = V_a ) ).
cnf(cls_mult__1__left_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Oone__class_Oone(T_a)),V_a) = V_a ) ).
cnf(cls_mult__1__right_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Oone__class_Oone(T_a)) = V_a ) ).
cnf(cls_one__neq__zero_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_COMBI__def_0,axiom,
hAPP(c_COMBI(T_a),V_P) = V_P ).
cnf(cls_differentiable__ident_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Odifferentiable(c_COMBI(T_a),V_x,T_a) ) ).
cnf(cls_DERIV__unique_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| V_D = V_E
| ~ c_Deriv_Oderiv(V_f,V_x,V_E,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_differentiable__def_1,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Odifferentiable(V_f,V_x,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_xa,T_a) ) ).
cnf(cls_differentiableI_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Odifferentiable(V_f,V_x,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_DERIV__ident_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(c_COMBI(T_a),V_x,c_HOL_Oone__class_Oone(T_a),T_a) ) ).
cnf(cls_LIM__ident_0,axiom,
( ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(c_COMBI(T_a),V_a,V_a,T_a,T_a) ) ).
cnf(cls_not__one__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__less__one_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ).
cnf(cls_less__1__mult_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_m),V_n),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a) ) ).
cnf(cls_less__add__one_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a) ) ).
cnf(cls_DERIV__chain2_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(T_a,T_a,T_a),V_f),V_g),V_x,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_Da),V_Db),T_a)
| ~ c_Deriv_Oderiv(V_g,V_x,V_Db,T_a)
| ~ c_Deriv_Oderiv(V_f,hAPP(V_g,V_x),V_Da,T_a) ) ).
cnf(cls_DERIV__chain_H_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(T_a,T_a,T_a),V_g),V_f),V_x,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_E),V_D),T_a)
| ~ c_Deriv_Oderiv(V_g,hAPP(V_f,V_x),V_E,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_DERIV__cmult_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(hAPP(hAPP(c_COMBB(T_a,T_a,T_a),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c)),V_f),V_x,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_D),T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a))),V_m) ) ).
cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a))),V_m) ) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a))),V_m) ) ).
cnf(cls_power__inject__exp_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| V_m = V_n ) ).
cnf(cls_divide__self__if_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_a) = c_HOL_Oone__class_Oone(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__self_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_a) = c_HOL_Oone__class_Oone(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_right__inverse__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_x) = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_right__inverse__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b) != c_HOL_Oone__class_Oone(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
cnf(cls_power__0_0,axiom,
( ~ class_Power_Opower(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_class__semiring_Opwr__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_power__one__over_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_a)),V_n) ) ).
cnf(cls_root0_0,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ).
cnf(cls_DERIV__iff_1,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(V_f,V_x,V_D,T_a)
| ~ c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),hAPP(hAPP(c_COMBB(T_a,T_a,T_a),V_f),hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x)))),hAPP(V_f,V_x))),c_COMBI(T_a),T_a,T_a,T_a),c_HOL_Ozero__class_Ozero(T_a),V_D,T_a,T_a) ) ).
cnf(cls_DERIV__D_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),hAPP(hAPP(c_COMBB(T_a,T_a,T_a),V_f),hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x)))),hAPP(V_f,V_x))),c_COMBI(T_a),T_a,T_a,T_a),c_HOL_Ozero__class_Ozero(T_a),V_D,T_a,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_sums__def_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osums(V_f,V_s,T_a)
| ~ c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),T_a,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),V_s,T_a) ) ).
cnf(cls_sums__def_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),T_a,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),V_s,T_a)
| ~ c_Series_Osums(V_f,V_s,T_a) ) ).
cnf(cls_DERIV__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_D),hAPP(V_g,V_x))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(V_f,V_x)),V_E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(V_g,V_x)),hAPP(V_g,V_x))),T_a)
| hAPP(V_g,V_x) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Deriv_Oderiv(V_g,V_x,V_E,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_DERIV__iff2_1,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(V_f,V_x,V_D,T_a)
| ~ c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),V_f)),hAPP(V_f,V_x))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Ominus__class_Ominus(T_a)),V_x),T_a,T_a,T_a),V_x,V_D,T_a,T_a) ) ).
cnf(cls_DERIV__iff2_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),V_f)),hAPP(V_f,V_x))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Ominus__class_Ominus(T_a)),V_x),T_a,T_a,T_a),V_x,V_D,T_a,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_D,T_a) ) ).
cnf(cls_geometric__sum_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),V_x)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),V_n)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),c_HOL_Oone__class_Oone(T_a))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),c_HOL_Oone__class_Oone(T_a)))
| V_x = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_LIMSEQ__diff__approach__zero2_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(V_g,V_L,T_a)
| ~ c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_f),V_g,tc_nat,T_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_SEQ_OLIMSEQ(V_f,V_L,T_a) ) ).
cnf(cls_LIMSEQ__diff__approach__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(V_f,V_L,T_a)
| ~ c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_f),V_g,tc_nat,T_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_SEQ_OLIMSEQ(V_g,V_L,T_a) ) ).
cnf(cls_suminf__mult2_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Series_Osuminf(V_f,T_a)),V_c) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_f)),V_c),T_a)
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_mult__left_Osuminf_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Series_Osuminf(V_X,T_a)),V_y) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X)),V_y),T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_divide_Osuminf_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_Series_Osuminf(V_X,T_a)),V_y) = c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_X)),V_y),T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_suminf__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Series_Osuminf(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_f)),V_c),T_a) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_Series_Osuminf(V_f,T_a)),V_c)
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_setsum__op__ivl__Suc_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(V_m,tc_nat),c_Suc(V_n))) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
cnf(cls_mult__less__cancel__right__disj_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_not__square__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)) != c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)) != c_HOL_Ozero__class_Ozero(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),V_d))
| V_c = V_d
| V_r = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_root__summation__inv_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(V_n))),V_k))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),V_n)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(V_k,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
cnf(cls_DERIV__LIM__iff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ class_HOL_Oinverse(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),V_f)),hAPP(V_f,V_a))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Ominus__class_Ominus(T_a)),V_a),T_a,T_a,T_a),V_a,V_D,T_a,T_a)
| ~ c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),hAPP(hAPP(c_COMBB(T_a,T_a,T_a),V_f),hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a)))),hAPP(V_f,V_a))),c_COMBI(T_a),T_a,T_a,T_a),c_HOL_Ozero__class_Ozero(T_a),V_D,T_a,T_a) ) ).
cnf(cls_DERIV__LIM__iff_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ class_HOL_Oinverse(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),hAPP(hAPP(c_COMBB(T_a,T_a,T_a),V_f),hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a)))),hAPP(V_f,V_a))),c_COMBI(T_a),T_a,T_a,T_a),c_HOL_Ozero__class_Ozero(T_a),V_D,T_a,T_a)
| ~ c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),V_f)),hAPP(V_f,V_a))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Ominus__class_Ominus(T_a)),V_a),T_a,T_a,T_a),V_a,V_D,T_a,T_a) ) ).
cnf(cls_DERIV__quotient_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Oderiv(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_d),hAPP(V_g,V_x))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_e),hAPP(V_f,V_x)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(V_g,V_x)),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))),T_a)
| hAPP(V_g,V_x) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Deriv_Oderiv(V_g,V_x,V_e,T_a)
| ~ c_Deriv_Oderiv(V_f,V_x,V_d,T_a) ) ).
cnf(cls_summable__sumr__LIMSEQ__suminf_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),T_a,tc_nat),hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f)),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)),c_Series_Osuminf(V_f,T_a),T_a)
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_of__nat__0__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_of__nat__0__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
cnf(cls_LIM__add__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Oplus__class_Oplus(T_b)),V_f),V_g,T_a,T_b,T_b),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b) ) ).
cnf(cls_LIM__zero__iff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(V_f,V_a,V_l,T_a,T_b)
| ~ c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Ominus__class_Ominus(T_b)),V_f)),V_l),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b) ) ).
cnf(cls_LIM__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Ominus__class_Ominus(T_b)),V_f)),V_l),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,V_l,T_a,T_b) ) ).
cnf(cls_root__nonzero_0,axiom,
c_FFT__Mirabelle_Oroot(V_n) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
cnf(cls_LIMSEQ__diff__const_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_f)),V_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b),T_a)
| ~ c_SEQ_OLIMSEQ(V_f,V_a,T_a) ) ).
cnf(cls_LIMSEQ__add__const_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oplus__class_Oplus(T_a)),V_f)),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
| ~ c_SEQ_OLIMSEQ(V_f,V_a,T_a) ) ).
cnf(cls_Zseq__add_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oplus__class_Oplus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),T_a)
| ~ c_SEQ_OZseq(V_Y,T_a)
| ~ c_SEQ_OZseq(V_X,T_a) ) ).
cnf(cls_sums__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b),T_a)
| ~ c_Series_Osums(V_Y,V_b,T_a)
| ~ c_Series_Osums(V_X,V_a,T_a) ) ).
cnf(cls_Zseq__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),T_a)
| ~ c_SEQ_OZseq(V_Y,T_a)
| ~ c_SEQ_OZseq(V_X,T_a) ) ).
cnf(cls_summable__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),T_a)
| ~ c_Series_Osummable(V_Y,T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_LIMSEQ__add_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oplus__class_Oplus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
| ~ c_SEQ_OLIMSEQ(V_Y,V_b,T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_summable__add_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osummable(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oplus__class_Oplus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),T_a)
| ~ c_Series_Osummable(V_Y,T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_LIMSEQ__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b),T_a)
| ~ c_SEQ_OLIMSEQ(V_Y,V_b,T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_sums__add_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osums(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oplus__class_Oplus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
| ~ c_Series_Osums(V_Y,V_b,T_a)
| ~ c_Series_Osums(V_X,V_a,T_a) ) ).
cnf(cls_divide_Oadd_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_y),V_ya)) ) ).
cnf(cls_add__divide__distrib_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
cnf(cls_divide_Odiff_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_y),V_ya)) ) ).
cnf(cls_diff__divide__distrib_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
cnf(cls_DERIV__mult__lemma_0,axiom,
( ~ class_RealVector_Oreal__field(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_d))),V_h) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_d)),V_h))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_c)),V_h)),V_d)) ) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_gr0I_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_neq0__conv_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_tendsto__add_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_b)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Oplus__class_Oplus(T_b)),V_f),V_g,T_a,T_b,T_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),V_a),V_b),V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_g,V_b,V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_f,V_a,V_net,T_a,T_b) ) ).
cnf(cls_tendsto__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_b)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Ominus__class_Ominus(T_b)),V_f),V_g,T_a,T_b,T_b),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),V_a),V_b),V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_g,V_b,V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_f,V_a,V_net,T_a,T_b) ) ).
cnf(cls_LIM__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Ominus__class_Ominus(T_b)),V_f),V_g,T_a,T_b,T_b),V_x,hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_b),V_l),V_m),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_x,V_m,T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_x,V_l,T_a,T_b) ) ).
cnf(cls_LIM__add_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Oplus__class_Oplus(T_b)),V_f),V_g,T_a,T_b,T_b),V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),V_L),V_M),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,V_M,T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,V_L,T_a,T_b) ) ).
cnf(cls_differentiable__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Ominus__class_Ominus(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_g,V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_f,V_x,T_a) ) ).
cnf(cls_differentiable__sum_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oplus__class_Oplus(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_g,V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_f,V_x,T_a) ) ).
cnf(cls_mult__right_Osuminf_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),c_Series_Osuminf(V_X,T_a)) = c_Series_Osuminf(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x)),V_X),T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_suminf__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osuminf(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c)),V_f),T_a) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),c_Series_Osuminf(V_f,T_a))
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_mult__left_Odiff_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
cnf(cls_mult_Odiff__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
cnf(cls_mult_Odiff__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
cnf(cls_mult__right_Odiff_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
cnf(cls_combine__common__factor_0,axiom,
( ~ class_Ring__and__Field_Osemiring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_d)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_c)) ) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)) ) ).
cnf(cls_mult__right_Ocont_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_a,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_a),T_a,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
cnf(cls_mult__right_Oadd_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
cnf(cls_mult_Oadd__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
cnf(cls_mult__left_Oadd_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
cnf(cls_mult_Oadd__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_d)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c))
| V_c = V_d
| V_a = V_b ) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y))
| V_y = V_z
| V_w = V_x ) ).
cnf(cls_differentiable__compose_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Odifferentiable(hAPP(hAPP(c_COMBB(T_a,T_a,T_a),V_f),V_g),V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_g,V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_f,hAPP(V_g,V_x),T_a) ) ).
cnf(cls_LIM__compose_0,axiom,
( ~ class_RealVector_Ometric__space(T_a)
| ~ class_RealVector_Ometric__space(T_b)
| ~ class_RealVector_Ometric__space(T_c)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_a,T_b,T_c),V_g),V_f),V_a,hAPP(V_g,V_l),T_c,T_b)
| ~ c_Lim_OLIM(V_f,V_a,V_l,T_c,T_a)
| ~ c_Lim_OLIM(V_g,V_l,hAPP(V_g,V_l),T_a,T_b) ) ).
cnf(cls_sum__squares__gt__zero__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sum__squares__gt__zero__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_not__sum__squares__lt__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_sum__squares__gt__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),T_a) ) ).
cnf(cls_LIM__offset__zero__cancel_0,axiom,
( ~ class_RealVector_Ometric__space(T_b)
| ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Lim_OLIM(V_f,V_a,V_L,T_a,T_b)
| ~ c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_a,T_b,T_a),V_f),hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a),V_L,T_a,T_b) ) ).
cnf(cls_LIM__offset__zero_0,axiom,
( ~ class_RealVector_Ometric__space(T_b)
| ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_a,T_b,T_a),V_f),hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a),V_L,T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,V_L,T_a,T_b) ) ).
cnf(cls_LIM__isCont__iff_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ class_RealVector_Ometric__space(T_b)
| c_Lim_OLIM(V_f,V_a,hAPP(V_f,V_a),T_a,T_b)
| ~ c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_a,T_b,T_a),V_f),hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a),hAPP(V_f,V_a),T_a,T_b) ) ).
cnf(cls_LIM__isCont__iff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ class_RealVector_Ometric__space(T_b)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_a,T_b,T_a),V_f),hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a),hAPP(V_f,V_a),T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,hAPP(V_f,V_a),T_a,T_b) ) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = V_x ) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) ) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
cnf(cls_add__0__left_0,axiom,
( ~ class_OrderedGroup_Omonoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( ~ class_OrderedGroup_Omonoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a)
| V_x = V_y ) ).
cnf(cls_right__minus__eq_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
cnf(cls_double__eq__0__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_diff__self_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_diff__0__right_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = V_a ) ).
cnf(cls_right__minus__eq_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_double__eq__0__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ).
cnf(cls_Suc__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ).
cnf(cls_Suc__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_add__diff__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ) ).
cnf(cls_Suc__lessI_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)
| c_Suc(V_m) = V_n
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_Deriv_Oadd__diff__add_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_c),V_d)) ) ).
cnf(cls_add__neg__neg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ).
cnf(cls_gr0__conv__Suc_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ).
cnf(cls_mult_Oprod__diff__prod_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_a)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_a)),V_b))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_y),V_b))) ) ).
cnf(cls_nat__lt__two__imp__zero__or__one_0,axiom,
( V_x = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_x = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ).
cnf(cls_eq__eqI_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_xa),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)
| V_xa = V_y ) ).
cnf(cls_eq__eqI_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| V_x_H = V_y_H ) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_mult__pos__neg2_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__pos__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__neg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__less__mult__pos2_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a),T_a) ) ).
cnf(cls_zero__less__mult__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a) ) ).
cnf(cls_mult__pos__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__neg__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__strict__left__mono__comm_0,axiom,
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_5,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_4,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__strict__right__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__strict__right__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_5,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_4,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__strict__left__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__strict__left__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_mult__less__cancel__left__pos_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__less__cancel__left__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__less__cancel__left__neg_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__right_OLIM_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_b,T_b,T_a),hAPP(c_HOL_Otimes__class_Otimes(T_b),V_x)),V_g),V_a,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_b),V_x),V_l),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,V_l,T_a,T_b) ) ).
cnf(cls_mult__right_Otendsto_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| c_Limits_Otendsto(hAPP(hAPP(c_COMBB(T_b,T_b,T_a),hAPP(c_HOL_Otimes__class_Otimes(T_b),V_x)),V_g),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_b),V_x),V_a),V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_g,V_a,V_net,T_a,T_b) ) ).
cnf(cls_zero__less__power_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_power__0__Suc_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Suc(V_n)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_power__less__zero__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__left_Ocont_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Otimes__class_Otimes(T_a)),V_y),V_a,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_y),T_a,T_a) ) ).
cnf(cls_sums__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osums(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c)),V_f),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),T_a)
| ~ c_Series_Osums(V_f,V_a,T_a) ) ).
cnf(cls_mult__right_Osums_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osums(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x)),V_X),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_a),T_a)
| ~ c_Series_Osums(V_X,V_a,T_a) ) ).
cnf(cls_mult__right_Osummable_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osummable(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x)),V_X),T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_summable__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osummable(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c)),V_f),T_a)
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_Zseq__mult__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OZseq(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a)),V_X),T_a)
| ~ c_SEQ_OZseq(V_X,T_a) ) ).
cnf(cls_mult__right_OZseq_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OZseq(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x)),V_X),T_a)
| ~ c_SEQ_OZseq(V_X,T_a) ) ).
cnf(cls_mult__right_OLIMSEQ_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x)),V_X),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_a),T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_mult__right_OCauchy_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OCauchy(hAPP(hAPP(c_COMBB(T_a,T_a,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x)),V_X),T_a)
| ~ c_SEQ_OCauchy(V_X,T_a) ) ).
cnf(cls_divide__less__0__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_divide__pos__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_divide__neg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__strict__right__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_divide__strict__right__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_zero__less__divide__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__less__divide__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_divide__pos__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_divide__neg__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_less__divide__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a) ) ).
cnf(cls_divide__less__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a) ) ).
cnf(cls_zero__less__divide__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a) ) ).
cnf(cls_zero__less__divide__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a) ) ).
cnf(cls_zero__less__divide__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a) ) ).
cnf(cls_zero__less__divide__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a) ) ).
cnf(cls_divide__less__0__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Suc(V_q)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Suc(V_q)) ) ).
cnf(cls_class__semiring_Opwr__Suc_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).
cnf(cls_power__Suc2_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
cnf(cls_power__Suc_0,axiom,
( ~ class_Power_Opower(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Suc(V_q)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).
cnf(cls_of__nat__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide_Ocont_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Oinverse__class_Odivide(T_a)),V_y),V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_y),T_a,T_a) ) ).
cnf(cls_assms_0,axiom,
c_HOL_Oord__class_Oless(v_i,v_n,tc_nat) ).
cnf(cls_LIM__mult__right__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_b,T_b,T_a),hAPP(c_HOL_Otimes__class_Otimes(T_b),V_c)),V_f),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b) ) ).
cnf(cls_mult__right_OLIM__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_b,T_b,T_a),hAPP(c_HOL_Otimes__class_Otimes(T_b),V_x)),V_g),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b) ) ).
cnf(cls_mult__left_Otendsto_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| c_Limits_Otendsto(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Otimes__class_Otimes(T_b)),V_g)),V_y),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_b),V_a),V_y),V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_g,V_a,V_net,T_a,T_b) ) ).
cnf(cls_mult__left_OLIM_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Otimes__class_Otimes(T_b)),V_g)),V_y),V_a,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_b),V_l),V_y),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,V_l,T_a,T_b) ) ).
cnf(cls_divide__strict__left__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_divide__strict__left__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_add__frac__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_z))
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_less__divide__eq_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a) ) ).
cnf(cls_less__divide__eq_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a) ) ).
cnf(cls_divide__less__eq_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a) ) ).
cnf(cls_divide__less__eq_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a) ) ).
cnf(cls_add__num__frac_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__frac__num_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_less__divide__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a) ) ).
cnf(cls_less__divide__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a) ) ).
cnf(cls_divide__less__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a) ) ).
cnf(cls_divide__less__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a) ) ).
cnf(cls_diff__frac__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_z))
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__imp__less__div__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(V_z,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),V_y),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_mult__imp__div__pos__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y),V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),V_y),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_less__divide__eq_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a) ) ).
cnf(cls_less__divide__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a) ) ).
cnf(cls_divide__less__eq_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a) ) ).
cnf(cls_divide__less__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a) ) ).
cnf(cls_LIM__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Otimes__class_Otimes(T_b)),V_f),V_g,T_a,T_b,T_b),V_a,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_b),V_L),V_M),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,V_M,T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,V_L,T_a,T_b) ) ).
cnf(cls_mult_Otendsto_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Otimes__class_Otimes(T_b)),V_f),V_g,T_a,T_b,T_b),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_b),V_a),V_b),V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_g,V_b,V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_f,V_a,V_net,T_a,T_b) ) ).
cnf(cls_differentiable__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Otimes__class_Otimes(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_g,V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_f,V_x,T_a) ) ).
cnf(cls_zero__less__power__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_HOL_Ozero__class_Ozero(tc_nat)),T_a) ) ).
cnf(cls_zero__less__power__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_n),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide_Otendsto_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_b)
| c_Limits_Otendsto(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Oinverse__class_Odivide(T_b)),V_g)),V_y),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_b),V_a),V_y),V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_g,V_a,V_net,T_a,T_b) ) ).
cnf(cls_divide_OLIM_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Oinverse__class_Odivide(T_b)),V_g)),V_y),V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_b),V_l),V_y),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,V_l,T_a,T_b) ) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_add__cancel__21_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)) ) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) ) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)) ) ).
cnf(cls_order__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_LIMSEQ__Zseq__iff_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(V_X,V_L,T_a)
| ~ c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_X)),V_L),T_a) ) ).
cnf(cls_LIMSEQ__Zseq__iff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_X)),V_L),T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_L,T_a) ) ).
cnf(cls_diff__add__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ) ).
cnf(cls_less__Suc0_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ).
cnf(cls_LIMSEQ__imp__Cauchy_0,axiom,
( ~ class_RealVector_Ometric__space(T_a)
| c_SEQ_OCauchy(V_X,T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_eq__add__iff2_1,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d) ) ).
cnf(cls_even__less__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_even__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_LIM__offset_0,axiom,
( ~ class_RealVector_Ometric__space(T_b)
| ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBB(T_a,T_b,T_a),V_f),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Oplus__class_Oplus(T_a)),V_k)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_k),V_L,T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,V_L,T_a,T_b) ) ).
cnf(cls_linorder__neqE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
| c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| V_x = V_y ) ).
cnf(cls_nat__less__cases_0,axiom,
( hBOOL(hAPP(hAPP(V_P,V_n),V_m))
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_LIMSEQ__unique_0,axiom,
( ~ class_RealVector_Ometric__space(T_a)
| V_a = V_b
| ~ c_SEQ_OLIMSEQ(V_X,V_b,T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_nat__neq__iff_0,axiom,
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n ) ).
cnf(cls_LIM__unique_0,axiom,
( ~ class_RealVector_Ometric__space(T_b)
| ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| V_L = V_M
| ~ c_Lim_OLIM(V_f,V_a,V_M,T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,V_L,T_a,T_b) ) ).
cnf(cls_linorder__less__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
cnf(cls_less__trans__Suc_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ).
cnf(cls_lessI_0,axiom,
c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ).
cnf(cls_suminf__add_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Series_Osuminf(V_X,T_a)),c_Series_Osuminf(V_Y,T_a)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oplus__class_Oplus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),T_a)
| ~ c_Series_Osummable(V_Y,T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_pos__add__strict_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_suminf__diff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),c_Series_Osuminf(V_X,T_a)),c_Series_Osuminf(V_Y,T_a)) = c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_X),V_Y,tc_nat,T_a,T_a),T_a)
| ~ c_Series_Osummable(V_Y,T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n ).
cnf(cls_setsum__op__ivl__Suc_1,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(V_m,tc_nat),c_Suc(V_n))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(V_m,tc_nat),V_n))),hAPP(V_f,V_n))
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
cnf(cls_less__SucI_0,axiom,
( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_Suc__lessD_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ).
cnf(cls_less__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ).
cnf(cls_less__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)
| c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_setsum__head__upt__Suc_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(V_m,tc_nat),V_n)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(V_m),tc_nat),V_n)))
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ).
cnf(cls_not__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)
| V_y = V_z ) ).
cnf(cls_add__imp__eq_0,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
| V_b = V_c ) ).
cnf(cls_add__left__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)
| V_b = V_c ) ).
cnf(cls_add__right__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)
| V_b = V_c ) ).
cnf(cls_add__cancel__21_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ).
cnf(cls_sums__summable_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osummable(V_f,T_a)
| ~ c_Series_Osums(V_f,V_l,T_a) ) ).
cnf(cls_sums__iff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osummable(V_f,T_a)
| ~ c_Series_Osums(V_f,V_x,T_a) ) ).
cnf(cls_eq__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c)) ) ).
cnf(cls_eq__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c) = V_d ) ).
cnf(cls_eq__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)
| V_c = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d) ) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a) ) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x) ) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a) ) ).
cnf(cls_nat_Oinject_0,axiom,
( c_Suc(V_nat) != c_Suc(V_nat_H)
| V_nat = V_nat_H ) ).
cnf(cls_Suc__inject_0,axiom,
( c_Suc(V_x) != c_Suc(V_y)
| V_x = V_y ) ).
cnf(cls_less__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c),V_d,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d),T_a) ) ).
cnf(cls_less__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c),V_d,T_a) ) ).
cnf(cls_less__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(V_c,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d),T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d),T_a) ) ).
cnf(cls_less__add__iff2_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d),T_a) ) ).
cnf(cls_less__Suc0_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( V_n = V_m
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
cnf(cls_less__antisym_0,axiom,
( V_m = V_n
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
cnf(cls_less__SucE_0,axiom,
( V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_add__pos__pos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_add__strict__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_of__nat__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).
cnf(cls_of__nat__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_summable__LIMSEQ__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_SEQ_OLIMSEQ(V_f,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_sums__unique_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| V_s = c_Series_Osuminf(V_f,T_a)
| ~ c_Series_Osums(V_f,V_s,T_a) ) ).
cnf(cls_sums__iff_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osuminf(V_f,T_a) = V_x
| ~ c_Series_Osums(V_f,V_x,T_a) ) ).
cnf(cls_summable__sums_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_Series_Osums(V_f,c_Series_Osuminf(V_f,T_a),T_a)
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_sums__iff_2,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| ~ c_Series_Osummable(V_f,T_a)
| c_Series_Osums(V_f,c_Series_Osuminf(V_f,T_a),T_a) ) ).
cnf(cls_add__less__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) ) ).
cnf(cls_add__less__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__strict__left__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__less__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ).
cnf(cls_add__less__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__strict__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_setsum__subtractf_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_HOL_Ominus__class_Ominus(T_a)),V_f),V_g,T_b,T_a,T_a)),V_A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_f),V_A)),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_g),V_A)) ) ).
cnf(cls_setsum__addf_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_HOL_Oplus__class_Oplus(T_a)),V_f),V_g,T_b,T_a,T_a)),V_A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_f),V_A)),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_g),V_A)) ) ).
cnf(cls_setsum__product_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_f),V_A)),hAPP(hAPP(c_Finite__Set_Osetsum(T_c,T_a),V_g),V_B)) = hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_bool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_bool),T_a),T_b),c_Finite__Set_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_HOL_Otimes__class_Otimes(T_a)),V_f))),V_g))),V_B)),V_A) ) ).
cnf(cls_LIMSEQ__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X),V_Y,tc_nat,T_a,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
| ~ c_SEQ_OLIMSEQ(V_Y,V_b,T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_Zseq__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OZseq(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X),V_Y,tc_nat,T_a,T_a),T_a)
| ~ c_SEQ_OZseq(V_Y,T_a)
| ~ c_SEQ_OZseq(V_X,T_a) ) ).
cnf(cls_sums__mult2_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_f)),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a)
| ~ c_Series_Osums(V_f,V_a,T_a) ) ).
cnf(cls_mult__left_Osums_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X)),V_y),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_y),T_a)
| ~ c_Series_Osums(V_X,V_a,T_a) ) ).
cnf(cls_summable__mult2_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_f)),V_c),T_a)
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_mult__left_Osummable_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X)),V_y),T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_mult__left_OCauchy_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X)),V_y),T_a)
| ~ c_SEQ_OCauchy(V_X,T_a) ) ).
cnf(cls_mult__left_OLIMSEQ_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X)),V_y),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_y),T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_Zseq__mult__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X)),V_a),T_a)
| ~ c_SEQ_OZseq(V_X,T_a) ) ).
cnf(cls_mult__left_OZseq_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_X)),V_y),T_a)
| ~ c_SEQ_OZseq(V_X,T_a) ) ).
cnf(cls_divide_Osummable_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_X)),V_y),T_a)
| ~ c_Series_Osummable(V_X,T_a) ) ).
cnf(cls_summable__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Series_Osummable(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_f)),V_c),T_a)
| ~ c_Series_Osummable(V_f,T_a) ) ).
cnf(cls_divide_OLIMSEQ_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_SEQ_OLIMSEQ(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_X)),V_y),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_y),T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_divide_OZseq_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_SEQ_OZseq(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_X)),V_y),T_a)
| ~ c_SEQ_OZseq(V_X,T_a) ) ).
cnf(cls_divide_OCauchy_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_SEQ_OCauchy(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_X)),V_y),T_a)
| ~ c_SEQ_OCauchy(V_X,T_a) ) ).
cnf(cls_divide_Osums_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_X)),V_y),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_y),T_a)
| ~ c_Series_Osums(V_X,V_a,T_a) ) ).
cnf(cls_sums__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Series_Osums(hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_f)),V_c),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_c),T_a)
| ~ c_Series_Osums(V_f,V_a,T_a) ) ).
cnf(cls_root__summation_0,axiom,
( hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(V_n)),V_k))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),V_n)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(V_k,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat) ) ).
cnf(cls_LIM__mult__left__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Otimes__class_Otimes(T_b)),V_f)),V_c),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b) ) ).
cnf(cls_mult__left_OLIM__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Otimes__class_Otimes(T_b)),V_g)),V_y),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b) ) ).
cnf(cls_LIM__mult__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Otimes__class_Otimes(T_b)),V_f),V_g,T_a,T_b,T_b),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_f,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b) ) ).
cnf(cls_divide_OLIM__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_b)
| ~ class_RealVector_Ometric__space(T_a)
| c_Lim_OLIM(hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Oinverse__class_Odivide(T_b)),V_g)),V_y),V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b)
| ~ c_Lim_OLIM(V_g,V_a,c_HOL_Ozero__class_Ozero(T_b),T_a,T_b) ) ).
cnf(cls_differentiable__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_Deriv_Odifferentiable(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_HOL_Oinverse__class_Odivide(T_a)),V_f),V_g,T_a,T_a,T_a),V_x,T_a)
| hAPP(V_g,V_x) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Deriv_Odifferentiable(V_g,V_x,T_a)
| ~ c_Deriv_Odifferentiable(V_f,V_x,T_a) ) ).
cnf(cls_tendsto__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_b)
| c_Limits_Otendsto(c_COMBS(hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_HOL_Oinverse__class_Odivide(T_b)),V_f),V_g,T_a,T_b,T_b),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_b),V_a),V_b),V_net,T_a,T_b)
| V_b = c_HOL_Ozero__class_Ozero(T_b)
| ~ c_Limits_Otendsto(V_g,V_b,V_net,T_a,T_b)
| ~ c_Limits_Otendsto(V_f,V_a,V_net,T_a,T_b) ) ).
cnf(cls_LIMSEQ__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_SEQ_OLIMSEQ(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Oinverse__class_Odivide(T_a)),V_X),V_Y,tc_nat,T_a,T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_SEQ_OLIMSEQ(V_Y,V_b,T_a)
| ~ c_SEQ_OLIMSEQ(V_X,V_a,T_a) ) ).
cnf(cls_setsum__shift__lb__Suc0__0__upt_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(V_f,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),V_k)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),V_k)) ) ).
cnf(cls_powser__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| c_Series_Osuminf(c_COMBS(hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Otimes__class_Otimes(T_a)),V_f),hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),tc_nat,T_a,T_a),T_a) = hAPP(V_f,c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_sumr__diff__mult__const2_0,axiom,
( ~ class_Ring__and__Field_Oring__1(T_a)
| hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),V_f),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),V_n))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)),V_r)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,T_a),hAPP(hAPP(c_COMBC(tc_nat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_nat),c_HOL_Ominus__class_Ominus(T_a)),V_f)),V_r)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),V_n)) ) ).
cnf(cls_setsum__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_bool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_bool),T_a),T_b),c_Finite__Set_Osetsum(T_c,T_a)),V_f)),V_B)),V_A) = hAPP(hAPP(c_Finite__Set_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_bool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_bool),T_a),T_c),c_Finite__Set_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f))),V_A)),V_B) ) ).
cnf(cls_divide__eq__eq_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)),V_c) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_frac__eq__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_y)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_w),V_z) ) ).
cnf(cls_frac__eq__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_w),V_z)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_y) ) ).
cnf(cls_eq__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)) ) ).
cnf(cls_nonzero__power__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__zero__right_0,axiom,
( ~ class_Ring__and__Field_Omult__zero(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__zero__left_0,axiom,
( ~ class_Ring__and__Field_Omult__zero(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__right_Ozero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult_Ozero__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult_Ozero__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__left_Ozero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_y) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)),V_c) = V_b
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| V_b = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)),V_c)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)),V_c) ) ).
cnf(cls_power__commutes_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
cnf(cls_setsum__divide__distrib_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_f),V_A)),V_r) = hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_HOL_Oinverse__class_Odivide(T_a)),V_f)),V_r)),V_A) ) ).
cnf(cls_divide_Osetsum_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_g),V_A)),V_y) = hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_HOL_Oinverse__class_Odivide(T_a)),V_g)),V_y)),V_A) ) ).
cnf(cls_setsum__right__distrib_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_f),V_A)) = hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r)),V_f)),V_A) ) ).
cnf(cls_mult__right_Osetsum_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_g),V_A)) = hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x)),V_g)),V_A) ) ).
cnf(cls_of__nat__0_0,axiom,
( ~ class_Ring__and__Field_Osemiring__1(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__self__if_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_z)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),V_z) ) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
cnf(cls_power__mult__distrib_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
cnf(cls_setsum__left__distrib_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_f),V_A)),V_r) = hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_HOL_Otimes__class_Otimes(T_a)),V_f)),V_r)),V_A) ) ).
cnf(cls_mult__left_Osetsum_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),V_g),V_A)),V_y) = hAPP(hAPP(c_Finite__Set_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_HOL_Otimes__class_Otimes(T_a)),V_g)),V_y)),V_A) ) ).
cnf(cls_mult__idem_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
cnf(cls_power__0__left_1,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_n) = c_HOL_Ozero__class_Ozero(T_a)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_power__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_n) = c_HOL_Ozero__class_Ozero(T_a)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_field__power__not__zero_0,axiom,
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_power__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__left__idem_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y) ) ).
cnf(cls_mult__frac__frac_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_w)) ) ).
cnf(cls_power__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
cnf(cls_eq__divide__imp_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| V_a = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),V_c) ) ).
cnf(cls_divide__eq__imp_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),V_c) = V_a ) ).
cnf(cls_eq__divide__eq_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| V_a = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),V_c)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),V_c) = V_a
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) != c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_no__zero__divisors_0,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) != c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_of__nat__eq__iff_0,axiom,
( ~ class_Nat_Osemiring__char__0(T_a)
| c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
| V_m = V_n ) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_x) ) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
cnf(cls_power__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P),V_Q),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)) ).
cnf(cls_divide__zero__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__zero_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide_Ozero_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_y) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__divide__mult__cancel__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__divide__mult__cancel__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__frac__num_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)),V_y) ) ).
cnf(cls_conjecture_0,negated_conjecture,
hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_fun(tc_nat,tc_bool),tc_Complex_Ocomplex),tc_nat),c_Finite__Set_Osetsum(tc_nat,tc_Complex_Ocomplex)),c_COMBS(hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),tc_fun(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex)),tc_nat),c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_Complex_Ocomplex),tc_fun(tc_nat,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex)),tc_nat),hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex))),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),c_Power_Opower__class_Opower(tc_Complex_Ocomplex)),hAPP(hAPP(c_COMBC(tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_COMBB(tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex)),hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n)),v_i))))),v_a,tc_nat,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex)))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),v_n))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),v_n)) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(v_n,tc_Complex_Ocomplex)),hAPP(v_a,v_i)) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat) ).
cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_nat) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat) ).
cnf(clsarity_nat__Power_Opower,axiom,
class_Power_Opower(tc_nat) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Ometric__space,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__HOL_Oinverse,axiom,
class_HOL_Oinverse(tc_Complex_Ocomplex) ).
cnf(cls_ATP__Linkup_OCOMBS__def_0,axiom,
hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R) = hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)) ).
cnf(cls_ATP__Linkup_OCOMBC__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P),V_Q),V_R) = hAPP(hAPP(V_P,V_R),V_Q) ).
cnf(cls_ATP__Linkup_OCOMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P),V_Q),V_R) = hAPP(V_P,hAPP(V_Q,V_R)) ).
cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(V_x,V_x,T_a) ).
cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( V_X = V_Y
| ~ c_fequal(V_X,V_Y,T_a) ) ).
%------------------------------------------------------------------------------