TSTP Solution File: SWW232+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW232+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:26 EDT 2022
% Result : Timeout 300.07s 300.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWW232+1 : TPTP v8.1.0. Released v5.2.0.
% 0.13/0.15 % Command : bliksem %s
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Sat Jun 4 13:53:10 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.26/1.63 *** allocated 10000 integers for termspace/termends
% 1.26/1.63 *** allocated 10000 integers for clauses
% 1.26/1.63 *** allocated 10000 integers for justifications
% 1.26/1.63 *** allocated 15000 integers for termspace/termends
% 1.26/1.63 *** allocated 22500 integers for termspace/termends
% 1.26/1.63 *** allocated 33750 integers for termspace/termends
% 1.26/1.63 Bliksem 1.12
% 1.26/1.63
% 1.26/1.63
% 1.26/1.63 Automatic Strategy Selection
% 1.26/1.63
% 1.26/1.63 *** allocated 50625 integers for termspace/termends
% 1.26/1.63 *** allocated 75937 integers for termspace/termends
% 1.26/1.63 *** allocated 113905 integers for termspace/termends
% 1.26/1.63
% 1.26/1.63 Clauses:
% 1.26/1.63
% 1.26/1.63 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.26/1.63 { ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.26/1.63 tc_Complex_Ocomplex ) ) }.
% 1.26/1.63 { ! c_Polynomial_OpCons( tc_Complex_Ocomplex, v_c____, v_cs____ ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( tc_Complex_Ocomplex ) )
% 1.26/1.63 }.
% 1.26/1.63 { v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.26/1.63 tc_Complex_Ocomplex ) ), ! c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 tc_RealDef_Oreal, skol2( X, Y ), c_RealVector_Onorm__class_Onorm(
% 1.26/1.63 tc_Complex_Ocomplex, Z ) ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 tc_RealDef_Oreal, Y, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.26/1.63 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.26/1.63 tc_Complex_Ocomplex, X, v_cs____ ) ), Z ) ) ) }.
% 1.26/1.63 { ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.26/1.63 tc_Complex_Ocomplex ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.26/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.63 ( X, Y ) ) ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.26/1.63 , Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.26/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.63 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.63 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.63 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.63 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.26/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.26/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.26/1.63 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Z, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Y, Z ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.26/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.26/1.63 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.26/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.26/1.63 hAPP( Y, U ) ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.26/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.26/1.63 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.26/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.26/1.63 hAPP( Y, U ) ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( X, Z, Y ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.26/1.63 ( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.26/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.26/1.63 hAPP( Y, U ) ) }.
% 1.26/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.26/1.63 ( Z, skol3( X, Y, Z ) ), hAPP( Y, skol3( X, Y, Z ) ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Y, T ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 T, Y ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 T, Y ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Y, Z ), T = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Y, Z ) }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 T, Y ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 T, Y ) }.
% 1.26/1.63 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.26/1.63 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.26/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.26/1.63 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.26/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.26/1.63 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.63 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.63 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.26/1.63 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.26/1.63 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.26/1.63 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.26/1.63 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.26/1.63 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol4( X, Y ) ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.26/1.63 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.26/1.63 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.26/1.63 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.26/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.26/1.63 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.26/1.63 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.63 , Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.26/1.63 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), !
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.26/1.63 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.26/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.26/1.63 , Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.26/1.63 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.26/1.63 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.63 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.63 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, T, Y ) ) ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.26/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.26/1.63 c_Polynomial_OpCons( X, T,
% 1.26/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.26/1.63 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 1.26/1.63 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.26/1.63 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.26/1.63 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.26/1.63 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.63 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.63 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.63 Z ) ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.26/1.63 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.26/1.63 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.26/1.63 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.63 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.63 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.26/1.63 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.26/1.63 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.26/1.63 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.26/1.63 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.26/1.63 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.26/1.63 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.26/1.63 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.26/1.63 Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.26/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.26/1.63 , Y ) ) }.
% 1.26/1.63 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.26/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.26/1.63 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.26/1.63 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.26/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.26/1.63 .
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.26/1.63 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.26/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.26/1.63 .
% 1.26/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.63 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.26/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( X, Y, Z ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.26/1.63 ), U = Z, T = Y }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.26/1.63 ) ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.26/1.63 ), ! U = T }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.26/1.63 ), ! Z = Y }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.26/1.63 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.26/1.63 ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.26/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.26/1.63 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.26/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.26/1.63 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.26/1.63 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.26/1.63 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.26/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.26/1.63 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.63 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.63 ( X, Y ) ) ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ) ) = X }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), X ) = X }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.63 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.26/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.26/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.63 W ) ), U ), Y ) }.
% 1.26/1.63 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.63 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) }.
% 1.26/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.63 Z ) ), U ), T ) = Y }.
% 1.26/1.63 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.63 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), U ), Y ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.63 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.63 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.26/1.63 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.26/1.63 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.26/1.63 }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) }.
% 1.26/1.63 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.26/1.63 ) ), T ), Y ) }.
% 1.26/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ) ), alpha1( X, Y, Z ), alpha15( X, Y, Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ) ) }.
% 1.26/1.63 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ), Y ), alpha15( X, Y, Z ) }.
% 1.26/1.63 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.63 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 1.26/1.63 , Z ), alpha16( X, Y, Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ) }.
% 1.26/1.63 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.63 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.26/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.26/1.63 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.26/1.63 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.26/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.26/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.26/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.26/1.63 .
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.26/1.63 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol7( X ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Z, T ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol8( X, Y ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol10( X ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol11( X, Y ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol12( X, Y ) ) ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.26/1.63 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.63 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.63 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.26/1.63 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.63 , ! Y = Z }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.63 , ! Z = Y }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.63 , ! Z = Y }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.63 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.63 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 Y ), ! Z = Y }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 Z ), ! Z = Y }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.63 Y ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.63 { alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.26/1.63 { alpha26( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.26/1.63 ( X, Y ), Z ) ) }.
% 1.26/1.63 { ! alpha26( X, Y, Z ), alpha27( X, Y, Z ), Z = Y }.
% 1.26/1.63 { ! alpha26( X, Y, Z ), alpha27( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.26/1.63 ) ) }.
% 1.26/1.63 { ! alpha27( X, Y, Z ), alpha26( X, Y, Z ) }.
% 1.26/1.63 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha26( X, Y, Z ) }.
% 1.26/1.63 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.26/1.63 }.
% 1.26/1.63 { ! alpha27( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.26/1.63 X, Y ), Z ) ), alpha27( X, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.26/1.63 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.26/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Polynomial_Opoly( X ) ) ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.63 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.63 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.63 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.26/1.63 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.63 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! Z = Y }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.64 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.64 , T ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , T, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , Y, T ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , T, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, T, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.26/1.64 = Y }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.26/1.64 = Y }.
% 1.26/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.26/1.64 = Y }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.26/1.64 = Y }.
% 1.26/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.26/1.64 = Y }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.26/1.64 = Y }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.26/1.64 , X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ) }.
% 1.26/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.26/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.26/1.64 , Y ), X ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.26/1.64 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha3( X, Y, Z, T ),
% 1.26/1.64 alpha17( X, Y, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha17( X, Y, Z, T ) }.
% 1.26/1.64 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.64 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha3( X, Y, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha4( X, Y, Z, T ),
% 1.26/1.64 alpha18( X, Y, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha18( X, Y, Z, T ) }.
% 1.26/1.64 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.26/1.64 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha4( X, Y, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.26/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , Y, T ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.26/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.64 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.26/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.26/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.26/1.64 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.26/1.64 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.64 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.64 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.26/1.64 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Z, W ) ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 X, W, Z ) ), U ), T ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.26/1.64 ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.26/1.64 ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.64 , ! alpha5( X, Y, Z ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.64 , ! alpha19( X, Y, Z ) }.
% 1.26/1.64 { alpha5( X, Y, Z ), alpha19( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.64 { ! alpha19( X, Y, Z ), ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ) }.
% 1.26/1.64 { ! alpha19( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.64 skol13( X, Y, Z ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.26/1.64 ) ), alpha19( X, Y, Z ) }.
% 1.26/1.64 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! alpha5( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5( X, Y, Z ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.64 , alpha6( X, Y, Z ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.64 , alpha20( X, Y, Z ) }.
% 1.26/1.64 { ! alpha6( X, Y, Z ), ! alpha20( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.64 { ! alpha20( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.64 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, skol14( T, U, Z ) ) ), alpha20( X, Y, Z ) }.
% 1.26/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol14( X, Y, Z ) ),
% 1.26/1.64 alpha20( X, Y, Z ) }.
% 1.26/1.64 { ! alpha6( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.26/1.64 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha6( X, Y, Z ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6
% 1.26/1.64 ( X, Y, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.26/1.64 ), Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.26/1.64 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.26/1.64 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 1.26/1.64 ( X, Y, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.64 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 1.26/1.64 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.26/1.64 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.64 alpha7( X, Y, Z ) }.
% 1.26/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.64 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( Z, Y
% 1.26/1.64 ), Y ) }.
% 1.26/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.64 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.64 skol15( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.26/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.64 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.26/1.64 , skol15( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.26/1.64 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.26/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.64 X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.26/1.64 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { ! X = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Nat_OSuc( X ) = X }.
% 1.26/1.64 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.26/1.64 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.26/1.64 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.26/1.64 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.26/1.64 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.64 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.26/1.64 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.64 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.26/1.64 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.26/1.64 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.64 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.26/1.64 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.26/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.26/1.64 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.26/1.64 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.26/1.64 = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.26/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ), Z ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.26/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Z ), Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.26/1.64 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.64 ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.26/1.64 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.26/1.64 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.26/1.64 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.26/1.64 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.64 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.64 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.64 Y ) ) = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 Z, Y ) ) = Y }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.26/1.64 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.26/1.64 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.26/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 1.26/1.64 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.26/1.64 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ) ) = Y }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.64 X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.26/1.64 .
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.26/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.26/1.64 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.26/1.64 c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.64 , c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.26/1.64 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.26/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.64 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.26/1.64 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 1.26/1.64 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 1.26/1.64 ), c_RComplete_Onatfloor( X ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.26/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.64 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ), Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 Z ) = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Z ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( X, Y ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 X, Y ) }.
% 1.26/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.26/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.26/1.64 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.64 , Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.26/1.64 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.64 X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.26/1.64 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 X, Y ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, Y ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol16( X ) ) }.
% 1.26/1.64 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.64 c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol17( Z, Y ) ) }.
% 1.26/1.64 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( X,
% 1.26/1.64 Y ), X ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.26/1.64 ), alpha8( X, Y ) }.
% 1.26/1.64 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha9( X, Y ), alpha21
% 1.26/1.64 ( X, Y ) }.
% 1.26/1.64 { ! alpha9( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 1.26/1.64 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha10( X, Y ), alpha22( X
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! alpha10( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! alpha22( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! alpha22( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 1.26/1.64 { ! alpha10( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! alpha10( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 1.26/1.64 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 1.26/1.64 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.26/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.26/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol18( X, Y ) ) ) }.
% 1.26/1.64 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.64 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.64 ), X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.26/1.64 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.26/1.64 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.64 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.64 ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.64 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.26/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 tc_Polynomial_Opoly( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 1.26/1.64 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.26/1.64 ) ) = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.26/1.64 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.26/1.64 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.26/1.64 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.26/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.26/1.64 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.26/1.64 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.26/1.64 = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.26/1.64 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.26/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.26/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.26/1.64 ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.26/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ) ) = Y }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.26/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.26/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.26/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.26/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.26/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.26/1.64 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.26/1.64 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.26/1.64 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.26/1.64 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Y ), Z = Y }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.64 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.26/1.64 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.26/1.64 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.26/1.64 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.26/1.64 ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Int_Oint ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.26/1.64 = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.26/1.64 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.26/1.64 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.64 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), X ) = X }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ) ) = X }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Int_Oint ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.64 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.64 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.26/1.64 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.64 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.26/1.64 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, X, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.26/1.64 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.26/1.64 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.26/1.64 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.26/1.64 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.26/1.64 Y ), c_RComplete_Onatceiling( X ) ) }.
% 1.26/1.64 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.26/1.64 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.26/1.64 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 1.26/1.64 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.26/1.64 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.26/1.64 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.26/1.64 Y ) ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.26/1.64 ), T ), U ), Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.26/1.64 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.26/1.64 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 Z, T ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.26/1.64 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.26/1.64 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.26/1.64 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.26/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.26/1.64 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.26/1.64 X, T, Z ), Y ) }.
% 1.26/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.26/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.26/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.26/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.26/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.26/1.64 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.26/1.64 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.26/1.64 , Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.26/1.64 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.26/1.64 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.26/1.64 ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.26/1.64 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 1.26/1.64 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha11( X
% 1.26/1.64 , Y, T ) }.
% 1.26/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha23( X
% 1.26/1.64 , Y, Z, T ) }.
% 1.26/1.64 { ! class_Fields_Ofield( X ), ! alpha11( X, Y, T ), ! alpha23( X, Y, Z, T )
% 1.26/1.64 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.26/1.64 ( X, T, Z ), Y ) }.
% 1.26/1.64 { ! alpha23( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.26/1.64 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z, T ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha23( X
% 1.26/1.64 , Y, Z, T ) }.
% 1.26/1.64 { ! alpha11( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.64 { Z = c_Groups_Ozero__class_Ozero( X ), alpha11( X, Y, Z ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X
% 1.26/1.64 , Y, Z ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.26/1.64 ( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.26/1.64 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.26/1.64 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.26/1.64 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.26/1.64 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.26/1.64 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.26/1.64 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.26/1.64 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.26/1.64 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.64 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.26/1.64 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.26/1.64 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.26/1.64 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.64 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.26/1.64 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.26/1.64 Y ) ) ), Y ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.26/1.64 }.
% 1.26/1.64 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.64 X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.26/1.64 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.26/1.64 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.26/1.64 , Z ), X ) ), T ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, U, T ) ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.26/1.64 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.26/1.64 ) ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.26/1.64 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.26/1.64 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.26/1.64 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.26/1.64 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.26/1.64 hAPP( Z, skol19( U, W, Z ) ) ) }.
% 1.26/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.26/1.64 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol19( X
% 1.26/1.64 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.26/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.26/1.64 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol32( X,
% 1.26/1.64 Y, Z ) ) ) ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol20( X, Y ) ), Y
% 1.26/1.64 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.26/1.64 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.26/1.64 ) }.
% 1.26/1.64 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.26/1.64 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha12( X, Y ), Y = X }
% 1.26/1.64 .
% 1.26/1.64 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! alpha12( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), alpha12( X, Y ) }.
% 1.26/1.64 { ! alpha13( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! alpha13( X, Y ), ! Y = X }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha13( X, Y ) }
% 1.26/1.64 .
% 1.26/1.64 { ! alpha13( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! alpha13( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), alpha13( X, Y ) }.
% 1.26/1.64 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, Y, Z ) }.
% 1.26/1.64 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, Y, Z ) }.
% 1.26/1.64 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.26/1.64 , Z ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.26/1.64 Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, Y, Z ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Int_Oint, Z, X ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.26/1.64 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.26/1.64 tc_Nat_Onat, Z, X ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol21( Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol21( X ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( Z, T ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol22( X, Y ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol23( Z, T ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol23( X, Y ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( T, U, W ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol24( X,
% 1.26/1.64 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 1.26/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 1.26/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.64 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.64 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 1.26/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.26/1.65 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.26/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 1.26/1.65 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 1.26/1.65 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.26/1.65 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.26/1.65 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.26/1.65 Y = X }.
% 1.26/1.65 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.26/1.65 , X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 1.26/1.65 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.26/1.65 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.65 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.65 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.26/1.65 ( tc_Nat_Onat, X ) ) }.
% 1.26/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.65 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 1.26/1.65 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 c_RComplete_Onatceiling( Y ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.65 , c_RComplete_Onatfloor( X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 1.26/1.65 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.26/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.65 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.26/1.65 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.65 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.26/1.65 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 1.26/1.65 tc_Nat_Onat, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.26/1.65 tc_RealDef_Oreal ) ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.26/1.65 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.65 , X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.26/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.65 , c_RComplete_Onatfloor( X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.26/1.65 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 c_RComplete_Onatceiling( X ), Y ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 1.26/1.65 tc_RealDef_Oreal ) ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.65 c_RComplete_Onatfloor( X ), Y ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.65 c_RComplete_Onatceiling( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.26/1.65 ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.65 c_RComplete_Onatfloor( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.65 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Int_Oint, X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.65 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.26/1.65 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.26/1.65 c_RComplete_Onatfloor( X ) = Y }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.65 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.26/1.65 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.26/1.65 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol25( X, Y, Z ) ) ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Nat_OSuc( skol33( X, Y ) ) ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol35( X, Y, Z ) ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol37( T, U ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol35( X, Y, Z ) ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol37( X, Y ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol26( X, Y, Z ) ) ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Nat_OSuc( skol34( X, Y ) ) ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol36( X, Y, Z ) ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol38( T, U ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol36( X, Y, Z ) ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol38( X, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol27( X ),
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, skol27( X ) ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, skol28( X, Y ) ) ), X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Nat_OSuc( skol28( X, Y ) ) ) ), X ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.26/1.65 ), c_Orderings_Oord__class_Oless__eq( X, T, skol29( X, U, W, T ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.26/1.65 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.26/1.65 ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.26/1.65 hAPP( Z, T ), hAPP( Z, skol29( X, Y, Z, T ) ) ) ),
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.26/1.65 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.26/1.65 ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Z, T ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.26/1.65 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol30( X, Y ) ) }.
% 1.26/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.26/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.26/1.65 ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.26/1.65 ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.26/1.65 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.26/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.26/1.65 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.26/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 1.26/1.65 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 1.26/1.65 ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( X, Z, Y ) = T }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.26/1.65 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 1.26/1.65 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 1.26/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.26/1.65 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.26/1.65 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 1.26/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 1.26/1.65 , Z ) ) }.
% 1.26/1.65 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.26/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 1.26/1.65 , Z ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 1.26/1.65 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 1.26/1.65 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.26/1.65 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 1.26/1.65 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.26/1.65 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.26/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.26/1.65 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.26/1.65 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.26/1.65 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 1.26/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! alpha14( X, Y ), alpha24( X, Y ), alpha25( X, Y ) }.
% 1.26/1.65 { ! alpha24( X, Y ), alpha14( X, Y ) }.
% 1.26/1.65 { ! alpha25( X, Y ), alpha14( X, Y ) }.
% 1.26/1.65 { ! alpha25( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! alpha25( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha25( X, Y ) }.
% 1.26/1.65 { ! alpha24( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! alpha24( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha24( X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.26/1.65 , Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.26/1.65 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 1.26/1.65 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, X, Y ), X ) }.
% 1.26/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.26/1.65 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.26/1.65 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.26/1.65 ) ) }.
% 1.26/1.65 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.26/1.65 .
% 1.26/1.65 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.26/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.26/1.65 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.26/1.65 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.26/1.65 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.26/1.65 { class_Power_Opower( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.26/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.26/1.65 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.26/1.65 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.26/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.26/1.65 .
% 1.26/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { ! class_Rings_Oidom( X ),
% 1.26/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.26/1.65 ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.26/1.65 X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.26/1.65 ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.26/1.65 }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.26/1.65 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.26/1.65 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.26/1.65 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.26/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.26/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.26/1.65 ( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.26/1.65 }.
% 1.26/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.26/1.65 ) ) }.
% 1.26/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.26/1.65 .
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.26/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.26/1.65 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.26/1.65 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, v_da____,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_aa____ ) ),
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.26/1.65 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.26/1.65 tc_Complex_Ocomplex, v_c____, v_cs____ ) ), skol31( Y ) ) ) ),
% 1.26/1.65 v_thesis____ }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, skol31( X ) ) ),
% 1.26/1.65 v_thesis____ }.
% 1.26/1.65 { ! v_thesis____ }.
% 1.26/1.65
% 1.26/1.65 *** allocated 15000 integers for clauses
% 1.26/1.65 *** allocated 22500 integers for clauses
% 1.26/1.65 *** allocated 33750 integers for clauses
% 1.26/1.65 *** allocated 50625 integers for clauses
% 1.26/1.65 *** allocated 75937 integers for clauses
% 1.26/1.65 percentage equality = 0.254027, percentage horn = 0.923333
% 1.26/1.65 This is a problem with some equality
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Options Used:
% 1.26/1.65
% 1.26/1.65 useres = 1
% 1.26/1.65 useparamod = 1
% 1.26/1.65 useeqrefl = 1
% 1.26/1.65 useeqfact = 1
% 1.26/1.65 usefactor = 1
% 1.26/1.65 usesimpsplitting = 0
% 1.26/1.65 usesimpdemod = 5
% 1.26/1.65 usesimpres = 3
% 1.26/1.65
% 1.26/1.65 resimpinuse = 1000
% 1.26/1.65 resimpclauses = 20000
% 1.26/1.65 substype = eqrewr
% 1.26/1.65 backwardsubs = 1
% 1.26/1.65 selectoldest = 5
% 1.26/1.65
% 1.26/1.65 litorderings [0] = split
% 1.26/1.65 litorderings [1] = extend the termordering, first sorting on arguments
% 1.26/1.65
% 1.26/1.65 termordering = kbo
% 1.26/1.65
% 1.26/1.65 litapriori = 0
% 1.26/1.65 termapriori = 1
% 1.26/1.65 litaposteriori = 0
% 1.26/1.65 termaposteriori = 0
% 1.26/1.65 demodaposteriori = 0
% 1.26/1.65 ordereqreflfact = 0
% 1.26/1.65
% 1.26/1.65 litselect = negord
% 1.26/1.65
% 1.26/1.65 maxweight = 15
% 1.26/1.65 maxdepth = 30000
% 1.26/1.65 maxlength = 115
% 1.26/1.65 maxnrvars = 195
% 1.26/1.65 excuselevel = 1
% 1.26/1.65 increasemaxweight = 1
% 1.26/1.65
% 1.26/1.65 maxselected = 10000000
% 1.26/1.65 maxnrclauses = 10000000
% 1.26/1.65
% 1.26/1.65 showgenerated = 0
% 1.26/1.65 showkept = 0
% 1.26/1.65 showselected = 0
% 1.26/1.65 showdeleted = 0
% 1.26/1.65 showresimp = 1
% 1.26/1.65 showstatus = 2000
% 1.26/1.65
% 1.26/1.65 prologoutput = 0
% 1.26/1.65 nrgoals = 5000000
% 1.26/1.65 totalproof = 1
% 1.26/1.65
% 1.26/1.65 Symbols occurring in the translation:
% 1.26/1.65
% 1.26/1.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.26/1.65 . [1, 2] (w:1, o:189, a:1, s:1, b:0),
% 1.26/1.65 ! [4, 1] (w:0, o:107, a:1, s:1, b:0),
% 1.26/1.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.26/1.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.26/1.65 hAPP [38, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.26/1.65 v_cs____ [39, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.26/1.65 tc_Complex_Ocomplex [40, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.26/1.65 tc_Polynomial_Opoly [41, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.26/1.65 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.26/1.65 v_c____ [43, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.26/1.65 c_Polynomial_OpCons [44, 3] (w:1, o:257, a:1, s:1, b:0),
% 1.26/1.65 tc_RealDef_Oreal [49, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.26/1.65 c_RealVector_Onorm__class_Onorm [50, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.26/1.65
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq [51, 3] (w:1, o:254, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 c_Polynomial_Opoly [52, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.26/1.65 v_p [53, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.26/1.65 class_RealVector_Oreal__normed__vector [57, 1] (w:1, o:120, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 c_Groups_Oplus__class_Oplus [58, 3] (w:1, o:259, a:1, s:1, b:0),
% 1.26/1.65 class_Orderings_Opreorder [59, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Ocomm__semiring__0 [62, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Ocomm__monoid__add [64, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.26/1.65
% 1.26/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le [69, 1] (w:1, o:
% 1.26/1.65 129, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oordered__ab__semigroup__add [71, 1] (w:1, o:130, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 class_Groups_Ozero [72, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Omonoid__add [75, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Olinordered__ab__group__add [76, 1] (w:1, o:132, a:1, s:
% 1.26/1.65 1, b:0),
% 1.26/1.65 class_Int_Oring__char__0 [77, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Oidom [78, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oordered__comm__monoid__add [79, 1] (w:1, o:136, a:1, s:
% 1.26/1.65 1, b:0),
% 1.26/1.65 class_Orderings_Olinorder [81, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.26/1.65 class_Orderings_Oord [83, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.26/1.65 tc_fun [84, 2] (w:1, o:237, a:1, s:1, b:0),
% 1.26/1.65 class_Orderings_Oorder [85, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Ocancel__semigroup__add [87, 1] (w:1, o:138, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Groups_Ocancel__ab__semigroup__add [88, 1] (w:1, o:139, a:1, s:
% 1.26/1.65 1, b:0),
% 1.26/1.65 class_Groups_Oab__semigroup__add [89, 1] (w:1, o:140, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 c_Polynomial_Oorder [94, 3] (w:1, o:256, a:1, s:1, b:0),
% 1.26/1.65 tc_Nat_Onat [95, 0] (w:1, o:53, a:1, s:1, b:0),
% 1.26/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [96
% 1.26/1.65 , 1] (w:1, o:169, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Ocomm__semiring__1 [97, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.26/1.65 c_Polynomial_Opoly__rec [99, 5] (w:1, o:297, a:1, s:1, b:0),
% 1.26/1.65 c_fequal [100, 2] (w:1, o:238, a:1, s:1, b:0),
% 1.26/1.65 c_If [101, 4] (w:1, o:290, a:1, s:1, b:0),
% 1.26/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [105, 3] (w:
% 1.26/1.65 1, o:258, a:1, s:1, b:0),
% 1.26/1.65 c_Polynomial_Osynthetic__div [106, 3] (w:1, o:260, a:1, s:1, b:0),
% 1.26/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [108, 2] (w:1, o:
% 1.26/1.65 239, a:1, s:1, b:0),
% 1.26/1.65 c_Polynomial_Osmult [110, 3] (w:1, o:261, a:1, s:1, b:0),
% 1.26/1.65 c_Polynomial_Omonom [111, 3] (w:1, o:262, a:1, s:1, b:0),
% 1.26/1.65 c_Groups_Ominus__class_Ominus [112, 3] (w:1, o:263, a:1, s:1, b:0),
% 1.26/1.65 c_Groups_Otimes__class_Otimes [113, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.26/1.65 class_RealVector_Oreal__normed__algebra [126, 1] (w:1, o:142, a:1, s:
% 1.26/1.65 1, b:0),
% 1.26/1.65 class_Rings_Oring [127, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oab__group__add [129, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Ocomm__ring [132, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oab__semigroup__mult [133, 1] (w:1, o:172, a:1, s:1, b:0
% 1.26/1.65 ),
% 1.26/1.65 class_RealVector_Oreal__normed__div__algebra [136, 1] (w:1, o:144, a:
% 1.26/1.65 1, s:1, b:0),
% 1.26/1.65 class_Groups_Ogroup__add [137, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oordered__ab__group__add [138, 1] (w:1, o:174, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Rings_Oordered__ring [143, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__ring__strict [144, 1] (w:1, o:155, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Rings_Olinordered__ring [145, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Ono__zero__divisors [149, 1] (w:1, o:153, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 class_Rings_Oring__no__zero__divisors [150, 1] (w:1, o:157, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Rings_Omult__zero [151, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Ocomm__semiring [152, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Osemiring [154, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Oordered__cancel__semiring [155, 1] (w:1, o:162, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Rings_Oordered__semiring [156, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.26/1.65
% 1.26/1.65 class_Rings_Oordered__comm__semiring [157, 1] (w:1, o:164, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 c_Polynomial_Opcompose [160, 3] (w:1, o:264, a:1, s:1, b:0),
% 1.26/1.65 c_Groups_Oone__class_Oone [164, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.26/1.65 c_Orderings_Oord__class_Oless [165, 3] (w:1, o:255, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__semidom [166, 1] (w:1, o:145, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 class_Rings_Olinordered__idom [167, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oone [168, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.26/1.65 class_RealVector_Oreal__normed__algebra__1 [169, 1] (w:1, o:165, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 hBOOL [171, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Ozero__neq__one [174, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oordered__cancel__ab__semigroup__add [175, 1] (w:1, o:
% 1.26/1.65 178, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Ocomm__monoid__mult [176, 1] (w:1, o:179, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 class_Groups_Omonoid__mult [177, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__semiring__1__strict [179, 1] (w:1, o:147, a:
% 1.26/1.65 1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__semiring__strict [180, 1] (w:1, o:148, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__comm__semiring__strict [181, 1] (w:1, o:149
% 1.26/1.65 , a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__semiring [182, 1] (w:1, o:150, a:1, s:1, b:0
% 1.26/1.65 ),
% 1.26/1.65 class_Rings_Oring__1 [183, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__semiring__1 [185, 1] (w:1, o:151, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Rings_Ocomm__ring__1 [186, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus [187, 2] (w:1, o:240, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 c_Polynomial_Opos__poly [188, 2] (w:1, o:241, a:1, s:1, b:0),
% 1.26/1.65 c_Power_Opower__class_Opower [190, 1] (w:1, o:181, a:1, s:1, b:0),
% 3.48/3.86 c_RComplete_Onatfloor [191, 1] (w:1, o:182, a:1, s:1, b:0),
% 3.48/3.86 c_Nat_OSuc [192, 1] (w:1, o:183, a:1, s:1, b:0),
% 3.48/3.86 tc_Int_Oint [195, 0] (w:1, o:93, a:1, s:1, b:0),
% 3.48/3.86 class_Rings_Oring__1__no__zero__divisors [198, 1] (w:1, o:160, a:1
% 3.48/3.86 , s:1, b:0),
% 3.48/3.86 class_Power_Opower [201, 1] (w:1, o:184, a:1, s:1, b:0),
% 3.48/3.86 class_Rings_Osemiring__0 [202, 1] (w:1, o:167, a:1, s:1, b:0),
% 3.48/3.86 c_RComplete_Onatceiling [208, 1] (w:1, o:185, a:1, s:1, b:0),
% 3.48/3.86 c_Power_Opower_Opower [209, 3] (w:1, o:265, a:1, s:1, b:0),
% 3.48/3.86 c_Complex_Oii [212, 0] (w:1, o:98, a:1, s:1, b:0),
% 3.48/3.86 c_Rings_Odvd__class_Odvd [213, 3] (w:1, o:266, a:1, s:1, b:0),
% 3.48/3.86 class_Rings_Odvd [214, 1] (w:1, o:168, a:1, s:1, b:0),
% 3.48/3.86 class_Fields_Ofield [215, 1] (w:1, o:127, a:1, s:1, b:0),
% 3.48/3.86 c_Nat__Transfer_Otsub [218, 2] (w:1, o:242, a:1, s:1, b:0),
% 3.48/3.86 c_RealDef_Oreal [219, 2] (w:1, o:243, a:1, s:1, b:0),
% 3.48/3.86 c_Divides_Odiv__class_Odiv [223, 3] (w:1, o:267, a:1, s:1, b:0),
% 3.48/3.86 class_Divides_Osemiring__div [224, 1] (w:1, o:187, a:1, s:1, b:0),
% 3.48/3.86 class_Divides_Oring__div [225, 1] (w:1, o:186, a:1, s:1, b:0),
% 3.48/3.86 class_Groups_Ocancel__comm__monoid__add [227, 1] (w:1, o:188, a:1, s:
% 3.48/3.86 1, b:0),
% 3.48/3.86 tc_HOL_Obool [229, 0] (w:1, o:92, a:1, s:1, b:0),
% 3.48/3.86 v_da____ [230, 0] (w:1, o:104, a:1, s:1, b:0),
% 3.48/3.86 v_aa____ [231, 0] (w:1, o:105, a:1, s:1, b:0),
% 3.48/3.86 v_thesis____ [232, 0] (w:1, o:106, a:1, s:1, b:0),
% 3.48/3.86 alpha1 [233, 3] (w:1, o:268, a:1, s:1, b:1),
% 3.48/3.86 alpha2 [234, 3] (w:1, o:273, a:1, s:1, b:1),
% 3.48/3.86 alpha3 [235, 4] (w:1, o:292, a:1, s:1, b:1),
% 3.48/3.86 alpha4 [236, 4] (w:1, o:293, a:1, s:1, b:1),
% 3.48/3.86 alpha5 [237, 3] (w:1, o:274, a:1, s:1, b:1),
% 3.48/3.86 alpha6 [238, 3] (w:1, o:275, a:1, s:1, b:1),
% 3.48/3.86 alpha7 [239, 3] (w:1, o:276, a:1, s:1, b:1),
% 3.48/3.86 alpha8 [240, 2] (w:1, o:244, a:1, s:1, b:1),
% 3.48/3.86 alpha9 [241, 2] (w:1, o:245, a:1, s:1, b:1),
% 3.48/3.86 alpha10 [242, 2] (w:1, o:246, a:1, s:1, b:1),
% 3.48/3.86 alpha11 [243, 3] (w:1, o:269, a:1, s:1, b:1),
% 3.48/3.86 alpha12 [244, 2] (w:1, o:247, a:1, s:1, b:1),
% 3.48/3.86 alpha13 [245, 2] (w:1, o:248, a:1, s:1, b:1),
% 3.48/3.86 alpha14 [246, 2] (w:1, o:249, a:1, s:1, b:1),
% 3.48/3.86 alpha15 [247, 3] (w:1, o:270, a:1, s:1, b:1),
% 3.48/3.86 alpha16 [248, 3] (w:1, o:271, a:1, s:1, b:1),
% 3.48/3.86 alpha17 [249, 4] (w:1, o:294, a:1, s:1, b:1),
% 3.48/3.86 alpha18 [250, 4] (w:1, o:295, a:1, s:1, b:1),
% 3.48/3.86 alpha19 [251, 3] (w:1, o:272, a:1, s:1, b:1),
% 3.48/3.86 alpha20 [252, 3] (w:1, o:277, a:1, s:1, b:1),
% 3.48/3.86 alpha21 [253, 2] (w:1, o:250, a:1, s:1, b:1),
% 3.48/3.86 alpha22 [254, 2] (w:1, o:251, a:1, s:1, b:1),
% 3.48/3.86 alpha23 [255, 4] (w:1, o:291, a:1, s:1, b:1),
% 3.48/3.86 alpha24 [256, 2] (w:1, o:252, a:1, s:1, b:1),
% 3.48/3.86 alpha25 [257, 2] (w:1, o:253, a:1, s:1, b:1),
% 3.48/3.86 alpha26 [258, 3] (w:1, o:278, a:1, s:1, b:1),
% 3.48/3.86 alpha27 [259, 3] (w:1, o:279, a:1, s:1, b:1),
% 3.48/3.86 skol1 [260, 2] (w:1, o:216, a:1, s:1, b:1),
% 3.48/3.86 skol2 [261, 2] (w:1, o:222, a:1, s:1, b:1),
% 3.48/3.86 skol3 [262, 3] (w:1, o:283, a:1, s:1, b:1),
% 3.48/3.86 skol4 [263, 2] (w:1, o:228, a:1, s:1, b:1),
% 3.48/3.86 skol5 [264, 2] (w:1, o:229, a:1, s:1, b:1),
% 3.48/3.86 skol6 [265, 2] (w:1, o:230, a:1, s:1, b:1),
% 3.48/3.86 skol7 [266, 1] (w:1, o:112, a:1, s:1, b:1),
% 3.48/3.86 skol8 [267, 2] (w:1, o:231, a:1, s:1, b:1),
% 3.48/3.86 skol9 [268, 2] (w:1, o:232, a:1, s:1, b:1),
% 3.48/3.86 skol10 [269, 1] (w:1, o:113, a:1, s:1, b:1),
% 3.48/3.86 skol11 [270, 2] (w:1, o:217, a:1, s:1, b:1),
% 3.48/3.86 skol12 [271, 2] (w:1, o:218, a:1, s:1, b:1),
% 3.48/3.86 skol13 [272, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.48/3.86 skol14 [273, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.48/3.86 skol15 [274, 2] (w:1, o:219, a:1, s:1, b:1),
% 3.48/3.86 skol16 [275, 1] (w:1, o:114, a:1, s:1, b:1),
% 3.48/3.86 skol17 [276, 2] (w:1, o:220, a:1, s:1, b:1),
% 3.48/3.86 skol18 [277, 2] (w:1, o:221, a:1, s:1, b:1),
% 3.48/3.86 skol19 [278, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.48/3.86 skol20 [279, 2] (w:1, o:233, a:1, s:1, b:1),
% 3.48/3.86 skol21 [280, 1] (w:1, o:115, a:1, s:1, b:1),
% 3.48/3.86 skol22 [281, 2] (w:1, o:234, a:1, s:1, b:1),
% 3.48/3.86 skol23 [282, 2] (w:1, o:235, a:1, s:1, b:1),
% 3.48/3.86 skol24 [283, 3] (w:1, o:280, a:1, s:1, b:1),
% 42.93/43.30 skol25 [284, 3] (w:1, o:281, a:1, s:1, b:1),
% 42.93/43.30 skol26 [285, 3] (w:1, o:282, a:1, s:1, b:1),
% 42.93/43.30 skol27 [286, 1] (w:1, o:116, a:1, s:1, b:1),
% 42.93/43.30 skol28 [287, 2] (w:1, o:236, a:1, s:1, b:1),
% 42.93/43.30 skol29 [288, 4] (w:1, o:296, a:1, s:1, b:1),
% 42.93/43.30 skol30 [289, 2] (w:1, o:223, a:1, s:1, b:1),
% 42.93/43.30 skol31 [290, 1] (w:1, o:117, a:1, s:1, b:1),
% 42.93/43.30 skol32 [291, 3] (w:1, o:287, a:1, s:1, b:1),
% 42.93/43.30 skol33 [292, 2] (w:1, o:224, a:1, s:1, b:1),
% 42.93/43.30 skol34 [293, 2] (w:1, o:225, a:1, s:1, b:1),
% 42.93/43.30 skol35 [294, 3] (w:1, o:288, a:1, s:1, b:1),
% 42.93/43.30 skol36 [295, 3] (w:1, o:289, a:1, s:1, b:1),
% 42.93/43.30 skol37 [296, 2] (w:1, o:226, a:1, s:1, b:1),
% 42.93/43.30 skol38 [297, 2] (w:1, o:227, a:1, s:1, b:1).
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Starting Search:
% 42.93/43.30
% 42.93/43.30 *** allocated 113905 integers for clauses
% 42.93/43.30 *** allocated 170857 integers for clauses
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 3042
% 42.93/43.30 Kept: 2002
% 42.93/43.30 Inuse: 82
% 42.93/43.30 Deleted: 1
% 42.93/43.30 Deletedinuse: 0
% 42.93/43.30
% 42.93/43.30 *** allocated 256285 integers for clauses
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 170857 integers for termspace/termends
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 6198
% 42.93/43.30 Kept: 4002
% 42.93/43.30 Inuse: 194
% 42.93/43.30 Deleted: 6
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 *** allocated 384427 integers for clauses
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 256285 integers for termspace/termends
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 11503
% 42.93/43.30 Kept: 6024
% 42.93/43.30 Inuse: 257
% 42.93/43.30 Deleted: 6
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 576640 integers for clauses
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 17409
% 42.93/43.30 Kept: 8276
% 42.93/43.30 Inuse: 315
% 42.93/43.30 Deleted: 7
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 384427 integers for termspace/termends
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 25227
% 42.93/43.30 Kept: 10765
% 42.93/43.30 Inuse: 355
% 42.93/43.30 Deleted: 7
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 864960 integers for clauses
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 31695
% 42.93/43.30 Kept: 13052
% 42.93/43.30 Inuse: 380
% 42.93/43.30 Deleted: 7
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 36369
% 42.93/43.30 Kept: 15179
% 42.93/43.30 Inuse: 415
% 42.93/43.30 Deleted: 7
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 576640 integers for termspace/termends
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 41256
% 42.93/43.30 Kept: 17195
% 42.93/43.30 Inuse: 453
% 42.93/43.30 Deleted: 7
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 1297440 integers for clauses
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 45824
% 42.93/43.30 Kept: 19228
% 42.93/43.30 Inuse: 482
% 42.93/43.30 Deleted: 8
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 Resimplifying clauses:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 50539
% 42.93/43.30 Kept: 21282
% 42.93/43.30 Inuse: 504
% 42.93/43.30 Deleted: 284
% 42.93/43.30 Deletedinuse: 1
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 55296
% 42.93/43.30 Kept: 23316
% 42.93/43.30 Inuse: 522
% 42.93/43.30 Deleted: 285
% 42.93/43.30 Deletedinuse: 2
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 864960 integers for termspace/termends
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 60106
% 42.93/43.30 Kept: 25323
% 42.93/43.30 Inuse: 545
% 42.93/43.30 Deleted: 285
% 42.93/43.30 Deletedinuse: 2
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 1946160 integers for clauses
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 65675
% 42.93/43.30 Kept: 27341
% 42.93/43.30 Inuse: 589
% 42.93/43.30 Deleted: 285
% 42.93/43.30 Deletedinuse: 2
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 71418
% 42.93/43.30 Kept: 29375
% 42.93/43.30 Inuse: 629
% 42.93/43.30 Deleted: 285
% 42.93/43.30 Deletedinuse: 2
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 79633
% 42.93/43.30 Kept: 32035
% 42.93/43.30 Inuse: 669
% 42.93/43.30 Deleted: 286
% 42.93/43.30 Deletedinuse: 3
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30
% 42.93/43.30 Intermediate Status:
% 42.93/43.30 Generated: 89111
% 42.93/43.30 Kept: 34805
% 42.93/43.30 Inuse: 689
% 42.93/43.30 Deleted: 287
% 42.93/43.30 Deletedinuse: 4
% 42.93/43.30
% 42.93/43.30 Resimplifying inuse:
% 42.93/43.30 Done
% 42.93/43.30
% 42.93/43.30 *** allocated 1297440 integers for termspace/termends
% 42.93/43.30 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 98983
% 104.18/104.66 Kept: 36839
% 104.18/104.66 Inuse: 715
% 104.18/104.66 Deleted: 288
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 105268
% 104.18/104.66 Kept: 38851
% 104.18/104.66 Inuse: 749
% 104.18/104.66 Deleted: 288
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 *** allocated 2919240 integers for clauses
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 112709
% 104.18/104.66 Kept: 40875
% 104.18/104.66 Inuse: 763
% 104.18/104.66 Deleted: 288
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying clauses:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 122199
% 104.18/104.66 Kept: 42880
% 104.18/104.66 Inuse: 813
% 104.18/104.66 Deleted: 480
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 133060
% 104.18/104.66 Kept: 44899
% 104.18/104.66 Inuse: 844
% 104.18/104.66 Deleted: 480
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 152084
% 104.18/104.66 Kept: 47358
% 104.18/104.66 Inuse: 873
% 104.18/104.66 Deleted: 480
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 169144
% 104.18/104.66 Kept: 49374
% 104.18/104.66 Inuse: 883
% 104.18/104.66 Deleted: 480
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 181938
% 104.18/104.66 Kept: 51383
% 104.18/104.66 Inuse: 893
% 104.18/104.66 Deleted: 480
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 *** allocated 1946160 integers for termspace/termends
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 191825
% 104.18/104.66 Kept: 53430
% 104.18/104.66 Inuse: 928
% 104.18/104.66 Deleted: 480
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 200448
% 104.18/104.66 Kept: 58294
% 104.18/104.66 Inuse: 943
% 104.18/104.66 Deleted: 480
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 *** allocated 4378860 integers for clauses
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 207138
% 104.18/104.66 Kept: 62915
% 104.18/104.66 Inuse: 948
% 104.18/104.66 Deleted: 480
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying clauses:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 215566
% 104.18/104.66 Kept: 65017
% 104.18/104.66 Inuse: 955
% 104.18/104.66 Deleted: 603
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 224151
% 104.18/104.66 Kept: 67159
% 104.18/104.66 Inuse: 1003
% 104.18/104.66 Deleted: 603
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 251697
% 104.18/104.66 Kept: 69901
% 104.18/104.66 Inuse: 1008
% 104.18/104.66 Deleted: 603
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 280569
% 104.18/104.66 Kept: 73596
% 104.18/104.66 Inuse: 1038
% 104.18/104.66 Deleted: 603
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 *** allocated 2919240 integers for termspace/termends
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 309503
% 104.18/104.66 Kept: 76836
% 104.18/104.66 Inuse: 1048
% 104.18/104.66 Deleted: 603
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 321693
% 104.18/104.66 Kept: 78916
% 104.18/104.66 Inuse: 1068
% 104.18/104.66 Deleted: 603
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 330603
% 104.18/104.66 Kept: 81011
% 104.18/104.66 Inuse: 1098
% 104.18/104.66 Deleted: 603
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 360037
% 104.18/104.66 Kept: 83611
% 104.18/104.66 Inuse: 1108
% 104.18/104.66 Deleted: 603
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying clauses:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 384310
% 104.18/104.66 Kept: 86472
% 104.18/104.66 Inuse: 1117
% 104.18/104.66 Deleted: 1615
% 104.18/104.66 Deletedinuse: 4
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 397607
% 104.18/104.66 Kept: 89472
% 104.18/104.66 Inuse: 1121
% 104.18/104.66 Deleted: 1632
% 104.18/104.66 Deletedinuse: 5
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 408165
% 104.18/104.66 Kept: 93047
% 104.18/104.66 Inuse: 1125
% 104.18/104.66 Deleted: 1648
% 104.18/104.66 Deletedinuse: 5
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66 *** allocated 6568290 integers for clauses
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 415914
% 104.18/104.66 Kept: 96852
% 104.18/104.66 Inuse: 1132
% 104.18/104.66 Deleted: 1666
% 104.18/104.66 Deletedinuse: 5
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 104.18/104.66 Generated: 421312
% 104.18/104.66 Kept: 99776
% 104.18/104.66 Inuse: 1137
% 104.18/104.66 Deleted: 1666
% 104.18/104.66 Deletedinuse: 5
% 104.18/104.66
% 104.18/104.66 Resimplifying inuse:
% 104.18/104.66 Done
% 104.18/104.66
% 104.18/104.66
% 104.18/104.66 Intermediate Status:
% 233.03/233.44 Generated: 426508
% 233.03/233.44 Kept: 102562
% 233.03/233.44 Inuse: 1142
% 233.03/233.44 Deleted: 1666
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 431611
% 233.03/233.44 Kept: 105274
% 233.03/233.44 Inuse: 1147
% 233.03/233.44 Deleted: 1666
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying clauses:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 441147
% 233.03/233.44 Kept: 107279
% 233.03/233.44 Inuse: 1162
% 233.03/233.44 Deleted: 1800
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 *** allocated 4378860 integers for termspace/termends
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 448339
% 233.03/233.44 Kept: 110155
% 233.03/233.44 Inuse: 1177
% 233.03/233.44 Deleted: 1800
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 457719
% 233.03/233.44 Kept: 112844
% 233.03/233.44 Inuse: 1187
% 233.03/233.44 Deleted: 1800
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 466348
% 233.03/233.44 Kept: 115172
% 233.03/233.44 Inuse: 1197
% 233.03/233.44 Deleted: 1800
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 477685
% 233.03/233.44 Kept: 117716
% 233.03/233.44 Inuse: 1207
% 233.03/233.44 Deleted: 1800
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 489572
% 233.03/233.44 Kept: 120508
% 233.03/233.44 Inuse: 1217
% 233.03/233.44 Deleted: 1800
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 500673
% 233.03/233.44 Kept: 122921
% 233.03/233.44 Inuse: 1227
% 233.03/233.44 Deleted: 1800
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 509805
% 233.03/233.44 Kept: 124949
% 233.03/233.44 Inuse: 1259
% 233.03/233.44 Deleted: 1800
% 233.03/233.44 Deletedinuse: 5
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying clauses:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 530372
% 233.03/233.44 Kept: 129374
% 233.03/233.44 Inuse: 1272
% 233.03/233.44 Deleted: 5901
% 233.03/233.44 Deletedinuse: 14
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 546884
% 233.03/233.44 Kept: 133520
% 233.03/233.44 Inuse: 1282
% 233.03/233.44 Deleted: 5901
% 233.03/233.44 Deletedinuse: 14
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 556266
% 233.03/233.44 Kept: 135573
% 233.03/233.44 Inuse: 1306
% 233.03/233.44 Deleted: 5901
% 233.03/233.44 Deletedinuse: 14
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 567259
% 233.03/233.44 Kept: 137886
% 233.03/233.44 Inuse: 1327
% 233.03/233.44 Deleted: 5901
% 233.03/233.44 Deletedinuse: 14
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 591394
% 233.03/233.44 Kept: 141026
% 233.03/233.44 Inuse: 1337
% 233.03/233.44 Deleted: 5901
% 233.03/233.44 Deletedinuse: 14
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 613961
% 233.03/233.44 Kept: 143907
% 233.03/233.44 Inuse: 1342
% 233.03/233.44 Deleted: 5902
% 233.03/233.44 Deletedinuse: 15
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 *** allocated 9852435 integers for clauses
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 625963
% 233.03/233.44 Kept: 146119
% 233.03/233.44 Inuse: 1367
% 233.03/233.44 Deleted: 5902
% 233.03/233.44 Deletedinuse: 15
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying clauses:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 636831
% 233.03/233.44 Kept: 148401
% 233.03/233.44 Inuse: 1387
% 233.03/233.44 Deleted: 6039
% 233.03/233.44 Deletedinuse: 15
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 652973
% 233.03/233.44 Kept: 150524
% 233.03/233.44 Inuse: 1402
% 233.03/233.44 Deleted: 6039
% 233.03/233.44 Deletedinuse: 15
% 233.03/233.44
% 233.03/233.44 *** allocated 6568290 integers for termspace/termends
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 661750
% 233.03/233.44 Kept: 152535
% 233.03/233.44 Inuse: 1417
% 233.03/233.44 Deleted: 6039
% 233.03/233.44 Deletedinuse: 15
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 671925
% 233.03/233.44 Kept: 154851
% 233.03/233.44 Inuse: 1437
% 233.03/233.44 Deleted: 6039
% 233.03/233.44 Deletedinuse: 15
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 679836
% 233.03/233.44 Kept: 156922
% 233.03/233.44 Inuse: 1467
% 233.03/233.44 Deleted: 6039
% 233.03/233.44 Deletedinuse: 15
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 687142
% 233.03/233.44 Kept: 158932
% 233.03/233.44 Inuse: 1493
% 233.03/233.44 Deleted: 6039
% 233.03/233.44 Deletedinuse: 15
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44 Resimplifying inuse:
% 233.03/233.44 Done
% 233.03/233.44
% 233.03/233.44
% 233.03/233.44 Intermediate Status:
% 233.03/233.44 Generated: 696044
% 233.03/233.44 Kept: 161218
% 233.03/233.44 Inuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------