TSTP Solution File: SWW208+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW208+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 23:21:14 EDT 2022
% Result : Timeout 300.04s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW208+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n018.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 17:08:32 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.34/1.68 *** allocated 10000 integers for termspace/termends
% 1.34/1.68 *** allocated 10000 integers for clauses
% 1.34/1.68 *** allocated 10000 integers for justifications
% 1.34/1.68 *** allocated 15000 integers for termspace/termends
% 1.34/1.68 *** allocated 22500 integers for termspace/termends
% 1.34/1.68 *** allocated 33750 integers for termspace/termends
% 1.34/1.68 Bliksem 1.12
% 1.34/1.68
% 1.34/1.68
% 1.34/1.68 Automatic Strategy Selection
% 1.34/1.68
% 1.34/1.68 *** allocated 50625 integers for termspace/termends
% 1.34/1.68 *** allocated 75937 integers for termspace/termends
% 1.34/1.68 *** allocated 113905 integers for termspace/termends
% 1.34/1.68
% 1.34/1.68 Clauses:
% 1.34/1.68
% 1.34/1.68 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), v_r ) ) }.
% 1.34/1.68 { c_SEQ_Osubseq( v_f____ ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_OIm, hAPP(
% 1.34/1.68 v_s, X ) ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal
% 1.34/1.68 ), v_r ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ) }.
% 1.34/1.68 { c_SEQ_Osubseq( v_ga____ ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s, X ) ) )
% 1.34/1.68 , v_r ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.34/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ),
% 1.34/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), X ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone(
% 1.34/1.68 X ) ), c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, hAPP
% 1.34/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) ), ! Y = c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), v_r ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ) ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) ) }.
% 1.34/1.68 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 1.34/1.68 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.34/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.34/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 1.34/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.34/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.34/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.34/1.68 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.34/1.68 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.34/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.68 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.34/1.68 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.68 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.34/1.68 , X ), Y ) ), Y = X }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.68 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.34/1.68 , X ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.68 tc_RealDef_Oreal, Y ), Z ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X
% 1.34/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 1.34/1.68 ), Y ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), X
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.34/1.68 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 1.34/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 1.34/1.68 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Z ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.34/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.68 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 1.34/1.68 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Oabs__class_Oabs( X,
% 1.34/1.68 Y ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.68 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y )
% 1.34/1.68 , X ) ), Y = X }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y )
% 1.34/1.68 , X ) ) }.
% 1.34/1.68 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.34/1.68 , Y ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y )
% 1.34/1.68 , X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.34/1.68 ), ! Y = X }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.68 X ) ), Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.68 tc_RealDef_Oreal, Y ), X ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.34/1.68 ), c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y
% 1.34/1.68 ) ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.34/1.68 }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 1.34/1.68 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.68 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.34/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.68 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) )
% 1.34/1.68 }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ) ) ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ) ) ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.34/1.68 ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.34/1.68 , c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.68 X ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.34/1.68 , c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 1.34/1.68 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X ) ) )
% 1.34/1.68 , c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, U ) ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), T ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_RealDef_Oreal ) ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_RealDef_Oreal ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.34/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_RealDef_Oreal ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.34/1.68 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ) ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 1.34/1.68 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 1.34/1.68 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol2( X, Y, Z ) ) ), hAPP
% 1.34/1.68 ( Y, skol2( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! Z = Y }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Z = Y }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Y = Z }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z, ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.34/1.68 ( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 Z ), T ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.34/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z, hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.34/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.68 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { hAPP( c_Complex_OIm, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 1.34/1.68 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.68 { hAPP( c_Complex_OIm, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 1.34/1.68 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.34/1.68 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.68 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y )
% 1.34/1.68 ), hAPP( c_Complex_OIm, X ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 1.34/1.68 tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! class_Groups_Ozero( X ), !
% 1.34/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.68 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_Polynomial_Opoly( X ) ),
% 1.34/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__1__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.34/1.68 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.34/1.68 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 1.34/1.68 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 1.34/1.68 , tc_Nat_Onat, v_f____, v_ga____ ) ) ) ) }.
% 1.34/1.68 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.34/1.68 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 1.34/1.68 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 1.34/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 1.34/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol3
% 1.34/1.68 ( X, Y ) ) }.
% 1.34/1.68 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.34/1.68 ( tc_fun( T, X ), Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.34/1.68 ( tc_fun( T, X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ) }.
% 1.34/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z ), Y ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.34/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.34/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.34/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP(
% 1.34/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.68 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.34/1.68 }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.68 { alpha42( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.68 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.34/1.68 { alpha42( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.34/1.68 ( X, Y ), Z ) ) }.
% 1.34/1.68 { ! alpha42( X, Y, Z ), alpha45( X, Y, Z ), Z = Y }.
% 1.34/1.68 { ! alpha42( X, Y, Z ), alpha45( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! alpha45( X, Y, Z ), alpha42( X, Y, Z ) }.
% 1.34/1.68 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha42( X, Y, Z ) }.
% 1.34/1.68 { ! alpha45( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.68 tc_Nat_Onat, Z ), Y ) ) }.
% 1.34/1.68 { ! alpha45( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ),
% 1.34/1.68 hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha45( X, Y, Z ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.34/1.68 , X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.34/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 1.34/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 1.34/1.68 ), Y = X }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.34/1.68 ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 1.34/1.68 ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.34/1.68 , X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.68 Y = X }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.68 X = Y }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 1.34/1.68 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), Y
% 1.34/1.68 = X }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.34/1.68 , X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.68 Y = X }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 1.34/1.68 ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 1.34/1.68 .
% 1.34/1.68 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.68 Y = X }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), !
% 1.34/1.68 Y = X }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 1.34/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 1.34/1.68 .
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.34/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.34/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 1.34/1.68 .
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 1.34/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.34/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.34/1.68 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.34/1.68 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.34/1.68 .
% 1.34/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.34/1.68 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.34/1.68 .
% 1.34/1.68 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.68 ( tc_Nat_Onat, Z ), X ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.68 ( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_Nat_Onat ) ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_Nat_Onat ) ), Z ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_Nat_Onat ) ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_Nat_Onat ) ), X ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.68 tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.68 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.34/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, U ) ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) ) }.
% 1.34/1.68 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.68 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.68 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.68 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.68 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.68 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.34/1.68 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 1.34/1.68 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.68 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.68 = Y }.
% 1.34/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.68 = Y }.
% 1.34/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.34/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.34/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.34/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.34/1.68 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.34/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.34/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.34/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.68 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.34/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ), X ) = hAPP
% 1.34/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.34/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.68 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 1.34/1.68 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 1.34/1.68 , Y ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.34/1.68 , Z ) }.
% 1.34/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.34/1.68 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.34/1.68 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.68 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 }.
% 1.34/1.68 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.34/1.68 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) }.
% 1.34/1.68 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.34/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), alpha1( X, Y, Z ), alpha16( X, Y, Z
% 1.34/1.68 ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ), hBOOL
% 1.34/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ), hBOOL
% 1.34/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! alpha16( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! alpha16( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), alpha16( X, Y, Z ) }.
% 1.34/1.68 { ! alpha1( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.34/1.68 { ! alpha1( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 1.34/1.68 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), alpha1( X, Y, Z ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha2( X
% 1.34/1.68 , Y, Z ), alpha17( X, Y, Z ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ), hBOOL
% 1.34/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ), hBOOL
% 1.34/1.68 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.34/1.68 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.34/1.68 { ! alpha17( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! alpha17( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.68 ) ) ), alpha17( X, Y, Z ) }.
% 1.34/1.68 { ! alpha2( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.34/1.68 { ! alpha2( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , Y ) ), alpha2( X, Y, Z ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__comm__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), T ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.68 ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 1.34/1.68 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), alpha3( X, Y, Z, T ),
% 1.34/1.68 alpha18( X, Y, Z, T ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z, T ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.34/1.68 { ! alpha18( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 1.34/1.68 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! alpha18( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 1.34/1.68 ), Z ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), alpha18( X, Y, Z, T ) }.
% 1.34/1.68 { ! alpha3( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), T ) ) }.
% 1.34/1.68 { ! alpha3( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 1.34/1.68 ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), T ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), alpha3( X, Y, Z, T ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), alpha4( X, Y, Z, T ),
% 1.34/1.68 alpha19( X, Y, Z, T ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 1.34/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! alpha19( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 1.34/1.68 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! alpha19( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 1.34/1.68 ), T ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), T ) ), alpha19( X, Y, Z, T ) }.
% 1.34/1.68 { ! alpha4( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.34/1.68 { ! alpha4( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 1.34/1.68 ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, T ), Y ) ), alpha4( X, Y, Z, T ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Oone__class_Oone( X ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 1.34/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.34/1.68 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, U ) ), T ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.34/1.68 c_Groups_Oabs__class_Oabs( X, U ) ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ), hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 1.34/1.68 ( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ) }.
% 1.34/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ), hBOOL( hAPP
% 1.34/1.68 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 1.34/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 1.34/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 1.34/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.34/1.68 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.34/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) ) )
% 1.34/1.68 }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.68 c_Groups_Osgn__class_Osgn( X, Y ) ) ), hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.68 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y ) ) )
% 1.34/1.68 }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 1.34/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.34/1.68 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.68 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.34/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.34/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring__abs( X ), alpha43( X, Z ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Y ) ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring__abs( X ), alpha43( X, Z ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.69 ) ) ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.34/1.69 { ! alpha43( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.34/1.69 { ! alpha43( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 1.34/1.69 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.69 ) ) ), alpha43( X, Y ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) = c_Groups_Oabs__class_Oabs( X,
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ), hBOOL
% 1.34/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 1.34/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 1.34/1.69 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.34/1.69 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), T ), Z ) ), Y ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.34/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), X ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 1.34/1.69 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.69 X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.34/1.69 Y ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.34/1.69 Y ), X ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.34/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.34/1.69 c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }
% 1.34/1.69 .
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.34/1.69 = c_Groups_Oone__class_Oone( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }
% 1.34/1.69 .
% 1.34/1.69 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.34/1.69 { c_SEQ_Osubseq( skol4 ) }.
% 1.34/1.69 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.34/1.69 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 1.34/1.69 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 1.34/1.69 , tc_Nat_Onat, v_f____, skol4 ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, T ) ) ) ), Z =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ), ! Z =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.69 }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 1.34/1.69 ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 1.34/1.69 ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), alpha5( X, Y ),
% 1.34/1.69 alpha20( X, Y ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! alpha5( X, Y ), c_SEQ_Omonoseq( X, Y ) }
% 1.34/1.69 .
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! alpha20( X, Y ), c_SEQ_Omonoseq( X, Y )
% 1.34/1.69 }.
% 1.34/1.69 { ! alpha20( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol5( X, Y
% 1.34/1.69 ) ), skol61( X, Y ) ) ), alpha20( X, Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol61( X,
% 1.34/1.69 Y ) ) ), hAPP( Y, skol5( X, Y ) ) ) ), alpha20( X, Y ) }.
% 1.34/1.69 { ! alpha5( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol6( X, Y
% 1.34/1.69 ) ), skol62( X, Y ) ) ), alpha5( X, Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol6( X, Y
% 1.34/1.69 ) ) ), hAPP( Y, skol62( X, Y ) ) ) ), alpha5( X, Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ) ), Y =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 1.34/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.34/1.69 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 1.34/1.69 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.34/1.69 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.34/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.34/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Nat_Onat ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Nat_Onat ) }.
% 1.34/1.69 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.34/1.69 }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.34/1.69 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.69 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.69 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.34/1.69 , Y ), X ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.34/1.69 { ! Y = X, hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ) }.
% 1.34/1.69 { ! Y = X, hAPP( c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ) }.
% 1.34/1.69 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 1.34/1.69 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 1.34/1.69 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 1.34/1.69 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 1.34/1.69 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.34/1.69 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.34/1.69 ) ), hAPP( c_Complex_ORe, X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.34/1.69 c_Complex_ORe, X ) ), c_RealVector_Onorm__class_Onorm(
% 1.34/1.69 tc_Complex_Ocomplex, X ) ) ) }.
% 1.34/1.69 { hAPP( c_Complex_ORe, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 1.34/1.69 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y )
% 1.34/1.69 ), hAPP( c_Complex_ORe, X ) ) }.
% 1.34/1.69 { hAPP( c_Complex_ORe, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X ) ) )
% 1.34/1.69 , c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol7
% 1.34/1.69 ( X, Y ) ) }.
% 1.34/1.69 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! c_SEQ_Osubseq( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, hAPP( X, Y ) ), hAPP( X, Z ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol8( X ) ),
% 1.34/1.69 skol63( X ) ) ), c_SEQ_Osubseq( X ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol8
% 1.34/1.69 ( X ) ) ), hAPP( X, skol63( X ) ) ) ), c_SEQ_Osubseq( X ) }.
% 1.34/1.69 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Y ), hAPP( X, Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.69 .
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.69 .
% 1.34/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.69 { c_SEQ_Oconvergent( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.34/1.69 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 1.34/1.69 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ), X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z = Y, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Ometric__space( X ), c_SEQ_Oconvergent( X, c_COMBK( X
% 1.34/1.69 , tc_Nat_Onat, Y ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 1.34/1.69 ), c_SEQ_Oconvergent( X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 1.34/1.69 ), c_SEQ_Oconvergent( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun
% 1.34/1.69 ( X, X ), tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 1.34/1.69 ), ! c_SEQ_Oconvergent( X, Z ), c_SEQ_Oconvergent( X, c_COMBS(
% 1.34/1.69 tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X, Y
% 1.34/1.69 ), ! c_SEQ_Oconvergent( X, Z ), c_SEQ_Oconvergent( X, c_COMBS(
% 1.34/1.69 tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.34/1.69 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.34/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.69 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.34/1.69 .
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol9 ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 1.34/1.69 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol9 ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol10 ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 1.34/1.69 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol10 ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol11 ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 1.34/1.69 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol11 ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol12 ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 1.34/1.69 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol12 ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol13( Z, T ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol13( X, Y ) ) ) ) }.
% 1.34/1.69 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 1.34/1.69 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.34/1.69 tc_Nat_Onat, c_Complex_ORe, X ) ) }.
% 1.34/1.69 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 1.34/1.69 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.34/1.69 tc_Nat_Onat, c_Complex_OIm, X ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol14( Y ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol14( X ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol15( Z, T ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 1.34/1.69 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol16 ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 1.34/1.69 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol17 ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol18( X, Y ) ), skol64
% 1.34/1.69 ( X, Y ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol64( X, Y ) ) ), hAPP(
% 1.34/1.69 Y, skol18( X, Y ) ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.34/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.34/1.69 hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 skol19( Z, Y ) ), Y ) ) }.
% 1.34/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.34/1.69 hAPP( X, Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Z ), skol19( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.34/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.34/1.69 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_Nat_Onat ), skol19( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.34/1.69 ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol20( Y ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol20( X ) ) ) ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), c_SEQ_Omonoseq( X
% 1.34/1.69 , Y ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol21( Z, T ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol21( X, Y ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol22( Z, T ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol22( X, Y ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol23( Z, T ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol23( X, Y ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol65( X, Y, Z ) ) ) ), Z )
% 1.34/1.69 ), c_SEQ_OBseq( X, Y ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol24( X, Y ) ), skol66
% 1.34/1.69 ( X, Y ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol24( X, Y ) ) ), hAPP(
% 1.34/1.69 Y, skol66( X, Y ) ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, c_COMBB
% 1.34/1.69 ( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 1.34/1.69 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ) ) ),
% 1.34/1.69 c_SEQ_OBseq( X, Y ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.69 c_SEQ_OBseq( X, c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC(
% 1.34/1.69 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_Nat_Onat ), Z ) ) ) }.
% 1.34/1.69 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), ! c_SEQ_Omonoseq( tc_RealDef_Oreal
% 1.34/1.69 , X ), c_SEQ_Oconvergent( tc_RealDef_Oreal, X ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), c_SEQ_Omonoseq( X
% 1.34/1.69 , Y ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol25( X, Y, Z ) ) ) ), Y )
% 1.34/1.69 ), c_SEQ_OBseq( X, Z ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol26( Z, T ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol26( X, Y ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.34/1.69 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.34/1.69 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.34/1.69 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.34/1.69 ) }.
% 1.34/1.69 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.34/1.69 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatceiling( X
% 1.34/1.69 ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.69 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_RComplete_Onatceiling( Y ) ), c_RComplete_Onatceiling( X ) ) ) }.
% 1.34/1.69 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.34/1.69 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.34/1.69 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.69 }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.34/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 1.34/1.69 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.34/1.69 X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.34/1.69 { c_Complex_Oexpi( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), c_Complex_Oexpi( Y
% 1.34/1.69 ) ), c_Complex_Oexpi( X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.34/1.69 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.34/1.69 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.34/1.69 c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.34/1.69 c_RComplete_Onatceiling( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.34/1.69 ), c_RComplete_Onatfloor( Y ) ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) ) }.
% 1.34/1.69 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol27( X ) ), skol67( X
% 1.34/1.69 ) ) ), c_SEQ_Oconvergent( tc_RealDef_Oreal, X ) }.
% 1.34/1.69 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( X, skol27( X )
% 1.34/1.69 ) ), hAPP( X, skol67( X ) ) ) ), c_SEQ_Oconvergent( tc_RealDef_Oreal, X
% 1.34/1.69 ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ) ) }.
% 1.34/1.69 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.34/1.69 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.34/1.69 c_RComplete_Onatfloor( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), X ) ) }.
% 1.34/1.69 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.34/1.69 Y = X }.
% 1.34/1.69 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.34/1.69 , X ) }.
% 1.34/1.69 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 1.34/1.69 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.34/1.69 c_RComplete_Onatfloor( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.69 ( tc_Nat_Onat, Y ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_RealDef_Oreal ) ) ) ) }.
% 1.34/1.69 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.69 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_RealDef_Oreal ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.34/1.69 ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X )
% 1.34/1.69 ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.34/1.69 ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), Y ) ) }.
% 1.34/1.69 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.34/1.69 ( tc_Nat_Onat, X ) ) }.
% 1.34/1.69 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.34/1.69 ( tc_Nat_Onat, X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.34/1.69 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor(
% 1.34/1.69 X ) ), Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor( Y )
% 1.34/1.69 ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ) ) }.
% 1.34/1.69 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.34/1.69 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.34/1.69 c_RComplete_Onatfloor( X ) = Y }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) ) }.
% 1.34/1.69 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.34/1.69 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X )
% 1.34/1.69 ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.69 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.34/1.69 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_RealDef_Oreal ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.34/1.69 .
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.34/1.69 Y ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.34/1.69 c_RComplete_Onatfloor( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal
% 1.34/1.69 ( tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.34/1.69 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_RealDef_Oreal, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), c_RealDef_Oreal
% 1.34/1.69 ( tc_Nat_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) )
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.34/1.69 ( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.34/1.69 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatceiling
% 1.34/1.69 ( X ) ), Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.34/1.69 ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), skol28( U, W, V0, T
% 1.34/1.69 ) ) ), c_SEQ_OBseq( X, Y ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol28( X, Y, Z, T ) ) ) ),
% 1.34/1.69 Z ) ), c_SEQ_OBseq( X, Y ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol29( X, Y, Z ) ) ) ), Z )
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_Nat_OSuc( skol68( X, Y ) ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol73( X, Y, Z ) ) ) ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol75( T, U ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol73( X, Y, Z ) ) ) ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol75( X, Y ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol30( X, Y, Z ) ) ) ), Z )
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_Nat_OSuc( skol69( X, Y ) ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol74( X, Y, Z ) ) ) ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol76( T, U ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol74( X, Y, Z ) ) ) ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol76( X, Y ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), c_Nat_OSuc
% 1.34/1.69 ( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 1.34/1.69 ), c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Nat_Onat ) ) = Y }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 1.34/1.69 ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 1.34/1.69 ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y )
% 1.34/1.69 , X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 1.34/1.69 ), Z ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 c_Nat_OSuc( Y ) = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.34/1.69 ( X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.34/1.69 ( X ) ) ), X = Y }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.34/1.69 ( X ) ) ), Y = X }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), ! Y
% 1.34/1.69 = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 1.34/1.69 ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 1.34/1.69 ), c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.34/1.69 ( X ) ) ) }.
% 1.34/1.69 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), c_Nat_OSuc
% 1.34/1.69 ( Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.34/1.69 c_Nat_OSuc( Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Nat_OSuc( Y ) )
% 1.34/1.69 , X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Nat_OSuc( Y ) )
% 1.34/1.69 , X ) = c_Nat_OSuc( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.34/1.69 ), Y ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), c_Nat_OSuc(
% 1.34/1.69 X ) ) = c_Nat_OSuc( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.34/1.69 ), Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ), Y = c_Nat_OSuc( X ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( Y ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( Y ) ), c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ), Y = c_Nat_OSuc( X ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! Y = c_Nat_OSuc( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Y ), c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 X ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( X ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( X ) ), X ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.34/1.69 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.34/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.34/1.69 { ! X = c_Nat_OSuc( X ) }.
% 1.34/1.69 { ! c_Nat_OSuc( X ) = X }.
% 1.34/1.69 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.34/1.69 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.34/1.69 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.34/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.34/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.34/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra__1( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = c_Nat_OSuc(
% 1.34/1.69 skol31( X ) ) }.
% 1.34/1.69 { ! X = c_Nat_OSuc( Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.34/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.69 alpha6( X, Y ) }.
% 1.34/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! alpha6( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.34/1.69 , Y ), c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! alpha6( X, Y ), Y = c_Nat_OSuc( skol32( Z, Y ) ) }.
% 1.34/1.69 { ! alpha6( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.34/1.69 , skol32( X, Y ) ), X ) ) }.
% 1.34/1.69 { ! Y = c_Nat_OSuc( Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Z ), X ) ), alpha6( X, Y ) }.
% 1.34/1.69 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha7( X, Y ),
% 1.34/1.69 alpha21( X, Y ) }.
% 1.34/1.69 { ! alpha7( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.69 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) }.
% 1.34/1.69 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.69 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) }.
% 1.34/1.69 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 1.34/1.69 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha8( X, Y )
% 1.34/1.69 , alpha22( X, Y ) }.
% 1.34/1.69 { ! alpha8( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.34/1.69 , Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! alpha22( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.34/1.69 , Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! alpha22( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 1.34/1.69 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.34/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.34/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.34/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), X
% 1.34/1.69 = c_Nat_OSuc( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y )
% 1.34/1.69 , skol33( X, Y ) ) ) }.
% 1.34/1.69 { ! X = c_Nat_OSuc( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.34/1.69 , Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.34/1.69 ), X ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.34/1.69 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.34/1.69 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 Y ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 Y ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.34/1.69 c_Nat_OSuc( X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 Y ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.34/1.69 c_Nat_OSuc( Y ) ) ), X = Y }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! X = Y, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.34/1.69 c_Nat_OSuc( Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 Y ), X ) ) }.
% 1.34/1.69 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.34/1.69 ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y )
% 1.34/1.69 , X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.34/1.69 ), X ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.34/1.69 ( X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.34/1.69 ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.34/1.69 ) ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.34/1.69 ) ), X ) ) ) }.
% 1.34/1.69 { c_Nat_OSuc( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.34/1.69 , c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.34/1.69 { c_Nat_OSuc( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.34/1.69 , X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, c_Nat_OSuc
% 1.34/1.69 ( Z ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y,
% 1.34/1.69 c_Nat_OSuc( T ) ) ), hAPP( Y, T ) ) ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol34( X, Y ) ) ), hAPP(
% 1.34/1.69 Y, c_Nat_OSuc( skol34( X, Y ) ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.34/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, c_Nat_OSuc( skol70( X, Y )
% 1.34/1.69 ) ) ), hAPP( Y, skol70( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.34/1.69 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, hAPP( X, Y ) ), hAPP( X, c_Nat_OSuc( Y ) ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X,
% 1.34/1.69 skol35( X ) ) ), hAPP( X, c_Nat_OSuc( skol35( X ) ) ) ) ), c_SEQ_Osubseq
% 1.34/1.69 ( X ) }.
% 1.34/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ) =
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) ) }.
% 1.34/1.69 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.69 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_Nat_OSuc( skol36( X, Y ) ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol71( X, Y, Z ) ) ) ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), c_SEQ_OBseq( X, Y )
% 1.34/1.69 }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_Nat_OSuc( skol37( X, Y ) ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol72( X, Y, Z ) ) ) ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), c_SEQ_OBseq( X, Y )
% 1.34/1.69 }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_Omonoseq(
% 1.34/1.69 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.34/1.69 , X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_Oconvergent(
% 1.34/1.69 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.34/1.69 , X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_OBseq(
% 1.34/1.69 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.34/1.69 , X ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), T ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 1.34/1.69 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.34/1.69 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.34/1.69 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.34/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.34/1.69 tc_Int_Oint, Y ) ), X ) ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Int_Oint ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Int_Oint ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.34/1.69 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Int_Oint ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.34/1.69 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), Y ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.34/1.69 , Y ), X ) ) ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.34/1.69 , Y ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.34/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.69 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.69 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.69 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.34/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.34/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.34/1.69 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.69 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.34/1.69 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.34/1.69 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.34/1.69 ( X ) }.
% 1.34/1.69 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.69 = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.34/1.69 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.34/1.69 ) }.
% 1.34/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.34/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Nat_Onat ) ) = Y }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 1.34/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.69 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.69 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.69 .
% 1.34/1.69 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.69 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.69 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) }.
% 1.34/1.69 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.69 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.69 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.34/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.34/1.69 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP
% 1.34/1.69 ( c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP
% 1.34/1.69 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.34/1.69 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.69 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.34/1.69 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.34/1.69 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.34/1.69 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.34/1.69 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ) ), ! hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y )
% 1.34/1.69 ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), ! hBOOL( hAPP
% 1.34/1.69 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.69 ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), Z = Y }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 1.34/1.69 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.69 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.69 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), T ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.34/1.69 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 1.34/1.69 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ),
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.69 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), Z ) ), T = Y }.
% 1.34/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.34/1.69 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.69 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.34/1.69 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.34/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol38( X, Y ) ), Y
% 1.34/1.69 ) ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.34/1.69 c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) )
% 1.34/1.69 ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.69 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.34/1.69 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.34/1.69 tc_Int_Oint, Y ) ), X ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Int_Oint ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Int_Oint ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 1.34/1.69 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.34/1.69 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.34/1.69 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.34/1.69 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.34/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Z ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Int_Oint ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.34/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.34/1.69 ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ), c_Groups_Oone__class_Oone
% 1.34/1.69 ( tc_Int_Oint ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.34/1.69 tc_Int_Oint, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.34/1.69 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y =
% 1.34/1.69 X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.34/1.69 Y = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.69 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X
% 1.34/1.69 ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Int_Oint ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.34/1.69 ( tc_Int_Oint ) ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Int_Oint ) ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.34/1.69 }.
% 1.34/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.34/1.69 ( tc_Int_Oint ) }.
% 1.34/1.69 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.34/1.69 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.34/1.69 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.34/1.69 ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), X =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), Y ) ) }.
% 1.34/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.34/1.69 , Y ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.34/1.69 , Y ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.34/1.69 ( tc_Int_Oint ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 1.34/1.69 ), Y = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 1.34/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 1.34/1.69 ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 1.34/1.69 .
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), W ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.69 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.69 ( tc_Int_Oint, Y ), U ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), Z ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 1.34/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.69 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.69 ( tc_Int_Oint, U ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), U ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), U ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Int_Oint ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.69 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 1.34/1.69 ( tc_Int_Oint ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_Int_Oint ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.34/1.69 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, skol39( X ) ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_Nat_OSuc( skol39( X ) ) ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol40( Z, T ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol40( X, Y ) ), X ) =
% 1.34/1.69 Y }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 1.34/1.69 skol40( X, Y ) }.
% 1.34/1.69 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 1.34/1.69 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 1.34/1.69 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.34/1.69 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.34/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol41( Z, T ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol41( X, Y ) ), X ) =
% 1.34/1.69 Y }.
% 1.34/1.69 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Y ) ) ), X
% 1.34/1.69 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.34/1.69 c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, skol42( X, Y ) ) ), X ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, c_Nat_OSuc( skol42( X, Y ) ) ) ), X ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.34/1.69 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis( hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.34/1.69 { c_Complex_Ocis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.34/1.69 { c_Complex_Ocis( X ) = c_Complex_Orcis( c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_RealDef_Oreal ), X ) }.
% 1.34/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.34/1.69 c_Complex_Ocis( Y ) ), X ) = c_Complex_Ocis( hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, X ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.34/1.69 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.69 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 1.34/1.69 { c_Transcendental_Ocos( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ) = hAPP(
% 1.34/1.69 c_Complex_ORe, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.69 tc_Complex_Ocomplex ), c_Complex_Ocis( X ) ), Y ) ) }.
% 1.34/1.69 { c_Transcendental_Osin( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ) = hAPP(
% 1.34/1.69 c_Complex_OIm, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.69 tc_Complex_Ocomplex ), c_Complex_Ocis( X ) ), Y ) ) }.
% 1.34/1.69 { c_Transcendental_Osin( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_RealDef_Oreal ), c_Transcendental_Osin( Y ) ), c_Transcendental_Ocos(
% 1.34/1.69 X ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_Transcendental_Ocos( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 1.34/1.69 ( X ) ), c_Transcendental_Ocos( X ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 1.34/1.69 ( X ) ), c_Transcendental_Osin( X ) ) ) = c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! c_Transcendental_Osin( X ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.34/1.69 c_Transcendental_Ocos( X ) ) = c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! c_Transcendental_Ocos( X ) = c_Groups_Oone__class_Oone(
% 1.34/1.69 tc_RealDef_Oreal ), c_Transcendental_Osin( X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { c_Transcendental_Ocos( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.34/1.69 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Transcendental_Ocos( X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.34/1.69 ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Transcendental_Osin( X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.34/1.69 ) ) ) }.
% 1.34/1.69 { c_Transcendental_Osin( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.34/1.69 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { hAPP( c_Complex_OIm, c_Complex_Ocis( X ) ) = c_Transcendental_Osin( X ) }
% 1.34/1.69 .
% 1.34/1.69 { hAPP( c_Complex_ORe, c_Complex_Ocis( X ) ) = c_Transcendental_Ocos( X ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.69 ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), Y ) ), hBOOL( hAPP
% 1.34/1.69 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln(
% 1.34/1.69 X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), !
% 1.34/1.69 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! X = Y,
% 1.34/1.69 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.69 ) ), X ) ) }.
% 1.34/1.69 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Transcendental_Osin( X ) )
% 1.34/1.69 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Transcendental_Ocos( X ) )
% 1.34/1.69 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.69 { hAPP( c_Complex_OIm, c_Complex_Orcis( Y, X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.34/1.69 c_Transcendental_Osin( X ) ) }.
% 1.34/1.69 { hAPP( c_Complex_ORe, c_Complex_Orcis( Y, X ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.34/1.69 c_Transcendental_Ocos( X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.34/1.69 ( X ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ), hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Transcendental_Oln( X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.34/1.69 X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.34/1.69 X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.69 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.69 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.69 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), !
% 1.34/1.69 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.34/1.69 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! X =
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 1.34/1.69 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.34/1.69 X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.34/1.69 X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.34/1.69 X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.34/1.69 X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.34/1.69 X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.34/1.69 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.34/1.69 X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ),
% 1.34/1.69 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.69 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( tc_RealDef_Oreal ), c_Transcendental_Oln( X ) ), c_Transcendental_Oln(
% 1.34/1.69 Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.34/1.69 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_Transcendental_Ocos
% 1.34/1.69 ( c_Transcendental_Oarccos( X ) ) = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.69 tc_Nat_Onat, skol43( X, Y ) ) ), X ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol44( Z, T ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hAPP( hAPP(
% 1.34/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol44( X, Y ) ),
% 1.34/1.69 c_Nat_OSuc( Y ) ) = X }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol45( X, Y ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol46( X, Y ) ) ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol47( X ) ) ) ) }.
% 1.34/1.69 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.34/1.69 ( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.34/1.69 ), Z ), Y ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.34/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.69 ( X, Y ) ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.34/1.69 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.34/1.69 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.69 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T
% 1.34/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y
% 1.34/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 1.34/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ), Y ) = Z }.
% 1.34/1.69 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) = Z }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.34/1.69 ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.34/1.69 ), ! X = Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.34/1.69 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z
% 1.34/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) = X }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.34/1.69 Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.34/1.69 ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.34/1.69 ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, U, Z ) ), c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( X, T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ominus__class_Ominus( X
% 1.34/1.69 , T, Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.34/1.69 Z ) ), U ) ), T ) = Y }.
% 1.34/1.69 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) = Y, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.34/1.69 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.69 W ) ), U ) ), Y ) }.
% 1.34/1.69 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ) ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.34/1.69 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), U ), c_Groups_Ominus__class_Ominus( X
% 1.34/1.69 , T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.34/1.69 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.34/1.69 ) ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.34/1.69 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.34/1.69 ) ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ), c_Groups_Oabs__class_Oabs( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.34/1.69 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.34/1.69 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.34/1.69 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.34/1.69 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.69 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( X, Y, Z ) ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.34/1.69 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.34/1.69 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.69 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.34/1.69 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.69 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.34/1.69 ) }.
% 1.34/1.69 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.34/1.69 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.34/1.69 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.34/1.69 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.34/1.69 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.34/1.69 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, U ), T ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, U ), T ) ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.34/1.69 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.34/1.69 ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), Z ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.34/1.69 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.34/1.69 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.34/1.69 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.34/1.69 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP
% 1.34/1.69 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Y ) = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( tc_Nat_Onat, X, Y ) ), Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.34/1.69 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) )
% 1.34/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ), hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hAPP
% 1.34/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.34/1.69 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), c_Nat_OSuc( Y ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.69 W ) ), U ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.69 W ) ), U ) ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.34/1.69 Z ) ), U ) ), T ) ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.34/1.69 Z ) ), U ) ), T ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.69 W ) ), U ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.69 W ) ), U ) ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 1.34/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) ), Y ) ) }.
% 1.34/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) ), Y ) ), hBOOL(
% 1.34/1.69 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.34/1.69 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.34/1.69 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) )
% 1.34/1.69 }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ) }.
% 1.34/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.69 ( X ), U ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) )
% 1.34/1.69 ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.34/1.69 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z ) )
% 1.34/1.69 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Y
% 1.34/1.69 ) ) ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.34/1.69 ) ), T ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 1.34/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.34/1.69 ) ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ) }.
% 1.34/1.69 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.69 Y ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.34/1.69 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.34/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.34/1.69 ( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) ), X ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.34/1.69 , ! alpha9( X, Y, Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.34/1.69 , ! alpha23( X, Y, Z ) }.
% 1.34/1.69 { alpha9( X, Y, Z ), alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.69 { ! alpha23( X, Y, Z ), ! hBOOL( hAPP( Z, skol48( T, U, Z ) ) ) }.
% 1.34/1.69 { ! alpha23( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_Nat_Onat ), X ), skol48( X, Y, Z ) ) }.
% 1.34/1.69 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 1.34/1.69 hBOOL( hAPP( Z, T ) ), alpha23( X, Y, Z ) }.
% 1.34/1.69 { ! alpha9( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.34/1.69 { ! alpha9( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha9( X
% 1.34/1.69 , Y, Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.34/1.69 , alpha10( X, Y, Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.34/1.69 , alpha24( X, Y, Z ) }.
% 1.34/1.69 { ! alpha10( X, Y, Z ), ! alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.69 { ! alpha24( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.69 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( Z, skol49( T, U, Z ) ) ), alpha24( X, Y, Z ) }.
% 1.34/1.69 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol49(
% 1.34/1.69 X, Y, Z ) ), alpha24( X, Y, Z ) }.
% 1.34/1.69 { ! alpha10( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.69 tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.34/1.69 tc_Nat_Onat ) ) ) }.
% 1.34/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.69 alpha10( X, Y, Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha10
% 1.34/1.69 ( X, Y, Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), c_Nat_OSuc( X ) ) }
% 1.34/1.69 .
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ), T = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 1.34/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) =
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 1.34/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ) }.
% 1.34/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 1.34/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ),
% 1.34/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.34/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ), hAPP( hAPP
% 1.34/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z,
% 1.34/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 1.34/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) =
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 1.34/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 1.34/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.70 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.34/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.34/1.70 Z ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) ) ) }.
% 1.34/1.70 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = c_Nat_OSuc(
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 1.34/1.70 ( tc_Nat_Onat ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_Nat_OSuc(
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 1.34/1.70 ( tc_Nat_Onat ) ) ) = X }.
% 1.34/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = X }.
% 1.34/1.70 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.34/1.70 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 1.34/1.70 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 1.34/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 1.34/1.70 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ),
% 1.34/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 1.34/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.70 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.34/1.70 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.34/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.70 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.34/1.70 ( tc_Nat_Onat ) ) ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.34/1.70 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.70 Y ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.34/1.70 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.34/1.70 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.34/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.70 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.70 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.70 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol50( X ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), c_RealDef_Oreal(
% 1.34/1.70 tc_Nat_Onat, skol50( X ) ) ) ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.34/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), skol51( X, U
% 1.34/1.70 , W, T ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.34/1.70 V0 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) ) ) ) ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.34/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.34/1.70 hAPP( Z, T ), hAPP( Z, skol51( X, Y, Z, T ) ) ) ) ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), U ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) ) ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.70 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 1.34/1.70 { hAPP( c_Complex_OIm, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.34/1.70 Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 1.34/1.70 c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) }.
% 1.34/1.70 { hAPP( c_Complex_ORe, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.34/1.70 Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 1.34/1.70 c_Complex_ORe, Y ), hAPP( c_Complex_ORe, X ) ) }.
% 1.34/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.34/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.70 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) ) }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) ) ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.70 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( c_Complex_ORe, Y )
% 1.34/1.70 , hAPP( c_Complex_ORe, X ) ) ) ), c_Groups_Oabs__class_Oabs(
% 1.34/1.70 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 1.34/1.70 c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) ) ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.34/1.70 ( tc_Int_Oint ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, Y ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.34/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.34/1.70 ( tc_Int_Oint ) ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Nat_Onat, X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.70 c_RealDef_Oreal( tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }
% 1.34/1.70 .
% 1.34/1.70 { c_Transcendental_Osin( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 1.34/1.70 , X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 1.34/1.70 ( Y ) ), c_Transcendental_Ocos( X ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 1.34/1.70 ( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 1.34/1.70 { c_Transcendental_Osin( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 1.34/1.70 , X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 1.34/1.70 ( X ) ), c_Transcendental_Osin( Y ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 1.34/1.70 ( X ) ), c_Transcendental_Ocos( Y ) ) ) }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.34/1.70 { c_Transcendental_Ocos( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.70 tc_RealDef_Oreal ), Y ), X ) ) = c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.70 tc_RealDef_Oreal ), c_Transcendental_Ocos( Y ) ), c_Transcendental_Ocos(
% 1.34/1.70 X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.70 c_Transcendental_Osin( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 1.34/1.70 { c_Transcendental_Ocos( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 1.34/1.70 , X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.70 c_Transcendental_Ocos( Y ) ), c_Transcendental_Ocos( X ) ) ), hAPP( hAPP
% 1.34/1.70 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.70 c_Transcendental_Osin( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 1.34/1.70 { c_Transcendental_Ocos( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 1.34/1.70 , X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.34/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.70 c_Transcendental_Ocos( X ) ), c_Transcendental_Ocos( Y ) ) ), hAPP( hAPP
% 1.34/1.70 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.70 c_Transcendental_Osin( X ) ), c_Transcendental_Osin( Y ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), c_RComplete_Onatfloor(
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.34/1.70 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.34/1.70 c_RComplete_Onatfloor( X ), Y ) }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_RealDef_Oreal(
% 1.34/1.70 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), c_RComplete_Onatceiling(
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.34/1.70 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.34/1.70 c_RComplete_Onatceiling( X ), Y ) }.
% 1.34/1.70 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.70 tc_Complex_Ocomplex ), Y ), X ) ) = c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.70 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 1.34/1.70 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.34/1.70 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.34/1.70 ( tc_Int_Oint, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 1.34/1.70 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.34/1.70 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Int_Oint, Z, Y ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X
% 1.34/1.70 ) ) ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.34/1.70 tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ) ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) ) }.
% 1.34/1.70 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ), c_Complex_Oii )
% 1.34/1.70 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.34/1.70 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.70 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Int_Oint, X, Y ) }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.34/1.70 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.34/1.70 ) }.
% 1.34/1.70 { hAPP( c_Complex_ORe, c_Complex_Oii ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_RealDef_Oreal ) }.
% 1.34/1.70 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { hAPP( c_Complex_OIm, c_Complex_Oii ) = c_Groups_Oone__class_Oone(
% 1.34/1.70 tc_RealDef_Oreal ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Transfer_Otsub( X, Y
% 1.34/1.70 ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.70 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Int_Oint, X, Y ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), Y ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.34/1.70 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP(
% 1.34/1.70 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.34/1.70 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.34/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U, Z
% 1.34/1.70 ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 1.34/1.70 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Int_Oint, Z, Y ), X ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.34/1.70 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.34/1.70 }.
% 1.34/1.70 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.34/1.70 ( tc_Int_Oint, X, Y ) ) ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.34/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.34/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.34/1.70 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.34/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.70 ( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.70 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.34/1.70 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.70 ( tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.34/1.70 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.70 ( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.70 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ),
% 1.34/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 1.34/1.70 .
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ),
% 1.34/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ), ! hBOOL( hAPP
% 1.34/1.70 ( c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.70 ( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.34/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 1.34/1.70 .
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.34/1.70 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.34/1.70 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.34/1.70 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.70 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 1.34/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.70 { ! alpha11( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.70 { ! alpha11( X, Y ), alpha25( X, Y ), alpha30( X, Y ) }.
% 1.34/1.70 { ! alpha25( X, Y ), alpha11( X, Y ) }.
% 1.34/1.70 { ! alpha30( X, Y ), alpha11( X, Y ) }.
% 1.34/1.70 { ! alpha30( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! alpha30( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, X ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), alpha30( X, Y ) }
% 1.34/1.70 .
% 1.34/1.70 { ! alpha25( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.34/1.70 { ! alpha25( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, Y ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), alpha25( X, Y ) }
% 1.34/1.70 .
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.70 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y
% 1.34/1.70 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.70 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y
% 1.34/1.70 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.70 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.34/1.70 ( X ), Y ), Z ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.34/1.70 alpha12( X, Z ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.34/1.70 alpha26( X, Y, Z ) }.
% 1.34/1.70 { ! alpha12( X, Z ), ! alpha26( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.70 { ! alpha26( X, Y, Z ), alpha31( X, Y, Z ) }.
% 1.34/1.70 { ! alpha26( X, Y, Z ), alpha34( X, Y, Z ) }.
% 1.34/1.70 { ! alpha31( X, Y, Z ), ! alpha34( X, Y, Z ), alpha26( X, Y, Z ) }.
% 1.34/1.70 { ! alpha34( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha37
% 1.34/1.70 ( X, Y, Z ) }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha34( X, Y, Z ) }.
% 1.34/1.70 { ! alpha37( X, Y, Z ), alpha34( X, Y, Z ) }.
% 1.34/1.70 { ! alpha37( X, Y, Z ), ! alpha39( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Z, skol52( T, U, Z ) ) ), alpha37( X, Y, Z ) }.
% 1.34/1.70 { alpha39( X, Y, skol52( X, Y, Z ) ), alpha37( X, Y, Z ) }.
% 1.34/1.70 { ! alpha39( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, X ), skol53( X, T, U ) ) ) }.
% 1.34/1.70 { ! alpha39( X, Y, Z ), alpha41( X, Y, Z, skol53( X, Y, Z ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), T ) ), !
% 1.34/1.70 alpha41( X, Y, Z, T ), alpha39( X, Y, Z ) }.
% 1.34/1.70 { ! alpha41( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { ! alpha41( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.70 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.70 X ), Z ) ), T ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y = hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha41( X
% 1.34/1.70 , Y, Z, T ) }.
% 1.34/1.70 { ! alpha31( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha35
% 1.34/1.70 ( X, Y, Z ) }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha31( X, Y, Z ) }
% 1.34/1.70 .
% 1.34/1.70 { ! alpha35( X, Y, Z ), alpha31( X, Y, Z ) }.
% 1.34/1.70 { ! alpha35( X, Y, Z ), ! alpha38( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Z, skol54( T, U, Z ) ) ), alpha35( X, Y, Z ) }.
% 1.34/1.70 { alpha38( X, Y, skol54( X, Y, Z ) ), alpha35( X, Y, Z ) }.
% 1.34/1.70 { ! alpha38( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol55( T, U,
% 1.34/1.70 W ) ) ) }.
% 1.34/1.70 { ! alpha38( X, Y, Z ), alpha40( X, Y, Z, skol55( X, Y, Z ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha40( X, Y, Z,
% 1.34/1.70 T ), alpha38( X, Y, Z ) }.
% 1.34/1.70 { ! alpha40( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, T ), X ) ) }.
% 1.34/1.70 { ! alpha40( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.70 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.70 X ), Z ) ), T ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), X ) ), !
% 1.34/1.70 Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha40( X
% 1.34/1.70 , Y, Z, T ) }.
% 1.34/1.70 { ! alpha12( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.34/1.70 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha12( X, Y ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha12
% 1.34/1.70 ( X, Y ) }.
% 1.34/1.70 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.34/1.70 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha44
% 1.34/1.70 ( X, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), Z =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Int_Oint, T, Z ) = Y }.
% 1.34/1.70 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.34/1.70 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha44
% 1.34/1.70 ( X, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Z )
% 1.34/1.70 , X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.34/1.70 ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), Z =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Int_Oint, T, Z ) = Y }.
% 1.34/1.70 { ! alpha44( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.34/1.70 { ! alpha44( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL
% 1.34/1.70 ( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha44( X, Y ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), alpha44( X, Y ) }
% 1.34/1.70 .
% 1.34/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), X
% 1.34/1.70 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.70 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 1.34/1.70 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.34/1.70 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.34/1.70 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.34/1.70 ) ), hAPP( c_Complex_ORe, X ) ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.34/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.34/1.70 Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol56( T, U, W ) ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.34/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.34/1.70 Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ) ), skol56( X, Y
% 1.34/1.70 , Z ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_RealDef_Oreal, Y ), T ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.34/1.70 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.34/1.70 Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ) ), skol56( X, Y
% 1.34/1.70 , Z ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_RealDef_Oreal, T ), Z ) ) }.
% 1.34/1.70 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Nat_Onat, Z, Y ), X ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.70 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.34/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) ) }.
% 1.34/1.70 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.70 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) ) }.
% 1.34/1.70 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.34/1.70 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 1.34/1.70 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 1.34/1.70 , Z, X ) ) }.
% 1.34/1.70 { c_Complex_Ocomplex_OComplex( hAPP( c_Complex_ORe, X ), hAPP(
% 1.34/1.70 c_Complex_OIm, X ) ) = X }.
% 1.34/1.70 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 1.34/1.70 ), T = Y }.
% 1.34/1.70 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 1.34/1.70 ), Z = X }.
% 1.34/1.70 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 1.34/1.70 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 1.34/1.70 { hAPP( c_Complex_OIm, c_Complex_Ocomplex_OComplex( Y, X ) ) = X }.
% 1.34/1.70 { hAPP( c_Complex_ORe, c_Complex_Ocomplex_OComplex( Y, X ) ) = Y }.
% 1.34/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 1.34/1.70 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 1.34/1.70 ) ) = c_Complex_Ocomplex_OComplex( hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }.
% 1.34/1.70 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.34/1.70 ) }.
% 1.34/1.70 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.34/1.70 ) }.
% 1.34/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.70 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Complex_Ocomplex ) }.
% 1.34/1.70 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 1.34/1.70 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.70 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X =
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.34/1.70 c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 1.34/1.70 { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 1.34/1.70 ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.34/1.70 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.34/1.70 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.34/1.70 }.
% 1.34/1.70 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.34/1.70 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.34/1.70 ) }.
% 1.34/1.70 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.70 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.34/1.70 tc_Complex_Ocomplex ) }.
% 1.34/1.70 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 1.34/1.70 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.34/1.70 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.70 { c_Complex_Ocis( X ) = c_Complex_Ocomplex_OComplex( c_Transcendental_Ocos
% 1.34/1.70 ( X ), c_Transcendental_Osin( X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.34/1.70 alpha13( X, Z ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.34/1.70 alpha27( X, Y, Z ) }.
% 1.34/1.70 { ! alpha13( X, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.70 { ! alpha27( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.70 alpha32( X, Y, Z ) }.
% 1.34/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha27( X, Y, Z ) }.
% 1.34/1.70 { ! alpha32( X, Y, Z ), alpha27( X, Y, Z ) }.
% 1.34/1.70 { ! alpha32( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Nat_Onat, T ), X ) ), alpha36( X, Y, Z, T ) }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol57( X, T, U
% 1.34/1.70 ) ), X ) ), alpha32( X, Y, Z ) }.
% 1.34/1.70 { ! alpha36( X, Y, Z, skol57( X, Y, Z ) ), alpha32( X, Y, Z ) }.
% 1.34/1.70 { ! alpha36( X, Y, Z, T ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.70 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.70 X ), U ) ), T ), hBOOL( hAPP( Z, U ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Z, skol58( U, W, Z, V0 ) ) ), alpha36( X, Y, Z, T ) }.
% 1.34/1.70 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol58( X, Y, Z, T ) )
% 1.34/1.70 ), T ), alpha36( X, Y, Z, T ) }.
% 1.34/1.70 { ! alpha13( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.70 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.34/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha13( X, Y ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 1.34/1.70 ( X, Y ) }.
% 1.34/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.34/1.70 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 1.34/1.70 ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.70 tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.70 tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.70 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.70 tc_RealDef_Oreal ), T ), X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.70 ( tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 1.34/1.70 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.70 c_Complex_Ocomplex_OComplex( c_Transcendental_Ocos( X ),
% 1.34/1.70 c_Transcendental_Osin( X ) ) ) = c_Groups_Oone__class_Oone(
% 1.34/1.70 tc_RealDef_Oreal ) }.
% 1.34/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X )
% 1.34/1.70 = c_Complex_Ocomplex_OComplex( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.34/1.70 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 1.34/1.70 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 1.34/1.70 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.34/1.70 alpha14( X, Z ), alpha28( X, Y, Z ) }.
% 1.34/1.70 { ! alpha14( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.70 { ! alpha28( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.34/1.70 tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.70 { ! alpha28( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.34/1.70 ), skol59( X, Y, T ) ) ), Y ) ) }.
% 1.34/1.70 { ! alpha28( X, Y, Z ), alpha33( X, Y, Z, skol59( X, Y, Z ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ) ), Y ) ), !
% 1.34/1.70 alpha33( X, Y, Z, T ), alpha28( X, Y, Z ) }.
% 1.34/1.70 { ! alpha33( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.34/1.70 tc_Nat_Onat, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 1.34/1.70 ), X ), c_Nat_OSuc( T ) ) ) ) }.
% 1.34/1.70 { ! alpha33( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T )
% 1.34/1.70 ) ) ), ! hBOOL( hAPP( Z, T ) ), alpha33( X, Y, Z, T ) }.
% 1.34/1.70 { ! alpha14( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.70 { ! alpha14( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Nat_Onat ) ) ) }.
% 1.34/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14( X, Y ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ), ! hBOOL
% 1.34/1.70 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) )
% 1.34/1.70 , Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z =
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.34/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.34/1.70 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 1.34/1.70 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.34/1.70 c_Transcendental_Ocos( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.70 c_Transcendental_Ocos( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.34/1.70 c_Transcendental_Ocos( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 1.34/1.70 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Nat_Onat ) }.
% 1.34/1.70 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 1.34/1.70 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 1.34/1.70 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 1.34/1.70 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.70 tc_Nat_Onat ) ), Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), X ), c_RealDef_Oreal
% 1.34/1.70 ( tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.34/1.70 c_RComplete_Onatfloor( X ), Y ) }.
% 1.34/1.70 { c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, X ) = hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), X ),
% 1.34/1.70 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Y ), c_Groups_Oone__class_Oone( X )
% 1.34/1.70 ) = Y }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , ! hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) =
% 1.34/1.70 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , ! Z = Y, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) =
% 1.34/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.34/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.34/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.34/1.70 hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.34/1.70 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Z
% 1.34/1.70 ) ), Y ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_SEQ_Oconvergent( X, Y )
% 1.34/1.70 , c_SEQ_Oconvergent( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X
% 1.34/1.70 , X ), tc_Nat_Onat, c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.34/1.70 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.34/1.70 class_RealVector_Oreal__normed__field( X ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.34/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), hAPP(
% 1.34/1.70 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , ! hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z, T =
% 1.34/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), hAPP(
% 1.34/1.70 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , ! T = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), hAPP
% 1.34/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.70 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.34/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP
% 1.34/1.70 ( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.70 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.70 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.70 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.34/1.70 { hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), hAPP(
% 1.34/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ), hAPP
% 1.34/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 1.34/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), X ), Y )
% 1.34/1.70 }.
% 1.34/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), Y ), X ) ) ),
% 1.34/1.70 alpha15( X, Y ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), Y ), X ) ) ),
% 1.34/1.70 alpha29( X, Y ) }.
% 1.34/1.70 { ! alpha15( X, Y ), ! alpha29( X, Y ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 1.34/1.70 { ! alpha29( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y )
% 1.34/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X )
% 1.34/1.70 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), alpha29( X, Y )
% 1.34/1.70 }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), alpha29( X, Y ) }.
% 1.34/1.70 { ! alpha15( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.34/1.70 tc_RealDef_Oreal, Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.34/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), alpha15( X, Y ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), alpha15( X, Y )
% 1.34/1.70 }.
% 1.34/1.70 { hAPP( c_Complex_OIm, c_Groups_Osgn__class_Osgn( tc_Complex_Ocomplex, X )
% 1.34/1.70 ) = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ),
% 1.34/1.70 hAPP( c_Complex_OIm, X ) ), c_RealVector_Onorm__class_Onorm(
% 1.34/1.70 tc_Complex_Ocomplex, X ) ) }.
% 1.34/1.70 { hAPP( c_Complex_ORe, c_Groups_Osgn__class_Osgn( tc_Complex_Ocomplex, X )
% 1.34/1.70 ) = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ),
% 1.34/1.70 hAPP( c_Complex_ORe, X ) ), c_RealVector_Onorm__class_Onorm(
% 1.34/1.70 tc_Complex_Ocomplex, X ) ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ominus__class_Ominus( X, T
% 1.34/1.70 , Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.34/1.70 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ominus__class_Ominus( X, T
% 1.34/1.70 , Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.34/1.70 { ! class_RealVector_Oreal__field( X ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ominus__class_Ominus( X,
% 1.34/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ), Y ) = hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), W ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ominus__class_Ominus( X, U
% 1.34/1.70 , Z ) ), Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.34/1.70 hAPP( c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ominus__class_Ominus
% 1.34/1.70 ( X, W, T ) ), Y ) ), Z ) ) }.
% 1.34/1.70 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ), hAPP( hAPP
% 1.34/1.70 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 1.34/1.70 ) ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), Y )
% 1.34/1.70 ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP
% 1.34/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 1.34/1.70 ) ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), X )
% 1.34/1.70 ) }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_RealDef_Oreal( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y
% 1.34/1.70 , X ) ) ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal
% 1.34/1.70 ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X
% 1.34/1.70 ) ) ) ) }.
% 1.34/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.34/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ), hAPP
% 1.34/1.70 ( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, T ) ) = hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ),
% 1.34/1.70 c_Transcendental_Oln( hAPP( hAPP( c_Rings_Oinverse__class_Odivide(
% 1.34/1.70 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Ominus__class_Ominus(
% 1.34/1.70 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 1.34/1.70 }.
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.70 tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal
% 1.34/1.70 ( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) ) ) }
% 1.34/1.70 .
% 1.34/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.70 tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal
% 1.34/1.70 ( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.34/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.70 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ) ) }.
% 1.34/1.70 { ! class_Fields_Olinordered__field( X ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.70 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) ) }.
% 1.34/1.70 { hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex ),
% 1.34/1.70 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis(
% 1.34/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.34/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.34/1.70 .
% 1.34/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.34/1.70 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.34/1.70 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.34/1.70 ) ) }.
% 1.34/1.70 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.34/1.70 .
% 1.34/1.70 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.34/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.70 tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.34/1.70 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.34/1.70 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.34/1.70 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.34/1.70 { class_Power_Opower( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.34/1.70 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.34/1.70 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.34/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.70 tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.34/1.70 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.34/1.70 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.34/1.70 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.34/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.70 tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.34/1.70 .
% 1.34/1.70 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_RealVector_Ometric__space( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.70 tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_RealVector_Ometric__space( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.34/1.70 { ! class_Rings_Oidom( X ),
% 1.34/1.70 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.34/1.70 ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.34/1.70 X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.34/1.70 ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.34/1.70 .
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.34/1.70 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.70 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.34/1.70 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.34/1.70 ( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.34/1.70 ( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.34/1.70 ) ) }.
% 1.34/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.34/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.70 { hAPP( c_COMBK( T, Z, Y ), X ) = Y }.
% 1.34/1.70 { hAPP( c_COMBB( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 1.34/1.70 { hAPP( c_COMBC( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 1.34/1.70 { hAPP( c_COMBS( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), hAPP( Y, X ) )
% 1.34/1.70 }.
% 1.34/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), v_r ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ), ! hBOOL( hAPP(
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.70 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_OIm, hAPP(
% 1.34/1.70 v_s, hAPP( v_f____, hAPP( v_ga____, skol60 ) ) ) ) ) ), hAPP( hAPP(
% 1.34/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), v_r ),
% 1.34/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ) }.
% 1.34/1.70
% 1.34/1.70 *** allocated 15000 integers for clauses
% 1.34/1.70 *** allocated 22500 integers for clauses
% 1.34/1.70 *** allocated 33750 integers for clauses
% 1.34/1.70 *** allocated 50625 integers for clauses
% 1.34/1.70 *** allocated 75937 integers for clauses
% 1.34/1.70 percentage equality = 0.246296, percentage horn = 0.914880
% 1.34/1.70 This is a problem with some equality
% 1.34/1.70
% 1.34/1.70
% 1.34/1.70
% 1.34/1.70 Options Used:
% 1.34/1.70
% 1.34/1.70 useres = 1
% 1.34/1.70 useparamod = 1
% 1.34/1.70 useeqrefl = 1
% 1.34/1.70 useeqfact = 1
% 1.34/1.70 usefactor = 1
% 1.34/1.70 usesimpsplitting = 0
% 1.34/1.70 usesimpdemod = 5
% 1.34/1.70 usesimpres = 3
% 1.34/1.70
% 1.34/1.70 resimpinuse = 1000
% 1.34/1.70 resimpclauses = 20000
% 1.34/1.70 substype = eqrewr
% 1.34/1.70 backwardsubs = 1
% 1.34/1.70 selectoldest = 5
% 1.34/1.70
% 1.34/1.70 litorderings [0] = split
% 1.34/1.70 litorderings [1] = extend the termordering, first sorting on arguments
% 1.34/1.70
% 1.34/1.70 termordering = kbo
% 1.34/1.70
% 1.34/1.70 litapriori = 0
% 1.34/1.70 termapriori = 1
% 1.34/1.70 litaposteriori = 0
% 1.34/1.70 termaposteriori = 0
% 1.34/1.70 demodaposteriori = 0
% 1.34/1.70 ordereqreflfact = 0
% 1.34/1.70
% 1.34/1.70 litselect = negord
% 1.34/1.70
% 1.34/1.70 maxweight = 15
% 1.34/1.70 maxdepth = 30000
% 1.34/1.70 maxlength = 115
% 1.34/1.70 maxnrvars = 195
% 1.34/1.70 excuselevel = 1
% 1.34/1.70 increasemaxweight = 1
% 1.34/1.70
% 1.34/1.70 maxselected = 10000000
% 1.34/1.70 maxnrclauses = 10000000
% 1.34/1.70
% 1.34/1.70 showgenerated = 0
% 1.34/1.70 showkept = 0
% 1.34/1.70 showselected = 0
% 1.34/1.70 showdeleted = 0
% 1.34/1.70 showresimp = 1
% 1.34/1.70 showstatus = 2000
% 1.34/1.70
% 1.34/1.70 prologoutput = 0
% 1.34/1.70 nrgoals = 5000000
% 1.34/1.70 totalproof = 1
% 1.34/1.70
% 1.34/1.70 Symbols occurring in the translation:
% 1.34/1.70
% 1.34/1.70 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.34/1.70 . [1, 2] (w:1, o:241, a:1, s:1, b:0),
% 1.34/1.70 ! [4, 1] (w:0, o:135, a:1, s:1, b:0),
% 1.34/1.70 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.34/1.70 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.34/1.70 hAPP [38, 2] (w:1, o:265, a:1, s:1, b:0),
% 1.34/1.70 tc_RealDef_Oreal [39, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.34/1.70 c_Groups_Ozero__class_Ozero [40, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.34/1.70 c_Orderings_Oord__class_Oless__eq [41, 2] (w:1, o:268, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 v_r [42, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.34/1.70 hBOOL [43, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.34/1.70 v_f____ [44, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.34/1.70 c_SEQ_Osubseq [45, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_OIm [47, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.34/1.70 v_s [48, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.34/1.70 c_Groups_Oabs__class_Oabs [49, 2] (w:1, o:270, a:1, s:1, b:0),
% 1.34/1.70 c_Groups_Oplus__class_Oplus [50, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.34/1.70 c_Groups_Oone__class_Oone [51, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.34/1.70 v_ga____ [52, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.34/1.70 tc_Complex_Ocomplex [53, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.34/1.70 c_RealVector_Onorm__class_Onorm [54, 2] (w:1, o:271, a:1, s:1, b:0),
% 1.34/1.70
% 1.34/1.70 c_Orderings_Oord__class_Oless [56, 2] (w:1, o:272, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Olinordered__semidom [58, 1] (w:1, o:150, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 class_Groups_Oordered__comm__monoid__add [61, 1] (w:1, o:155, a:1, s:
% 1.34/1.70 1, b:0),
% 1.34/1.70 class_Groups_Oordered__ab__group__add__abs [63, 1] (w:1, o:156, a:1
% 1.34/1.70 , s:1, b:0),
% 1.34/1.70 tc_Nat_Onat [65, 0] (w:1, o:45, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Ozero [69, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Olinordered__idom [71, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Ocancel__semigroup__add [72, 1] (w:1, o:159, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 class_Groups_Ocancel__ab__semigroup__add [73, 1] (w:1, o:160, a:1, s:
% 1.34/1.70 1, b:0),
% 1.34/1.70 class_Groups_Oab__semigroup__add [76, 1] (w:1, o:161, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 class_Groups_Oone [77, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Ocomm__monoid__add [81, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.34/1.70
% 1.34/1.70 class_Groups_Omonoid__add [82, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Olinordered__ab__group__add [83, 1] (w:1, o:164, a:1, s:
% 1.34/1.70 1, b:0),
% 1.34/1.70 class_Groups_Oordered__ab__semigroup__add__imp__le [84, 1] (w:1, o:
% 1.34/1.70 166, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Oordered__ab__semigroup__add [86, 1] (w:1, o:167, a:1
% 1.34/1.70 , s:1, b:0),
% 1.34/1.70 class_Groups_Oordered__cancel__ab__semigroup__add [87, 1] (w:1, o:168
% 1.34/1.70 , a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Ozero__neq__one [88, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.34/1.70 class_RealVector_Oreal__normed__vector [92, 1] (w:1, o:170, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 class_RealVector_Oreal__normed__algebra__1 [93, 1] (w:1, o:171, a:1
% 1.34/1.70 , s:1, b:0),
% 1.34/1.70 class_Orderings_Opreorder [94, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.34/1.70 class_Orderings_Oord [96, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.34/1.70 tc_fun [97, 2] (w:1, o:309, a:1, s:1, b:0),
% 1.34/1.70 class_Orderings_Olinorder [98, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.34/1.70 class_Orderings_Oorder [99, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Ocomm__semiring__1 [101, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.34/1.70
% 1.34/1.70 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.34/1.70 102, 1] (w:1, o:207, a:1, s:1, b:0),
% 1.34/1.70 c_Groups_Osgn__class_Osgn [103, 2] (w:1, o:310, a:1, s:1, b:0),
% 1.34/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [105, 2] (w:1, o:
% 1.34/1.70 269, a:1, s:1, b:0),
% 1.34/1.70 tc_Polynomial_Opoly [106, 1] (w:1, o:219, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Olinordered__semiring__1__strict [109, 1] (w:1, o:180, a:
% 1.34/1.70 1, s:1, b:0),
% 1.34/1.70 c_Groups_Otimes__class_Otimes [110, 1] (w:1, o:220, a:1, s:1, b:0),
% 1.34/1.70 c_COMBB [111, 5] (w:1, o:391, a:1, s:1, b:0),
% 1.34/1.70 c_SEQ_Omonoseq [112, 2] (w:1, o:312, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_ORe [113, 0] (w:1, o:92, a:1, s:1, b:0),
% 1.34/1.70 class_RealVector_Oreal__normed__div__algebra [115, 1] (w:1, o:181, a:
% 1.34/1.70 1, s:1, b:0),
% 1.34/1.70 class_Groups_Oab__semigroup__mult [127, 1] (w:1, o:221, a:1, s:1, b:0
% 1.34/1.70 ),
% 1.34/1.70 class_RealVector_Oreal__normed__algebra [131, 1] (w:1, o:182, a:1, s:
% 1.34/1.70 1, b:0),
% 1.34/1.70 class_Rings_Ono__zero__divisors [132, 1] (w:1, o:188, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 class_Rings_Oring__no__zero__divisors [133, 1] (w:1, o:189, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 class_Rings_Omult__zero [134, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Osemiring [136, 1] (w:1, o:193, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Ocomm__semiring [137, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Ocomm__monoid__mult [142, 1] (w:1, o:222, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 class_Groups_Omonoid__mult [143, 1] (w:1, o:223, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Osgn__if [146, 1] (w:1, o:224, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Oordered__cancel__semiring [147, 1] (w:1, o:195, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 class_Rings_Oordered__ring [148, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Oordered__semiring [149, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.34/1.70
% 1.34/1.70 class_Rings_Oordered__comm__semiring [150, 1] (w:1, o:199, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 class_Rings_Olinordered__ring__strict [151, 1] (w:1, o:148, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 class_Rings_Olinordered__ring [152, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Olinordered__comm__semiring__strict [153, 1] (w:1, o:183
% 1.34/1.70 , a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Olinordered__semiring__strict [154, 1] (w:1, o:184, a:1
% 1.34/1.70 , s:1, b:0),
% 1.34/1.70 class_Rings_Olinordered__semiring [155, 1] (w:1, o:185, a:1, s:1, b:0
% 1.34/1.70 ),
% 1.34/1.70 class_Rings_Oordered__ring__abs [156, 1] (w:1, o:197, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 class_Rings_Olinordered__semiring__1 [157, 1] (w:1, o:186, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 c_SEQ_Oconvergent [163, 2] (w:1, o:313, a:1, s:1, b:0),
% 1.34/1.70 class_RealVector_Ometric__space [164, 1] (w:1, o:200, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 c_COMBK [165, 3] (w:1, o:336, a:1, s:1, b:0),
% 1.34/1.70 c_COMBC [166, 5] (w:1, o:392, a:1, s:1, b:0),
% 1.34/1.70 c_COMBS [168, 5] (w:1, o:393, a:1, s:1, b:0),
% 1.34/1.70 c_SEQ_Odecseq [172, 2] (w:1, o:314, a:1, s:1, b:0),
% 1.34/1.70 c_SEQ_OBseq [174, 2] (w:1, o:315, a:1, s:1, b:0),
% 1.34/1.70 c_SEQ_Oincseq [175, 2] (w:1, o:316, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_Oexpi [177, 1] (w:1, o:225, a:1, s:1, b:0),
% 1.34/1.70 c_RComplete_Onatceiling [178, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.34/1.70 c_RComplete_Onatfloor [179, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.34/1.70 c_RealDef_Oreal [180, 2] (w:1, o:311, a:1, s:1, b:0),
% 1.34/1.70 c_Power_Opower__class_Opower [181, 1] (w:1, o:226, a:1, s:1, b:0),
% 1.34/1.70 c_Nat_OSuc [184, 1] (w:1, o:227, a:1, s:1, b:0),
% 1.34/1.70 tc_Int_Oint [192, 0] (w:1, o:119, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Oring__1__no__zero__divisors [193, 1] (w:1, o:190, a:1
% 1.34/1.70 , s:1, b:0),
% 1.34/1.70 class_Power_Opower [194, 1] (w:1, o:228, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Osemiring__0 [195, 1] (w:1, o:201, a:1, s:1, b:0),
% 1.34/1.70 c_Power_Opower_Opower [198, 3] (w:1, o:337, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_Orcis [205, 2] (w:1, o:317, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_Ocis [210, 1] (w:1, o:229, a:1, s:1, b:0),
% 1.34/1.70 c_Transcendental_Oln [211, 1] (w:1, o:230, a:1, s:1, b:0),
% 1.34/1.70 c_Transcendental_Ocos [212, 1] (w:1, o:231, a:1, s:1, b:0),
% 1.34/1.70 c_Transcendental_Osin [213, 1] (w:1, o:232, a:1, s:1, b:0),
% 1.34/1.70 c_Transcendental_Oarccos [214, 1] (w:1, o:233, a:1, s:1, b:0),
% 1.34/1.70 c_Groups_Ominus__class_Ominus [215, 3] (w:1, o:338, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Oordered__ab__group__add [216, 1] (w:1, o:234, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 class_Groups_Ogroup__add [217, 1] (w:1, o:235, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Oring [219, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Oab__group__add [220, 1] (w:1, o:236, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Oring__1 [223, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Ocomm__ring__1 [227, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_Oii [229, 0] (w:1, o:127, a:1, s:1, b:0),
% 1.34/1.70 c_Nat__Transfer_Otsub [230, 2] (w:1, o:266, a:1, s:1, b:0),
% 1.34/1.70 c_Divides_Odiv__class_Odiv [231, 3] (w:1, o:341, a:1, s:1, b:0),
% 1.34/1.70 class_Divides_Osemiring__div [232, 1] (w:1, o:237, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_Ocomplex_OComplex [236, 2] (w:1, o:318, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_Ocomplex_Ocomplex__size [245, 1] (w:1, o:238, a:1, s:1, b:0
% 1.34/1.70 ),
% 1.34/1.70 c_Complex_Oarg [246, 1] (w:1, o:239, a:1, s:1, b:0),
% 1.34/1.70 c_Nat_Osize__class_Osize [247, 2] (w:1, o:267, a:1, s:1, b:0),
% 1.34/1.70 c_Complex_Ocomplex_Ocomplex__rec [249, 3] (w:1, o:339, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 c_Complex_Ocomplex_Ocomplex__case [250, 3] (w:1, o:340, a:1, s:1, b:0
% 1.34/1.70 ),
% 1.34/1.70 c_Rings_Oinverse__class_Odivide [251, 1] (w:1, o:144, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 class_RealVector_Oreal__normed__field [252, 1] (w:1, o:202, a:1, s:1
% 1.34/1.70 , b:0),
% 1.34/1.70 class_Rings_Odivision__ring [253, 1] (w:1, o:203, a:1, s:1, b:0),
% 1.34/1.70 class_Rings_Odivision__ring__inverse__zero [254, 1] (w:1, o:204, a:1
% 1.34/1.70 , s:1, b:0),
% 1.34/1.70 class_Fields_Ofield [255, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.34/1.70 class_Fields_Ofield__inverse__zero [256, 1] (w:1, o:152, a:1, s:1, b:
% 1.34/1.70 0),
% 1.34/1.70 class_RealVector_Oreal__field [258, 1] (w:1, o:205, a:1, s:1, b:0),
% 1.34/1.70 class_Fields_Olinordered__field__inverse__zero [259, 1] (w:1, o:153
% 1.34/1.70 , a:1, s:1, b:0),
% 1.34/1.70 class_Fields_Olinordered__field [260, 1] (w:1, o:154, a:1, s:1, b:0)
% 1.34/1.70 ,
% 1.34/1.70 class_Rings_Oidom [262, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.34/1.70 class_Groups_Ocancel__comm__monoid__add [263, 1] (w:1, o:240, a:1, s:
% 1.34/1.70 1, b:0),
% 1.34/1.70 class_Rings_Ocomm__semiring__0 [264, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.34/1.70
% 1.34/1.70 class_Rings_Ocomm__ring [265, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.34/1.70 tc_HOL_Obool [267, 0] (w:1, o:118, a:1, s:1, b:0),
% 1.34/1.70 alpha1 [273, 3] (w:1, o:342, a:1, s:1, b:1),
% 1.34/1.70 alpha2 [274, 3] (w:1, o:346, a:1, s:1, b:1),
% 1.34/1.70 alpha3 [275, 4] (w:1, o:380, a:1, s:1, b:1),
% 1.34/1.70 alpha4 [276, 4] (w:1, o:383, a:1, s:1, b:1),
% 1.34/1.70 alpha5 [277, 2] (w:1, o:321, a:1, s:1, b:1),
% 1.34/1.70 alpha6 [278, 2] (w:1, o:322, a:1, s:1, b:1),
% 1.34/1.70 alpha7 [279, 2] (w:1, o:323, a:1, s:1, b:1),
% 1.34/1.70 alpha8 [280, 2] (w:1, o:324, a:1, s:1, b:1),
% 1.34/1.70 alpha9 [281, 3] (w:1, o:347, a:1, s:1, b:1),
% 1.34/1.70 alpha10 [282, 3] (w:1, o:343, a:1, s:1, b:1),
% 1.34/1.70 alpha11 [283, 2] (w:1, o:325, a:1, s:1, b:1),
% 1.34/1.70 alpha12 [284, 2] (w:1, o:326, a:1, s:1, b:1),
% 1.34/1.70 alpha13 [285, 2] (w:1, o:327, a:1, s:1, b:1),
% 1.34/1.70 alpha14 [286, 2] (w:1, o:328, a:1, s:1, b:1),
% 1.34/1.70 alpha15 [287, 2] (w:1, o:329, a:1, s:1, b:1),
% 1.34/1.70 alpha16 [288, 3] (w:1, o:344, a:1, s:1, b:1),
% 1.34/1.70 alpha17 [289, 3] (w:1, o:345, a:1, s:1, b:1),
% 1.34/1.70 alpha18 [290, 4] (w:1, o:384, a:1, s:1, b:1),
% 1.34/1.70 alpha19 [291, 4] (w:1, o:385, a:1, s:1, b:1),
% 1.34/1.70 alpha20 [292, 2] (w:1, o:330, a:1, s:1, b:1),
% 1.34/1.70 alpha21 [293, 2] (w:1, o:331, a:1, s:1, b:1),
% 1.34/1.70 alpha22 [294, 2] (w:1, o:332, a:1, s:1, b:1),
% 3.74/4.12 alpha23 [295, 3] (w:1, o:348, a:1, s:1, b:1),
% 3.74/4.12 alpha24 [296, 3] (w:1, o:349, a:1, s:1, b:1),
% 3.74/4.12 alpha25 [297, 2] (w:1, o:333, a:1, s:1, b:1),
% 3.74/4.12 alpha26 [298, 3] (w:1, o:350, a:1, s:1, b:1),
% 3.74/4.12 alpha27 [299, 3] (w:1, o:351, a:1, s:1, b:1),
% 3.74/4.12 alpha28 [300, 3] (w:1, o:352, a:1, s:1, b:1),
% 3.74/4.12 alpha29 [301, 2] (w:1, o:334, a:1, s:1, b:1),
% 3.74/4.12 alpha30 [302, 2] (w:1, o:335, a:1, s:1, b:1),
% 3.74/4.12 alpha31 [303, 3] (w:1, o:353, a:1, s:1, b:1),
% 3.74/4.12 alpha32 [304, 3] (w:1, o:354, a:1, s:1, b:1),
% 3.74/4.12 alpha33 [305, 4] (w:1, o:381, a:1, s:1, b:1),
% 3.74/4.12 alpha34 [306, 3] (w:1, o:355, a:1, s:1, b:1),
% 3.74/4.12 alpha35 [307, 3] (w:1, o:356, a:1, s:1, b:1),
% 3.74/4.12 alpha36 [308, 4] (w:1, o:382, a:1, s:1, b:1),
% 3.74/4.12 alpha37 [309, 3] (w:1, o:357, a:1, s:1, b:1),
% 3.74/4.12 alpha38 [310, 3] (w:1, o:358, a:1, s:1, b:1),
% 3.74/4.12 alpha39 [311, 3] (w:1, o:359, a:1, s:1, b:1),
% 3.74/4.12 alpha40 [312, 4] (w:1, o:386, a:1, s:1, b:1),
% 3.74/4.12 alpha41 [313, 4] (w:1, o:387, a:1, s:1, b:1),
% 3.74/4.12 alpha42 [314, 3] (w:1, o:360, a:1, s:1, b:1),
% 3.74/4.12 alpha43 [315, 2] (w:1, o:319, a:1, s:1, b:1),
% 3.74/4.12 alpha44 [316, 2] (w:1, o:320, a:1, s:1, b:1),
% 3.74/4.12 alpha45 [317, 3] (w:1, o:361, a:1, s:1, b:1),
% 3.74/4.12 skol1 [318, 2] (w:1, o:273, a:1, s:1, b:1),
% 3.74/4.12 skol2 [319, 3] (w:1, o:362, a:1, s:1, b:1),
% 3.74/4.12 skol3 [320, 2] (w:1, o:279, a:1, s:1, b:1),
% 3.74/4.12 skol4 [321, 0] (w:1, o:12, a:1, s:1, b:1),
% 3.74/4.12 skol5 [322, 2] (w:1, o:287, a:1, s:1, b:1),
% 3.74/4.12 skol6 [323, 2] (w:1, o:288, a:1, s:1, b:1),
% 3.74/4.12 skol7 [324, 2] (w:1, o:295, a:1, s:1, b:1),
% 3.74/4.12 skol8 [325, 1] (w:1, o:208, a:1, s:1, b:1),
% 3.74/4.12 skol9 [326, 0] (w:1, o:13, a:1, s:1, b:1),
% 3.74/4.12 skol10 [327, 0] (w:1, o:14, a:1, s:1, b:1),
% 3.74/4.12 skol11 [328, 0] (w:1, o:15, a:1, s:1, b:1),
% 3.74/4.12 skol12 [329, 0] (w:1, o:16, a:1, s:1, b:1),
% 3.74/4.12 skol13 [330, 2] (w:1, o:296, a:1, s:1, b:1),
% 3.74/4.12 skol14 [331, 1] (w:1, o:209, a:1, s:1, b:1),
% 3.74/4.12 skol15 [332, 2] (w:1, o:297, a:1, s:1, b:1),
% 3.74/4.12 skol16 [333, 0] (w:1, o:17, a:1, s:1, b:1),
% 3.74/4.12 skol17 [334, 0] (w:1, o:18, a:1, s:1, b:1),
% 3.74/4.12 skol18 [335, 2] (w:1, o:298, a:1, s:1, b:1),
% 3.74/4.12 skol19 [336, 2] (w:1, o:299, a:1, s:1, b:1),
% 3.74/4.12 skol20 [337, 1] (w:1, o:210, a:1, s:1, b:1),
% 3.74/4.12 skol21 [338, 2] (w:1, o:274, a:1, s:1, b:1),
% 3.74/4.12 skol22 [339, 2] (w:1, o:275, a:1, s:1, b:1),
% 3.74/4.12 skol23 [340, 2] (w:1, o:276, a:1, s:1, b:1),
% 3.74/4.12 skol24 [341, 2] (w:1, o:277, a:1, s:1, b:1),
% 3.74/4.12 skol25 [342, 3] (w:1, o:363, a:1, s:1, b:1),
% 3.74/4.12 skol26 [343, 2] (w:1, o:278, a:1, s:1, b:1),
% 3.74/4.12 skol27 [344, 1] (w:1, o:211, a:1, s:1, b:1),
% 3.74/4.12 skol28 [345, 4] (w:1, o:388, a:1, s:1, b:1),
% 3.74/4.12 skol29 [346, 3] (w:1, o:364, a:1, s:1, b:1),
% 3.74/4.12 skol30 [347, 3] (w:1, o:365, a:1, s:1, b:1),
% 3.74/4.12 skol31 [348, 1] (w:1, o:212, a:1, s:1, b:1),
% 3.74/4.12 skol32 [349, 2] (w:1, o:300, a:1, s:1, b:1),
% 3.74/4.12 skol33 [350, 2] (w:1, o:301, a:1, s:1, b:1),
% 3.74/4.12 skol34 [351, 2] (w:1, o:302, a:1, s:1, b:1),
% 3.74/4.12 skol35 [352, 1] (w:1, o:213, a:1, s:1, b:1),
% 3.74/4.12 skol36 [353, 2] (w:1, o:303, a:1, s:1, b:1),
% 3.74/4.12 skol37 [354, 2] (w:1, o:304, a:1, s:1, b:1),
% 3.74/4.12 skol38 [355, 2] (w:1, o:305, a:1, s:1, b:1),
% 3.74/4.12 skol39 [356, 1] (w:1, o:214, a:1, s:1, b:1),
% 3.74/4.12 skol40 [357, 2] (w:1, o:280, a:1, s:1, b:1),
% 3.74/4.12 skol41 [358, 2] (w:1, o:281, a:1, s:1, b:1),
% 3.74/4.12 skol42 [359, 2] (w:1, o:282, a:1, s:1, b:1),
% 3.74/4.12 skol43 [360, 2] (w:1, o:283, a:1, s:1, b:1),
% 3.74/4.12 skol44 [361, 2] (w:1, o:284, a:1, s:1, b:1),
% 3.74/4.12 skol45 [362, 2] (w:1, o:285, a:1, s:1, b:1),
% 3.74/4.12 skol46 [363, 2] (w:1, o:286, a:1, s:1, b:1),
% 3.74/4.12 skol47 [364, 1] (w:1, o:215, a:1, s:1, b:1),
% 3.74/4.12 skol48 [365, 3] (w:1, o:366, a:1, s:1, b:1),
% 3.74/4.12 skol49 [366, 3] (w:1, o:367, a:1, s:1, b:1),
% 3.74/4.12 skol50 [367, 1] (w:1, o:216, a:1, s:1, b:1),
% 3.74/4.12 skol51 [368, 4] (w:1, o:389, a:1, s:1, b:1),
% 3.74/4.12 skol52 [369, 3] (w:1, o:368, a:1, s:1, b:1),
% 3.74/4.12 skol53 [370, 3] (w:1, o:369, a:1, s:1, b:1),
% 3.74/4.12 skol54 [371, 3] (w:1, o:370, a:1, s:1, b:1),
% 3.74/4.12 skol55 [372, 3] (w:1, o:371, a:1, s:1, b:1),
% 3.74/4.12 skol56 [373, 3] (w:1, o:372, a:1, s:1, b:1),
% 29.42/29.77 skol57 [374, 3] (w:1, o:373, a:1, s:1, b:1),
% 29.42/29.77 skol58 [375, 4] (w:1, o:390, a:1, s:1, b:1),
% 29.42/29.77 skol59 [376, 3] (w:1, o:374, a:1, s:1, b:1),
% 29.42/29.77 skol60 [377, 0] (w:1, o:19, a:1, s:1, b:1),
% 29.42/29.77 skol61 [378, 2] (w:1, o:289, a:1, s:1, b:1),
% 29.42/29.77 skol62 [379, 2] (w:1, o:290, a:1, s:1, b:1),
% 29.42/29.77 skol63 [380, 1] (w:1, o:217, a:1, s:1, b:1),
% 29.42/29.77 skol64 [381, 2] (w:1, o:291, a:1, s:1, b:1),
% 29.42/29.77 skol65 [382, 3] (w:1, o:375, a:1, s:1, b:1),
% 29.42/29.77 skol66 [383, 2] (w:1, o:292, a:1, s:1, b:1),
% 29.42/29.77 skol67 [384, 1] (w:1, o:218, a:1, s:1, b:1),
% 29.42/29.77 skol68 [385, 2] (w:1, o:293, a:1, s:1, b:1),
% 29.42/29.77 skol69 [386, 2] (w:1, o:294, a:1, s:1, b:1),
% 29.42/29.77 skol70 [387, 2] (w:1, o:306, a:1, s:1, b:1),
% 29.42/29.77 skol71 [388, 3] (w:1, o:376, a:1, s:1, b:1),
% 29.42/29.77 skol72 [389, 3] (w:1, o:377, a:1, s:1, b:1),
% 29.42/29.77 skol73 [390, 3] (w:1, o:378, a:1, s:1, b:1),
% 29.42/29.77 skol74 [391, 3] (w:1, o:379, a:1, s:1, b:1),
% 29.42/29.77 skol75 [392, 2] (w:1, o:307, a:1, s:1, b:1),
% 29.42/29.77 skol76 [393, 2] (w:1, o:308, a:1, s:1, b:1).
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Starting Search:
% 29.42/29.77
% 29.42/29.77 *** allocated 113905 integers for clauses
% 29.42/29.77 *** allocated 170857 integers for clauses
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 2869
% 29.42/29.77 Kept: 2001
% 29.42/29.77 Inuse: 55
% 29.42/29.77 Deleted: 2
% 29.42/29.77 Deletedinuse: 0
% 29.42/29.77
% 29.42/29.77 *** allocated 256285 integers for clauses
% 29.42/29.77 *** allocated 170857 integers for termspace/termends
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 *** allocated 384427 integers for clauses
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 8493
% 29.42/29.77 Kept: 4029
% 29.42/29.77 Inuse: 138
% 29.42/29.77 Deleted: 3
% 29.42/29.77 Deletedinuse: 0
% 29.42/29.77
% 29.42/29.77 *** allocated 256285 integers for termspace/termends
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 13283
% 29.42/29.77 Kept: 6029
% 29.42/29.77 Inuse: 205
% 29.42/29.77 Deleted: 3
% 29.42/29.77 Deletedinuse: 0
% 29.42/29.77
% 29.42/29.77 *** allocated 576640 integers for clauses
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 *** allocated 384427 integers for termspace/termends
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 18265
% 29.42/29.77 Kept: 8099
% 29.42/29.77 Inuse: 263
% 29.42/29.77 Deleted: 3
% 29.42/29.77 Deletedinuse: 0
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 *** allocated 864960 integers for clauses
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 22882
% 29.42/29.77 Kept: 10611
% 29.42/29.77 Inuse: 303
% 29.42/29.77 Deleted: 3
% 29.42/29.77 Deletedinuse: 0
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 *** allocated 576640 integers for termspace/termends
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 29494
% 29.42/29.77 Kept: 12893
% 29.42/29.77 Inuse: 353
% 29.42/29.77 Deleted: 5
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 36342
% 29.42/29.77 Kept: 14895
% 29.42/29.77 Inuse: 388
% 29.42/29.77 Deleted: 5
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 *** allocated 864960 integers for termspace/termends
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 42898
% 29.42/29.77 Kept: 16955
% 29.42/29.77 Inuse: 448
% 29.42/29.77 Deleted: 5
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 *** allocated 1297440 integers for clauses
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 48244
% 29.42/29.77 Kept: 19050
% 29.42/29.77 Inuse: 487
% 29.42/29.77 Deleted: 6
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying clauses:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 53394
% 29.42/29.77 Kept: 21857
% 29.42/29.77 Inuse: 506
% 29.42/29.77 Deleted: 266
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 57193
% 29.42/29.77 Kept: 23871
% 29.42/29.77 Inuse: 535
% 29.42/29.77 Deleted: 266
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 66139
% 29.42/29.77 Kept: 26437
% 29.42/29.77 Inuse: 581
% 29.42/29.77 Deleted: 266
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 *** allocated 1297440 integers for termspace/termends
% 29.42/29.77 *** allocated 1946160 integers for clauses
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 76702
% 29.42/29.77 Kept: 29224
% 29.42/29.77 Inuse: 626
% 29.42/29.77 Deleted: 266
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 29.42/29.77 Generated: 83865
% 29.42/29.77 Kept: 31300
% 29.42/29.77 Inuse: 681
% 29.42/29.77 Deleted: 266
% 29.42/29.77 Deletedinuse: 2
% 29.42/29.77
% 29.42/29.77 Resimplifying inuse:
% 29.42/29.77 Done
% 29.42/29.77
% 29.42/29.77
% 29.42/29.77 Intermediate Status:
% 157.10/157.50 Generated: 91393
% 157.10/157.50 Kept: 34012
% 157.10/157.50 Inuse: 701
% 157.10/157.50 Deleted: 266
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 99253
% 157.10/157.50 Kept: 36911
% 157.10/157.50 Inuse: 721
% 157.10/157.50 Deleted: 266
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 107964
% 157.10/157.50 Kept: 38930
% 157.10/157.50 Inuse: 776
% 157.10/157.50 Deleted: 266
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 *** allocated 1946160 integers for termspace/termends
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 112851
% 157.10/157.50 Kept: 41348
% 157.10/157.50 Inuse: 791
% 157.10/157.50 Deleted: 266
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying clauses:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 *** allocated 2919240 integers for clauses
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 117405
% 157.10/157.50 Kept: 43625
% 157.10/157.50 Inuse: 801
% 157.10/157.50 Deleted: 435
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 120704
% 157.10/157.50 Kept: 45916
% 157.10/157.50 Inuse: 806
% 157.10/157.50 Deleted: 435
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 129661
% 157.10/157.50 Kept: 47933
% 157.10/157.50 Inuse: 836
% 157.10/157.50 Deleted: 435
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 138364
% 157.10/157.50 Kept: 49949
% 157.10/157.50 Inuse: 880
% 157.10/157.50 Deleted: 435
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 146454
% 157.10/157.50 Kept: 52079
% 157.10/157.50 Inuse: 911
% 157.10/157.50 Deleted: 435
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 155643
% 157.10/157.50 Kept: 54282
% 157.10/157.50 Inuse: 941
% 157.10/157.50 Deleted: 435
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 165260
% 157.10/157.50 Kept: 56512
% 157.10/157.50 Inuse: 950
% 157.10/157.50 Deleted: 435
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 179369
% 157.10/157.50 Kept: 63277
% 157.10/157.50 Inuse: 996
% 157.10/157.50 Deleted: 435
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying clauses:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 *** allocated 2919240 integers for termspace/termends
% 157.10/157.50 *** allocated 4378860 integers for clauses
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 194638
% 157.10/157.50 Kept: 66433
% 157.10/157.50 Inuse: 1041
% 157.10/157.50 Deleted: 1328
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 204823
% 157.10/157.50 Kept: 69946
% 157.10/157.50 Inuse: 1051
% 157.10/157.50 Deleted: 1328
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 218278
% 157.10/157.50 Kept: 72719
% 157.10/157.50 Inuse: 1076
% 157.10/157.50 Deleted: 1328
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 253259
% 157.10/157.50 Kept: 78748
% 157.10/157.50 Inuse: 1121
% 157.10/157.50 Deleted: 1328
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 262094
% 157.10/157.50 Kept: 80884
% 157.10/157.50 Inuse: 1151
% 157.10/157.50 Deleted: 1328
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 277150
% 157.10/157.50 Kept: 84540
% 157.10/157.50 Inuse: 1166
% 157.10/157.50 Deleted: 1328
% 157.10/157.50 Deletedinuse: 2
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying clauses:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 *** allocated 4378860 integers for termspace/termends
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 304218
% 157.10/157.50 Kept: 88940
% 157.10/157.50 Inuse: 1181
% 157.10/157.50 Deleted: 1412
% 157.10/157.50 Deletedinuse: 4
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 329329
% 157.10/157.50 Kept: 92559
% 157.10/157.50 Inuse: 1191
% 157.10/157.50 Deleted: 1412
% 157.10/157.50 Deletedinuse: 4
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 336956
% 157.10/157.50 Kept: 94559
% 157.10/157.50 Inuse: 1215
% 157.10/157.50 Deleted: 1413
% 157.10/157.50 Deletedinuse: 5
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 *** allocated 6568290 integers for clauses
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 343345
% 157.10/157.50 Kept: 96763
% 157.10/157.50 Inuse: 1231
% 157.10/157.50 Deleted: 1414
% 157.10/157.50 Deletedinuse: 6
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 361374
% 157.10/157.50 Kept: 100818
% 157.10/157.50 Inuse: 1241
% 157.10/157.50 Deleted: 1414
% 157.10/157.50 Deletedinuse: 6
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50 Resimplifying inuse:
% 157.10/157.50 Done
% 157.10/157.50
% 157.10/157.50
% 157.10/157.50 Intermediate Status:
% 157.10/157.50 Generated: 372579
% 157.10/157.50 KCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------