TSTP Solution File: SWW195+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW195+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 23:21:11 EDT 2022
% Result : Timeout 287.93s 288.41s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SWW195+1 : TPTP v8.1.0. Released v5.2.0.
% 0.13/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 10:19:16 EDT 2022
% 0.13/0.36 % CPUTime :
% 1.26/1.63 *** allocated 10000 integers for termspace/termends
% 1.26/1.63 *** allocated 10000 integers for clauses
% 1.26/1.63 *** allocated 10000 integers for justifications
% 1.26/1.63 *** allocated 15000 integers for termspace/termends
% 1.26/1.63 *** allocated 22500 integers for termspace/termends
% 1.26/1.63 *** allocated 33750 integers for termspace/termends
% 1.26/1.63 Bliksem 1.12
% 1.26/1.63
% 1.26/1.63
% 1.26/1.63 Automatic Strategy Selection
% 1.26/1.63
% 1.26/1.63 *** allocated 50625 integers for termspace/termends
% 1.26/1.63 *** allocated 75937 integers for termspace/termends
% 1.26/1.63 *** allocated 113905 integers for termspace/termends
% 1.26/1.63
% 1.26/1.63 Clauses:
% 1.26/1.63
% 1.26/1.63 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.26/1.63 { ! v_n = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! v_b = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.26/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.26/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.26/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.63 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.63 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.26/1.63 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.26/1.63 ), X ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.26/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.26/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.26/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.26/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.26/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.26/1.63 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.26/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.26/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Nat_Onat ) ) = Y }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Nat_Onat ) ) = Y }.
% 1.26/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( X ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.63 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.26/1.63 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.26/1.63 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.26/1.63 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.26/1.63 ), U = Z, T = Y }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.26/1.63 ) ), Z ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.26/1.63 ), ! U = T }.
% 1.26/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.26/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.26/1.63 ), ! Z = Y }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.26/1.63 = Y }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.26/1.63 = Y }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.26/1.63 = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.26/1.63 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.26/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.26/1.63 ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.26/1.63 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.63 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.26/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.26/1.63 , Y ), X ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.26/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Nat_Onat ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.26/1.63 tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.26/1.63 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.26/1.63 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.63 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_RealDef_Oreal ) ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.26/1.63 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, Y, Z ) }.
% 1.26/1.63 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 T, Y ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 T, Y ) }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Y, Z ), T = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Y, Z ) }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 T, Y ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 T, Y ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 Y, T ), Z = Y }.
% 1.26/1.63 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.26/1.63 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.26/1.63 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.26/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.26/1.63 .
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.26/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.26/1.63 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.26/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.26/1.63 .
% 1.26/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.26/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ) ) = X }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), X ) = X }.
% 1.26/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { alpha90( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.26/1.63 { alpha90( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.26/1.63 ( X, Y ), Z ) ) }.
% 1.26/1.63 { ! alpha90( X, Y, Z ), alpha93( X, Y, Z ), Z = Y }.
% 1.26/1.63 { ! alpha90( X, Y, Z ), alpha93( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.26/1.63 ) ) }.
% 1.26/1.63 { ! alpha93( X, Y, Z ), alpha90( X, Y, Z ) }.
% 1.26/1.63 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha90( X, Y, Z ) }.
% 1.26/1.63 { ! alpha93( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.26/1.63 }.
% 1.26/1.63 { ! alpha93( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.26/1.63 X, Y ), Z ) ), alpha93( X, Y, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.26/1.63 , X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.26/1.63 .
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.26/1.63 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.26/1.63 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.26/1.63 .
% 1.26/1.63 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.63 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.26/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.26/1.63 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.26/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, T, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.63 , Y, Z ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.63 , T, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.63 , Y, T ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.63 , T, Y ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.63 , T ) ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, Z, Y ) }.
% 1.26/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.26/1.63 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.26/1.63 ( X, Z, Y ) }.
% 1.26/1.63 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.63 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.26/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.63 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.63 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.26/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.63 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.26/1.63 ) ), T ), Y ) }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.26/1.63 = Y }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.26/1.63 = Y }.
% 1.26/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.26/1.63 = Y }.
% 1.26/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.26/1.63 = Y }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.26/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.26/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), Z ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.26/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.26/1.63 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.26/1.63 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.63 Y ), X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.26/1.63 tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.63 tc_Nat_Onat ), X ) }.
% 1.26/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.63 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha1( X, Y, Z, T ),
% 1.26/1.64 alpha29( X, Y, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha29( X, Y, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha29( X, Y, Z, T ) }.
% 1.26/1.64 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.64 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha1( X, Y, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha2( X, Y, Z, T ),
% 1.26/1.64 alpha30( X, Y, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha30( X, Y, Z, T ) }.
% 1.26/1.64 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.26/1.64 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha2( X, Y, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.26/1.64 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.26/1.64 ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), X ), Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.26/1.64 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.26/1.64 }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.26/1.64 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.26/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.26/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.26/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.26/1.64 .
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.26/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol2( Z, T ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol2( X, Y ) ), X ) =
% 1.26/1.64 Y }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol3( Z, T ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol3( X, Y ) ), X ) =
% 1.26/1.64 Y }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z = skol3
% 1.26/1.64 ( X, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.26/1.64 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.26/1.64 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.64 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.64 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.64 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.64 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.64 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.26/1.64 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.26/1.64 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.64 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.64 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.64 ( X, Y ) ) ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.26/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.26/1.64 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.26/1.64 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.26/1.64 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.26/1.64 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.64 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.64 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.26/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.26/1.64 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.64 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.64 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.64 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.64 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.64 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.64 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.64 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.64 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.64 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.64 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.64 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 1.26/1.64 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.64 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.64 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, T, Y ) ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.26/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.26/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.26/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.64 W ) ), U ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), U ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.64 Z ) ), U ), T ) = Y }.
% 1.26/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.26/1.64 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), U ), Y ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.64 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.26/1.64 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.26/1.64 Z ) ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ), alpha3( X, Y, Z ), alpha31( X, Y, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ) ) }.
% 1.26/1.64 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( X ), Y ), alpha31( X, Y, Z ) }.
% 1.26/1.64 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.64 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4( X, Y
% 1.26/1.64 , Z ), alpha32( X, Y, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha32( X, Y, Z ) }.
% 1.26/1.64 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.64 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 Z, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.26/1.64 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ) }.
% 1.26/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.26/1.64 , Y, T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, Z, X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.26/1.64 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( X, Z, W ) ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 X, W, Z ) ), U ), T ), Y ) }.
% 1.26/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), Z ), U ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.26/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.64 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.26/1.64 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.26/1.64 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.64 , alpha5( X, Y, Z ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.64 , alpha33( X, Y, Z ) }.
% 1.26/1.64 { ! alpha5( X, Y, Z ), ! alpha33( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.64 { ! alpha33( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.64 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, skol5( T, U, Z ) ) ), alpha33( X, Y, Z ) }.
% 1.26/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol5( X, Y, Z ) ),
% 1.26/1.64 alpha33( X, Y, Z ) }.
% 1.26/1.64 { ! alpha5( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.26/1.64 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha5( X, Y, Z ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5
% 1.26/1.64 ( X, Y, Z ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.64 , ! alpha6( X, Y, Z ) }.
% 1.26/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.26/1.64 , ! alpha34( X, Y, Z ) }.
% 1.26/1.64 { alpha6( X, Y, Z ), alpha34( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.64 { ! alpha34( X, Y, Z ), ! hBOOL( hAPP( Z, skol6( T, U, Z ) ) ) }.
% 1.26/1.64 { ! alpha34( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.64 skol6( X, Y, Z ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.26/1.64 ) ), alpha34( X, Y, Z ) }.
% 1.26/1.64 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.26/1.64 ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.26/1.64 ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.26/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.26/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.26/1.64 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.64 ( X, Y ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.64 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.26/1.64 ), Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.26/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.26/1.64 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.26/1.64 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Int_Oint ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.26/1.64 .
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.26/1.64 = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ) ) = X }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), X ) = X }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Int_Oint ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.64 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.26/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.26/1.64 hAPP( Y, U ) ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.26/1.64 ( Z, skol7( X, Y, Z ) ), hAPP( Y, skol7( X, Y, Z ) ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.26/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.26/1.64 hAPP( Y, U ) ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.26/1.64 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.26/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.26/1.64 hAPP( Y, U ) ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.26/1.64 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! Y = Z }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! Z = Y }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! Z = Y }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.64 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.26/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! Z = Y }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.64 Z ), ! Z = Y }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.64 Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol8( X, Y ) ) }.
% 1.26/1.64 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.64 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , ! Z = Y }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.26/1.64 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.26/1.64 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.26/1.64 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.64 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.64 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.26/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.64 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Int_Oint ), Y ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.64 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.26/1.64 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.64 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.26/1.64 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.26/1.64 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.26/1.64 }.
% 1.26/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.26/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.26/1.64 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.64 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.26/1.64 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.64 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.26/1.64 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Int_Oint, X, Y ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Int_Oint ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Int_Oint ) ) }.
% 1.26/1.64 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.26/1.64 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol9( Z, T ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Z, T ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol10( X, Y ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol11( Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol11( X ) ) ) }.
% 1.26/1.64 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.64 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.26/1.64 ) }.
% 1.26/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.64 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol12( Z, Y
% 1.26/1.64 ), Y ) }.
% 1.26/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.64 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.26/1.64 skol12( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.26/1.64 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.26/1.64 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.26/1.64 , skol12( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol13( X ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Z, T ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol14( X, Y ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.26/1.64 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Int_Oint, X, Y ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( Z, T ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol15( X, Y ) ) ) }.
% 1.26/1.64 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.26/1.64 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 1.26/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.26/1.64 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 1.26/1.64 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.26/1.64 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.26/1.64 Y ), c_RComplete_Onatceiling( X ) ) }.
% 1.26/1.64 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.26/1.64 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 1.26/1.64 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.26/1.64 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.26/1.64 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_RealDef_Oreal ) ) ) }.
% 1.26/1.64 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.26/1.64 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.64 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.26/1.64 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.26/1.64 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.26/1.64 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.64 , c_RComplete_Onatfloor( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.64 , c_RComplete_Onatfloor( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.64 c_RComplete_Onatfloor( X ), Y ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 1.26/1.64 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.26/1.64 Y = X }.
% 1.26/1.64 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.26/1.64 , X ) }.
% 1.26/1.64 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_RComplete_Onatfloor( X ), Y ) }.
% 1.26/1.64 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.26/1.64 ( tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 1.26/1.64 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 1.26/1.64 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.26/1.64 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.26/1.64 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.26/1.64 c_RComplete_Onatfloor( X ) = Y }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.26/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.64 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.64 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 1.26/1.64 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 1.26/1.64 ), c_RComplete_Onatfloor( X ) ) }.
% 1.26/1.64 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 1.26/1.64 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 1.26/1.64 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_RComplete_Onatceiling( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 1.26/1.64 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_RealDef_Oreal ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.26/1.64 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.64 , X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.26/1.64 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_RComplete_Onatceiling( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.26/1.64 c_RComplete_Onatceiling( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.26/1.64 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.26/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol16( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, skol16( X ) ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.26/1.64 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, X ) ), Y ) ) }.
% 1.26/1.64 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.26/1.64 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, T, skol17( X, U, W, T ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.26/1.64 hAPP( Z, T ), hAPP( Z, skol17( X, Y, Z, T ) ) ) ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.26/1.64 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 tc_Nat_Onat, skol18( X, Y ), skol53( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 hAPP( Y, skol53( X, Y ) ), hAPP( Y, skol18( X, Y ) ) ), c_SEQ_Odecseq( X
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.26/1.64 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.26/1.64 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 tc_RealDef_Oreal, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.26/1.64 ), c_Transcendental_Oln( Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.26/1.64 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 1.26/1.64 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.26/1.64 ), X ) }.
% 1.26/1.64 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.26/1.64 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 tc_RealDef_Oreal, X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.26/1.64 ( X ), c_Transcendental_Oln( Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.26/1.64 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.26/1.64 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.26/1.64 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.26/1.64 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.26/1.64 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 1.26/1.64 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.26/1.64 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.26/1.64 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.26/1.64 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.64 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.26/1.64 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.26/1.64 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( Z, T ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol19( X, Y ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol54( X, Y, Z ) ) ), Z ),
% 1.26/1.64 c_SEQ_OBseq( X, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.64 tc_Nat_Onat, skol20( X, Y ), skol55( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.26/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.64 hAPP( Y, skol20( X, Y ) ), hAPP( Y, skol55( X, Y ) ) ), c_SEQ_Oincseq( X
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol21( X, Y, Z ) ) ), Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, c_Nat_OSuc( skol56( X, Y ) ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol62( X, Y, Z ) ) ),
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol64( T, U ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol62( X, Y, Z ) ) ),
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol64( X, Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.64 X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.26/1.64 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.26/1.64 ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.26/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.26/1.64 .
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.26/1.64 .
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.26/1.64 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.64 X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.26/1.64 }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.26/1.64 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.26/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.64 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.64 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.26/1.64 { ! X = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Nat_OSuc( X ) = X }.
% 1.26/1.64 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.26/1.64 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.26/1.64 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.26/1.64 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.26/1.64 }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.26/1.64 c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.26/1.64 ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.26/1.64 , c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.26/1.64 .
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.26/1.64 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, c_Nat_OSuc( skol22( X, Y ) ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol57( X, Y, Z ) ) ),
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), c_RealDef_Oreal(
% 1.26/1.64 tc_Nat_Onat, c_Nat_OSuc( skol23( X, Y ) ) ) ) }.
% 1.26/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.64 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol58( X, Y, Z ) ) ),
% 1.26/1.64 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y ) }
% 1.26/1.64 .
% 1.26/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.64 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.26/1.64 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.26/1.64 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.64 c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! alpha7( X, Y ), Y = c_Nat_OSuc( skol24( Z, Y ) ) }.
% 1.26/1.64 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol24( X,
% 1.26/1.64 Y ), X ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.26/1.64 ), alpha7( X, Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol25( X ) ) }.
% 1.26/1.64 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha8( X, Y ), alpha35( X
% 1.26/1.64 , Y ) }.
% 1.26/1.64 { ! alpha8( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! alpha35( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! alpha35( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! alpha35( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha35( X, Y ) }.
% 1.26/1.64 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.26/1.64 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha9( X, Y ), alpha36
% 1.26/1.64 ( X, Y ) }.
% 1.26/1.64 { ! alpha9( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! alpha36( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.64 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! alpha36( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! alpha36( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha36( X, Y ) }.
% 1.26/1.64 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.64 tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.26/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.26/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol26( X, Y ) ) ) }.
% 1.26/1.64 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.26/1.64 .
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.64 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.64 ), X ) ) }.
% 1.26/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.26/1.64 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.26/1.64 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.64 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.26/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.26/1.64 ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.64 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.26/1.64 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.26/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.26/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.26/1.64 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.26/1.64 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.26/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.26/1.64 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.26/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.26/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.64 X ), Y ), Z = Y }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.26/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.26/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.26/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.64 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.64 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.26/1.64 ) ) = X }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.26/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.26/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.26/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.26/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.26/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.26/1.65 c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.65 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.26/1.65 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.26/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.26/1.65 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.26/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.26/1.65 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.26/1.65 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol27( X, Y, Z ) ) ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Nat_OSuc( skol59( X, Y ) ) ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol63( X, Y, Z ) ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol65( T, U ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol63( X, Y, Z ) ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol65( X, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, skol28( X, Y ) ) ), X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Nat_OSuc( skol28( X, Y ) ) ) ), X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol29( X, Y ) ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.26/1.65 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.26/1.65 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.26/1.65 }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 1.26/1.65 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.26/1.65 , Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.26/1.65 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y ) }.
% 1.26/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! alpha10( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! alpha10( X, Y ), alpha37( X, Y ), alpha56( X, Y ) }.
% 1.26/1.65 { ! alpha37( X, Y ), alpha10( X, Y ) }.
% 1.26/1.65 { ! alpha56( X, Y ), alpha10( X, Y ) }.
% 1.26/1.65 { ! alpha56( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! alpha56( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha56( X, Y ) }.
% 1.26/1.65 { ! alpha37( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! alpha37( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha37( X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, X, Y ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.26/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Z, Y ), X ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.26/1.65 ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.26/1.65 ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.26/1.65 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.26/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.26/1.65 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.26/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.26/1.65 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha91( X,
% 1.26/1.65 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, T, Z ) = Y }.
% 1.26/1.65 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha91( X,
% 1.26/1.65 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, T, Z ) = Y }.
% 1.26/1.65 { ! alpha91( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! alpha91( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha91( X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.26/1.65 , alpha91( X, Y ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.26/1.65 alpha11( X, Z ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.26/1.65 alpha38( X, Y, Z ) }.
% 1.26/1.65 { ! alpha11( X, Z ), ! alpha38( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.26/1.65 { ! alpha38( X, Y, Z ), alpha57( X, Y, Z ) }.
% 1.26/1.65 { ! alpha38( X, Y, Z ), alpha66( X, Y, Z ) }.
% 1.26/1.65 { ! alpha57( X, Y, Z ), ! alpha66( X, Y, Z ), alpha38( X, Y, Z ) }.
% 1.26/1.65 { ! alpha66( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha76( X, Y, Z ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha66( X, Y, Z ) }.
% 1.26/1.65 { ! alpha76( X, Y, Z ), alpha66( X, Y, Z ) }.
% 1.26/1.65 { ! alpha76( X, Y, Z ), ! alpha84( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, skol30( T, U, Z ) ) ), alpha76( X, Y, Z ) }.
% 1.26/1.65 { alpha84( X, Y, skol30( X, Y, Z ) ), alpha76( X, Y, Z ) }.
% 1.26/1.65 { ! alpha84( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 skol31( X, T, U ) ) }.
% 1.26/1.65 { ! alpha84( X, Y, Z ), alpha88( X, Y, Z, skol31( X, Y, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha88( X, Y, Z
% 1.26/1.65 , T ), alpha84( X, Y, Z ) }.
% 1.26/1.65 { ! alpha88( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! alpha88( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.26/1.65 .
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha88( X,
% 1.26/1.65 Y, Z, T ) }.
% 1.26/1.65 { ! alpha57( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha67( X, Y, Z ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), X ), alpha57( X, Y, Z ) }.
% 1.26/1.65 { ! alpha67( X, Y, Z ), alpha57( X, Y, Z ) }.
% 1.26/1.65 { ! alpha67( X, Y, Z ), ! alpha77( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, skol32( T, U, Z ) ) ), alpha67( X, Y, Z ) }.
% 1.26/1.65 { alpha77( X, Y, skol32( X, Y, Z ) ), alpha67( X, Y, Z ) }.
% 1.26/1.65 { ! alpha77( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol33( T, U, W ) ) }.
% 1.26/1.65 { ! alpha77( X, Y, Z ), alpha85( X, Y, Z, skol33( X, Y, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha85( X, Y, Z, T )
% 1.26/1.65 , alpha77( X, Y, Z ) }.
% 1.26/1.65 { ! alpha85( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.26/1.65 ) }.
% 1.26/1.65 { ! alpha85( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.26/1.65 .
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha85( X,
% 1.26/1.65 Y, Z, T ) }.
% 1.26/1.65 { ! alpha11( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.26/1.65 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.26/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha11
% 1.26/1.65 ( X, Y ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol34( X, Y, Z ) ) ), Y ),
% 1.26/1.65 c_SEQ_OBseq( X, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, skol35( X ) ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Nat_OSuc( skol35( X ) ) ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Nat_Onat, Z, Y ), X ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.26/1.65 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.26/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.26/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.26/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.26/1.65 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.26/1.65 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.26/1.65 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.26/1.65 alpha12( X, Z ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.26/1.65 alpha39( X, Y, Z ) }.
% 1.26/1.65 { ! alpha12( X, Z ), ! alpha39( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.65 { ! alpha39( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.65 alpha58( X, Y, Z ) }.
% 1.26/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha39( X, Y, Z ) }.
% 1.26/1.65 { ! alpha58( X, Y, Z ), alpha39( X, Y, Z ) }.
% 1.26/1.65 { ! alpha58( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.26/1.65 ), alpha68( X, Y, Z, T ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol36( X, T, U ), X ),
% 1.26/1.65 alpha58( X, Y, Z ) }.
% 1.26/1.65 { ! alpha68( X, Y, Z, skol36( X, Y, Z ) ), alpha58( X, Y, Z ) }.
% 1.26/1.65 { ! alpha68( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.26/1.65 hBOOL( hAPP( Z, U ) ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, skol37( U, W, Z, V0 ) ) ), alpha68( X, Y, Z, T ) }.
% 1.26/1.65 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol37( X, Y, Z, T ) )
% 1.26/1.65 , T ), alpha68( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha12( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.65 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.26/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha12( X, Y ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12
% 1.26/1.65 ( X, Y ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.26/1.65 alpha13( X, Z ), alpha40( X, Y, Z ) }.
% 1.26/1.65 { ! alpha13( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.65 { ! alpha40( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.65 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol38( X
% 1.26/1.65 , Y, T ) ), Y ) }.
% 1.26/1.65 { ! alpha40( X, Y, Z ), alpha59( X, Y, Z, skol38( X, Y, Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha59( X
% 1.26/1.65 , Y, Z, T ), alpha40( X, Y, Z ) }.
% 1.26/1.65 { ! alpha59( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 1.26/1.65 ( T ) ) ) }.
% 1.26/1.65 { ! alpha59( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 1.26/1.65 hBOOL( hAPP( Z, T ) ), alpha59( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha13( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { ! alpha13( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Nat_Onat ) ) ) }.
% 1.26/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13( X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 1.26/1.65 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 1.26/1.65 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 1.26/1.65 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 1.26/1.65 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 1.26/1.65 .
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.26/1.65 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.26/1.65 c_RComplete_Onatfloor( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 1.26/1.65 ) ), ! alpha14( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), alpha14( X, Y, skol39( X, Y, Z ), skol60( X, Y, Z )
% 1.26/1.65 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 1.26/1.65 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol39( X, Y, Z ) ), skol60
% 1.26/1.65 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.26/1.65 ) }.
% 1.26/1.65 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 1.26/1.65 { ! alpha14( X, Y, Z, T ), alpha41( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha41( X, Y, Z, T )
% 1.26/1.65 , alpha14( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.26/1.65 ) }.
% 1.26/1.65 { ! alpha41( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.26/1.65 .
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha41( X,
% 1.26/1.65 Y, Z, T ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ) ) = X }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( X ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.26/1.65 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.26/1.65 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.65 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.26/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 1.26/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 1.26/1.65 Y ) ), Y ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Int_Oint, Z, Y ), X ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Int_Oint, Z, X ), Y ) }.
% 1.26/1.65 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.26/1.65 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.26/1.65 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 1.26/1.65 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 1.26/1.65 , U ), Z ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.26/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.26/1.65 ( X, Z, Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.26/1.65 ( X, Y, Z ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.26/1.65 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 1.26/1.65 , Y ) ), Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.26/1.65 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.26/1.65 ), Z ), Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.26/1.65 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.26/1.65 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.26/1.65 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.65 T, Z ), Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 1.26/1.65 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.26/1.65 T, Y ), Z ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.26/1.65 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.26/1.65 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 1.26/1.65 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 1.26/1.65 ), Z ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.26/1.65 X, Z, Y ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.26/1.65 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.26/1.65 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.26/1.65 }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.65 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.65 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.65 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.26/1.65 , Y ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.26/1.65 ), Z ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.26/1.65 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.26/1.65 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.26/1.65 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.65 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.26/1.65 class_RealVector_Oreal__normed__field( X ),
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.26/1.65 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.65 ( X, Y ) ) }.
% 1.26/1.65 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.26/1.65 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.26/1.65 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.26/1.65 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.26/1.65 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.26/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.26/1.65 ( X, Y ) ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ), hAPP( hAPP
% 1.26/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 1.26/1.65 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), Y ) )
% 1.26/1.65 = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP(
% 1.26/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 1.26/1.65 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), X ) )
% 1.26/1.65 }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha15( X,
% 1.26/1.65 Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha42( X,
% 1.26/1.65 Y ) }.
% 1.26/1.65 { ! alpha15( X, Y ), ! alpha42( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 1.26/1.65 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 1.26/1.65 { ! alpha42( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha42( X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha42( X, Y ) }.
% 1.26/1.65 { ! alpha15( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 1.26/1.65 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha15( X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha15( X, Y ) }.
% 1.26/1.65 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol40( X, Y ) ) }.
% 1.26/1.65 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.26/1.65 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.26/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.26/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.26/1.65 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.26/1.65 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.26/1.65 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.26/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.26/1.65 ( X ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.26/1.65 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.26/1.65 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.26/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.65 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.65 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 1.26/1.65 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 1.26/1.65 , Z ) ) = Y }.
% 1.26/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.26/1.65 ), Y ) ) = Z }.
% 1.26/1.65 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.26/1.65 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.26/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.26/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.26/1.65 tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 1.26/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.65 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.26/1.65 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.26/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.26/1.65 ( tc_Int_Oint, X, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 1.26/1.65 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 1.26/1.65 }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.26/1.65 c_Transcendental_Oln( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.26/1.65 X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.26/1.65 c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) ) }.
% 1.26/1.65 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha92( X,
% 1.26/1.65 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.26/1.65 tc_Int_Oint, Z, Y ) = X }.
% 1.26/1.65 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha92( X,
% 1.26/1.65 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.26/1.65 tc_Int_Oint, Z, Y ) = X }.
% 1.26/1.65 { ! alpha92( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.26/1.65 { ! alpha92( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha92( X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.26/1.65 , alpha92( X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.65 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.26/1.65 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 1.26/1.65 alpha16( X, Y, Z ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 1.26/1.65 alpha43( X, Y, Z ) }.
% 1.26/1.65 { ! alpha16( X, Y, Z ), ! alpha43( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.26/1.65 { ! alpha43( X, Y, Z ), alpha60( X, Y, Z ) }.
% 1.26/1.65 { ! alpha43( X, Y, Z ), alpha69( X, Y, Z ) }.
% 1.26/1.65 { ! alpha60( X, Y, Z ), ! alpha69( X, Y, Z ), alpha43( X, Y, Z ) }.
% 1.26/1.65 { ! alpha69( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha78( X, Y, Z ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha69( X, Y, Z ) }.
% 1.26/1.65 { ! alpha78( X, Y, Z ), alpha69( X, Y, Z ) }.
% 1.26/1.65 { ! alpha78( X, Y, Z ), ! alpha86( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, skol41( T, U, Z ) ) ), alpha78( X, Y, Z ) }.
% 1.26/1.65 { alpha86( X, Y, skol41( X, Y, Z ) ), alpha78( X, Y, Z ) }.
% 1.26/1.65 { ! alpha86( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 1.26/1.65 }.
% 1.26/1.65 { ! alpha86( X, Y, Z ), alpha89( X, Y, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha89( X, Y, Z
% 1.26/1.65 ), alpha86( X, Y, Z ) }.
% 1.26/1.65 { ! alpha89( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! alpha89( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol42( X, Y,
% 1.26/1.65 Z ) ), Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha89( X,
% 1.26/1.65 Y, Z ) }.
% 1.26/1.65 { ! alpha60( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha70( X, Y, Z ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 tc_Int_Oint ), X ), alpha60( X, Y, Z ) }.
% 1.26/1.65 { ! alpha70( X, Y, Z ), alpha60( X, Y, Z ) }.
% 1.26/1.65 { ! alpha70( X, Y, Z ), ! alpha79( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, skol43( T, U, Z ) ) ), alpha70( X, Y, Z ) }.
% 1.26/1.65 { alpha79( X, Y, skol43( X, Y, Z ) ), alpha70( X, Y, Z ) }.
% 1.26/1.65 { ! alpha79( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 1.26/1.65 { ! alpha79( X, Y, Z ), alpha87( X, Y, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha87( X, Y, Z ),
% 1.26/1.65 alpha79( X, Y, Z ) }.
% 1.26/1.65 { ! alpha87( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 1.26/1.65 }.
% 1.26/1.65 { ! alpha87( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol44( X, Y,
% 1.26/1.65 Z ) ), Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha87( X,
% 1.26/1.65 Y, Z ) }.
% 1.26/1.65 { ! alpha16( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.26/1.65 hBOOL( hAPP( Z, Y ) ) }.
% 1.26/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha16( X, Y, Z ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, Y ) ), alpha16( X, Y, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 1.26/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 1.26/1.65 ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha17( X, Y, T,
% 1.26/1.65 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha17( X, Y, skol45( X, Y
% 1.26/1.65 , Z ), skol61( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.26/1.65 skol45( X, Y, Z ) ), skol61( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.26/1.65 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 1.26/1.65 ) }.
% 1.26/1.65 { ! alpha17( X, Y, Z, T ), alpha44( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha44( X, Y, Z
% 1.26/1.65 , T ), alpha17( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.26/1.65 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! alpha44( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.26/1.65 .
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha44( X,
% 1.26/1.65 Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 1.26/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.26/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, X, Y ), Y ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.26/1.65 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, Y, X ), X ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_Nat_Onat, Y, X ), X ) }.
% 1.26/1.65 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol46( X, Y ) ) }.
% 1.26/1.65 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.26/1.65 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.26/1.65 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.65 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 1.26/1.65 ) ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.26/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 1.26/1.65 ( tc_Nat_Onat, Y, X ) ) }.
% 1.26/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 1.26/1.65 ( tc_Nat_Onat, X, Y ) ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.26/1.65 { c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, c_Complex_Orcis( T
% 1.26/1.65 , Z ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, T, Y ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.26/1.65 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.26/1.65 alpha18( X, Y, Z ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.26/1.65 alpha45( X, Y, Z ) }.
% 1.26/1.65 { ! alpha18( X, Y, Z ), ! alpha45( X, Y, Z ), hBOOL( hAPP( Z,
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 1.26/1.65 { ! alpha45( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.65 alpha61( X, Y, Z ) }.
% 1.26/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha45( X, Y, Z ) }.
% 1.26/1.65 { ! alpha61( X, Y, Z ), alpha45( X, Y, Z ) }.
% 1.26/1.65 { ! alpha61( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.26/1.65 ), alpha71( X, Y, Z, T ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol47( X, T, U ), X ),
% 1.26/1.65 alpha61( X, Y, Z ) }.
% 1.26/1.65 { ! alpha71( X, Y, Z, skol47( X, Y, Z ) ), alpha61( X, Y, Z ) }.
% 1.26/1.65 { ! alpha71( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.26/1.65 hBOOL( hAPP( Z, T ) ) }.
% 1.26/1.65 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol48( X, Y, T ) ), T
% 1.26/1.65 ), alpha71( X, Y, Z, T ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, T ) ), alpha71( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha18( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.26/1.65 hBOOL( hAPP( Z, Y ) ) }.
% 1.26/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha18( X, Y, Z ) }.
% 1.26/1.65 { ! hBOOL( hAPP( Z, Y ) ), alpha18( X, Y, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.26/1.65 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 1.26/1.65 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.26/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.26/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.26/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( tc_Nat_Onat ), X ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 1.26/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.26/1.65 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.26/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ), alpha46
% 1.26/1.65 ( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha19( X, Y, Z
% 1.26/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha46( X, Y, Z
% 1.26/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! alpha46( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.65 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( X ), Y ), alpha46( X, Y, Z ) }.
% 1.26/1.65 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.65 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha20( X, Y, Z ), alpha47
% 1.26/1.65 ( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha20( X, Y, Z
% 1.26/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.65 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha47( X, Y, Z
% 1.26/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.26/1.65 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! alpha47( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.65 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), alpha47( X, Y, Z ) }.
% 1.26/1.65 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.65 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), alpha20( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , Y, Z ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , Y, Z ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.26/1.65 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha21( X, Y, Z ), alpha48( X,
% 1.26/1.65 Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha21( X, Y, Z
% 1.26/1.65 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha48( X, Y, Z
% 1.26/1.65 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.65 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.65 ), alpha48( X, Y, Z ) }.
% 1.26/1.65 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.65 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.65 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 ), alpha21( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha22( X, Y, Z ), alpha49
% 1.26/1.65 ( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha22( X, Y, Z
% 1.26/1.65 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha49( X, Y, Z
% 1.26/1.65 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! alpha49( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.65 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 ), alpha49( X, Y, Z ) }.
% 1.26/1.65 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.26/1.65 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.65 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.65 ), alpha22( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha50( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha23( X, Y, T ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha50( X, Y, Z, T ), !
% 1.26/1.65 alpha23( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.26/1.65 { ! alpha50( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.26/1.65 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.26/1.65 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha50( X, Y, Z, T ) }.
% 1.26/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha50(
% 1.26/1.65 X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha23( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { Y = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z ) }.
% 1.26/1.65 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha51( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha24( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha51( X, Y, Z, T ), !
% 1.26/1.65 alpha24( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.26/1.65 { ! alpha51( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.26/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.26/1.65 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha51( X, Y, Z, T ) }.
% 1.26/1.65 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha51(
% 1.26/1.65 X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha24( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.26/1.65 { Z = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z ) }.
% 1.26/1.65 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.26/1.65 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.65 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.26/1.65 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.26/1.65 X ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.26/1.65 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.26/1.65 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.26/1.65 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.26/1.65 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.65 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.26/1.65 X ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.26/1.65 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.26/1.65 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.26/1.65 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Y ), Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 Z, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 Z, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Y ), Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Y ), Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.26/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 Z, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Z ), Y ), alpha52( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Z ), Y ), alpha62( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha52( X, Y, Z
% 1.26/1.65 , T ), ! alpha62( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.26/1.65 { ! alpha62( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Z ), alpha72( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.65 , alpha62( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha72( X, Y, Z, T ), alpha62( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha72( X, Y, Z, T ), alpha80( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha72( X, Y, Z, T ), alpha25( X, Y, Z ) }.
% 1.26/1.65 { ! alpha80( X, Y, Z, T ), ! alpha25( X, Y, Z ), alpha72( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha80( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.65 alpha80( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha80( X, Y, Z, T )
% 1.26/1.65 }.
% 1.26/1.65 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.65 alpha52( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha52( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.65 , alpha25( X, Y, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.26/1.65 , alpha25( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 Z, Y ) ), alpha53( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 Z, Y ) ), alpha63( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha53( X, Y, Z
% 1.26/1.65 , T ), ! alpha63( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! alpha63( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), alpha73( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.26/1.65 , alpha63( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha73( X, Y, Z, T ), alpha63( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha73( X, Y, Z, T ), alpha81( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha73( X, Y, Z, T ), alpha26( X, Y, T ) }.
% 1.26/1.65 { ! alpha81( X, Y, Z, T ), ! alpha26( X, Y, T ), alpha73( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha81( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.65 alpha81( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha81( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.65 alpha53( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha53( X, Y, Z, T )
% 1.26/1.65 }.
% 1.26/1.65 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.65 , alpha26( X, Y, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.65 , alpha26( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.26/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.26/1.65 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.26/1.65 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.26/1.65 .
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.26/1.65 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.26/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.26/1.65 .
% 1.26/1.65 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.26/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.26/1.65 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.26/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.26/1.65 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.26/1.65 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.26/1.65 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ) ), alpha54( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ) ), alpha64( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha54( X, Y, Z
% 1.26/1.65 , T ), ! alpha64( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.26/1.65 { ! alpha64( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), alpha74( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.26/1.65 , alpha64( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha74( X, Y, Z, T ), alpha64( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha74( X, Y, Z, T ), alpha82( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha74( X, Y, Z, T ), alpha27( X, Y, T ) }.
% 1.26/1.65 { ! alpha82( X, Y, Z, T ), ! alpha27( X, Y, T ), alpha74( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha82( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.65 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.65 alpha82( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha82( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.26/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.26/1.65 alpha54( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha54( X, Y, Z, T )
% 1.26/1.65 }.
% 1.26/1.65 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.65 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.65 , alpha27( X, Y, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.26/1.65 ) ), alpha27( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Z ), Y ), alpha55( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Z ), Y ), alpha65( X, Y, Z, T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha55( X, Y, Z
% 1.26/1.65 , T ), ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.26/1.65 { ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Z ), alpha75( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.26/1.65 , alpha65( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha75( X, Y, Z, T ), alpha65( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha75( X, Y, Z, T ), alpha83( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha75( X, Y, Z, T ), alpha28( X, Y, Z ) }.
% 1.26/1.65 { ! alpha83( X, Y, Z, T ), ! alpha28( X, Y, Z ), alpha75( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha83( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.26/1.65 alpha83( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha83( X, Y, Z, T )
% 1.26/1.65 }.
% 1.26/1.65 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.26/1.65 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.26/1.65 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.26/1.65 alpha55( X, Y, Z, T ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha55( X, Y, Z, T ) }.
% 1.26/1.65 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.26/1.65 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.26/1.65 , alpha28( X, Y, Z ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.26/1.65 , Y ), alpha28( X, Y, Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Y ), Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Y ), Z ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.26/1.65 ( X, Z, Y ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.26/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.26/1.65 , T, Y ), Z ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol49( Z, T ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.26/1.65 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol49( X, Y ) ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol50( Z, T ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__field( X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.26/1.65 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol50( X, Y ) ) ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.26/1.65 skol51( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless( X, skol51( X, T, U ),
% 1.26/1.65 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.26/1.65 , Y ) }.
% 1.26/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), skol51( X, Y, Z ) ), Z ), Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.26/1.65 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.26/1.65 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Y ) ) ), X
% 1.26/1.65 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.26/1.65 c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, Y ) ), X ) ) ) }.
% 1.26/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.26/1.65 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis(
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.26/1.65 { c_Complex_Ocis( X ) = c_Complex_Orcis( c_Groups_Oone__class_Oone(
% 1.26/1.65 tc_RealDef_Oreal ), X ) }.
% 1.26/1.65 { c_Complex_Ocis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, c_Complex_Ocis( Y )
% 1.26/1.65 , c_Complex_Ocis( X ) ) = c_Complex_Ocis( c_Groups_Ominus__class_Ominus(
% 1.26/1.65 tc_RealDef_Oreal, Y, X ) ) }.
% 1.26/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.26/1.65 c_Complex_Ocis( Y ) ), X ) = c_Complex_Ocis( hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.26/1.65 tc_Nat_Onat, X ) ), Y ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol52( U, W, V0, T )
% 1.26/1.65 ), c_SEQ_OBseq( X, Y ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol52( X, Y, Z, T ) ) ), Z
% 1.26/1.65 ), c_SEQ_OBseq( X, Y ) }.
% 1.26/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.26/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.26/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.26/1.65 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.26/1.65 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.26/1.65 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.26/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.26/1.65 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.26/1.65 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.26/1.65 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.26/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.26/1.65 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.26/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.26/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.26/1.65 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.26/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.26/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.26/1.65 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.26/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.65 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.26/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.26/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.65 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.26/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.65 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.26/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.26/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.26/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.26/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.26/1.65 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.26/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.26/1.65 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.26/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.26/1.65 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.26/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.26/1.65 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.26/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.65 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.26/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.26/1.65 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.26/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.26/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.26/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.26/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 1.26/1.65 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.26/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.26/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.26/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.26/1.65 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.26/1.65 ) ) }.
% 1.26/1.65 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.26/1.65 .
% 1.26/1.65 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.26/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.26/1.65 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.26/1.65 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.26/1.65 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.26/1.65 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.26/1.65 { class_Power_Opower( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.26/1.65 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.26/1.65 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.26/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.26/1.65 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.26/1.65 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.26/1.65 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.26/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.26/1.65 .
% 1.26/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.26/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.26/1.65 tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.26/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.26/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.26/1.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.26/1.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), v_b ), hAPP( hAPP(
% 1.26/1.65 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_n ) ) ) ),
% 1.26/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.26/1.65
% 1.26/1.65 *** allocated 15000 integers for clauses
% 1.26/1.65 *** allocated 22500 integers for clauses
% 1.26/1.65 *** allocated 33750 integers for clauses
% 1.26/1.65 *** allocated 50625 integers for clauses
% 1.26/1.65 *** allocated 75937 integers for clauses
% 1.26/1.65 *** allocated 113905 integers for clauses
% 1.26/1.65 percentage equality = 0.232770, percentage horn = 0.892234
% 1.26/1.65 This is a problem with some equality
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Options Used:
% 1.26/1.65
% 1.26/1.65 useres = 1
% 1.26/1.65 useparamod = 1
% 1.26/1.65 useeqrefl = 1
% 1.26/1.65 useeqfact = 1
% 1.26/1.65 usefactor = 1
% 1.26/1.65 usesimpsplitting = 0
% 1.26/1.65 usesimpdemod = 5
% 1.26/1.65 usesimpres = 3
% 1.26/1.65
% 1.26/1.65 resimpinuse = 1000
% 1.26/1.65 resimpclauses = 20000
% 1.26/1.65 substype = eqrewr
% 1.26/1.65 backwardsubs = 1
% 1.26/1.65 selectoldest = 5
% 1.26/1.65
% 1.26/1.65 litorderings [0] = split
% 1.26/1.65 litorderings [1] = extend the termordering, first sorting on arguments
% 1.26/1.65
% 1.26/1.65 termordering = kbo
% 1.26/1.65
% 1.26/1.65 litapriori = 0
% 1.26/1.65 termapriori = 1
% 1.26/1.65 litaposteriori = 0
% 1.26/1.65 termaposteriori = 0
% 1.26/1.65 demodaposteriori = 0
% 1.26/1.65 ordereqreflfact = 0
% 1.26/1.65
% 1.26/1.65 litselect = negord
% 1.26/1.65
% 1.26/1.65 maxweight = 15
% 1.26/1.65 maxdepth = 30000
% 1.26/1.65 maxlength = 115
% 1.26/1.65 maxnrvars = 195
% 1.26/1.65 excuselevel = 1
% 1.26/1.65 increasemaxweight = 1
% 1.26/1.65
% 1.26/1.65 maxselected = 10000000
% 1.26/1.65 maxnrclauses = 10000000
% 1.26/1.65
% 1.26/1.65 showgenerated = 0
% 1.26/1.65 showkept = 0
% 1.26/1.65 showselected = 0
% 1.26/1.65 showdeleted = 0
% 1.26/1.65 showresimp = 1
% 1.26/1.65 showstatus = 2000
% 1.26/1.65
% 1.26/1.65 prologoutput = 0
% 1.26/1.65 nrgoals = 5000000
% 1.26/1.65 totalproof = 1
% 1.26/1.65
% 1.26/1.65 Symbols occurring in the translation:
% 1.26/1.65
% 1.26/1.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.26/1.65 . [1, 2] (w:1, o:193, a:1, s:1, b:0),
% 1.26/1.65 ! [4, 1] (w:0, o:108, a:1, s:1, b:0),
% 1.26/1.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.26/1.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.26/1.65 hAPP [38, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.26/1.65 v_n [39, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.26/1.65 tc_Nat_Onat [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.26/1.65 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.26/1.65 v_b [42, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.26/1.65 tc_Complex_Ocomplex [43, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__semidom [47, 1] (w:1, o:116, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 c_Groups_Oone__class_Oone [48, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.26/1.65 c_Orderings_Oord__class_Oless [49, 3] (w:1, o:271, a:1, s:1, b:0),
% 1.26/1.65 c_Groups_Otimes__class_Otimes [50, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.26/1.65 c_Power_Opower__class_Opower [51, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.26/1.65 class_RealVector_Oreal__normed__algebra__1 [52, 1] (w:1, o:120, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 c_RealVector_Onorm__class_Onorm [53, 2] (w:1, o:218, a:1, s:1, b:0),
% 1.26/1.65
% 1.26/1.65 tc_RealDef_Oreal [54, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.26/1.65 class_RealVector_Oreal__normed__vector [59, 1] (w:1, o:121, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 c_Groups_Oplus__class_Oplus [60, 3] (w:1, o:272, a:1, s:1, b:0),
% 1.26/1.65 class_RealVector_Oreal__normed__algebra [61, 1] (w:1, o:122, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Rings_Ocomm__semiring__1 [70, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.26/1.65 class_Power_Opower [71, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Omult__zero [72, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Ono__zero__divisors [73, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.26/1.65
% 1.26/1.65 class_Rings_Ozero__neq__one [74, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Omonoid__mult [78, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.26/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [80
% 1.26/1.65 , 1] (w:1, o:162, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Oring__1__no__zero__divisors [81, 1] (w:1, o:145, a:1, s:
% 1.26/1.65 1, b:0),
% 1.26/1.65 class_Rings_Osemiring__0 [82, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Ocomm__monoid__mult [98, 1] (w:1, o:163, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 class_RealVector_Oreal__normed__div__algebra [99, 1] (w:1, o:150, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__ring__strict [100, 1] (w:1, o:114, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Rings_Olinordered__ring [101, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oordered__comm__monoid__add [102, 1] (w:1, o:164, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 class_Groups_Ozero [105, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__idom [106, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oab__semigroup__mult [107, 1] (w:1, o:166, a:1, s:1, b:0
% 1.26/1.65 ),
% 1.26/1.65 class_Groups_Oab__semigroup__add [108, 1] (w:1, o:167, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 class_Groups_Ocancel__semigroup__add [109, 1] (w:1, o:168, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Groups_Ocancel__ab__semigroup__add [110, 1] (w:1, o:169, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 class_Groups_Oone [111, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.26/1.65 hBOOL [113, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Oring__no__zero__divisors [117, 1] (w:1, o:146, a:1, s:1
% 1.26/1.65 , b:0),
% 1.26/1.65 class_Groups_Omonoid__add [118, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Ocomm__monoid__add [119, 1] (w:1, o:173, a:1, s:1, b:0)
% 1.26/1.65 ,
% 1.26/1.65 class_Groups_Olinordered__ab__group__add [120, 1] (w:1, o:143, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le [121, 1] (w:1, o:
% 1.26/1.65 174, a:1, s:1, b:0),
% 1.26/1.65 class_Groups_Oordered__cancel__ab__semigroup__add [122, 1] (w:1, o:
% 1.26/1.65 175, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Ocomm__semiring [123, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Osemiring [125, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__semiring__strict [126, 1] (w:1, o:131, a:1
% 1.26/1.65 , s:1, b:0),
% 1.26/1.65 class_Rings_Olinordered__comm__semiring__strict [127, 1] (w:1, o:132
% 1.26/1.65 , a:1, s:1, b:0),
% 1.26/1.65 c_Power_Opower_Opower [128, 3] (w:1, o:274, a:1, s:1, b:0),
% 1.26/1.66 tc_Int_Oint [131, 0] (w:1, o:81, a:1, s:1, b:0),
% 1.26/1.66 c_Orderings_Oord__class_Oless__eq [139, 3] (w:1, o:273, a:1, s:1, b:0
% 1.26/1.66 ),
% 1.26/1.66 c_Groups_Ominus__class_Ominus [140, 3] (w:1, o:275, a:1, s:1, b:0),
% 1.26/1.66 class_Rings_Olinordered__semiring__1__strict [142, 1] (w:1, o:133, a:
% 1.26/1.66 1, s:1, b:0),
% 1.26/1.66 class_Groups_Oab__group__add [143, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.26/1.66 class_Groups_Oordered__ab__group__add [144, 1] (w:1, o:177, a:1, s:1
% 1.26/1.66 , b:0),
% 1.26/1.66 class_Rings_Oordered__ring [148, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.26/1.66 class_Groups_Ogroup__add [150, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.26/1.66 class_Groups_Oordered__ab__semigroup__add [151, 1] (w:1, o:179, a:1
% 1.26/1.66 , s:1, b:0),
% 1.26/1.66 class_Rings_Oring [153, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.26/1.66 class_Rings_Oordered__cancel__semiring [154, 1] (w:1, o:154, a:1, s:1
% 1.26/1.66 , b:0),
% 1.26/1.66 class_Rings_Oordered__semiring [155, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.26/1.66
% 1.26/1.66 class_Rings_Oordered__comm__semiring [156, 1] (w:1, o:156, a:1, s:1
% 1.26/1.66 , b:0),
% 1.26/1.66 class_Rings_Oring__1 [157, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.26/1.66 class_Rings_Olinordered__semiring [158, 1] (w:1, o:134, a:1, s:1, b:0
% 1.26/1.66 ),
% 1.26/1.66 class_Rings_Olinordered__semiring__1 [160, 1] (w:1, o:135, a:1, s:1
% 1.26/1.66 , b:0),
% 1.26/1.66 class_Orderings_Opreorder [161, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.26/1.66 class_Orderings_Oorder [162, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.26/1.66 class_Orderings_Oord [167, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.26/1.66 tc_fun [168, 2] (w:1, o:248, a:1, s:1, b:0),
% 1.26/1.66 class_Orderings_Olinorder [169, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.26/1.66 c_Complex_Oii [173, 0] (w:1, o:96, a:1, s:1, b:0),
% 1.26/1.66 c_Nat__Transfer_Otsub [177, 2] (w:1, o:249, a:1, s:1, b:0),
% 1.26/1.66 c_Complex_Oexpi [179, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.26/1.66 c_RComplete_Onatceiling [180, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.26/1.66 c_RComplete_Onatfloor [181, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.26/1.66 c_RealDef_Oreal [182, 2] (w:1, o:250, a:1, s:1, b:0),
% 1.26/1.66 c_Complex_Orcis [183, 2] (w:1, o:251, a:1, s:1, b:0),
% 1.26/1.66 c_SEQ_Odecseq [188, 2] (w:1, o:252, a:1, s:1, b:0),
% 1.26/1.66 c_Transcendental_Oln [190, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.26/1.66 c_SEQ_OBseq [191, 2] (w:1, o:253, a:1, s:1, b:0),
% 1.26/1.66 c_SEQ_Oincseq [192, 2] (w:1, o:254, a:1, s:1, b:0),
% 1.26/1.66 c_Nat_OSuc [194, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.26/1.66 class_Rings_Ocomm__ring__1 [200, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.26/1.66 c_Divides_Odiv__class_Odiv [201, 3] (w:1, o:276, a:1, s:1, b:0),
% 1.26/1.66 class_Divides_Osemiring__div [202, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.26/1.66 c_Rings_Oinverse__class_Odivide [209, 3] (w:1, o:277, a:1, s:1, b:0)
% 1.26/1.66 ,
% 1.26/1.66 c_Divides_Odiv__class_Omod [210, 3] (w:1, o:278, a:1, s:1, b:0),
% 1.26/1.66 class_RealVector_Oreal__normed__field [211, 1] (w:1, o:157, a:1, s:1
% 1.26/1.66 , b:0),
% 1.26/1.66 class_Rings_Odivision__ring [212, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.26/1.66 class_Divides_Oring__div [213, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.26/1.66 class_Fields_Ofield__inverse__zero [214, 1] (w:1, o:139, a:1, s:1, b:
% 1.26/1.66 0),
% 1.26/1.66 class_Rings_Odivision__ring__inverse__zero [215, 1] (w:1, o:159, a:1
% 1.26/1.66 , s:1, b:0),
% 1.26/1.66 class_Fields_Ofield [216, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.26/1.66 class_RealVector_Oreal__field [218, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.26/1.66 class_Fields_Olinordered__field__inverse__zero [220, 1] (w:1, o:141
% 1.26/1.66 , a:1, s:1, b:0),
% 1.26/1.66 class_Fields_Olinordered__field [221, 1] (w:1, o:142, a:1, s:1, b:0)
% 1.26/1.66 ,
% 1.26/1.66 c_Complex_Ocis [223, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.26/1.66 c_Groups_Ouminus__class_Ouminus [225, 2] (w:1, o:255, a:1, s:1, b:0)
% 1.26/1.66 ,
% 1.26/1.66 class_Rings_Oidom [226, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.26/1.66 tc_HOL_Obool [229, 0] (w:1, o:80, a:1, s:1, b:0),
% 1.26/1.66 alpha1 [230, 4] (w:1, o:354, a:1, s:1, b:1),
% 1.26/1.66 alpha2 [231, 4] (w:1, o:357, a:1, s:1, b:1),
% 1.26/1.66 alpha3 [232, 3] (w:1, o:288, a:1, s:1, b:1),
% 1.26/1.66 alpha4 [233, 3] (w:1, o:295, a:1, s:1, b:1),
% 1.26/1.66 alpha5 [234, 3] (w:1, o:303, a:1, s:1, b:1),
% 1.26/1.66 alpha6 [235, 3] (w:1, o:306, a:1, s:1, b:1),
% 1.26/1.66 alpha7 [236, 2] (w:1, o:256, a:1, s:1, b:1),
% 1.26/1.66 alpha8 [237, 2] (w:1, o:257, a:1, s:1, b:1),
% 1.26/1.66 alpha9 [238, 2] (w:1, o:258, a:1, s:1, b:1),
% 1.26/1.66 alpha10 [239, 2] (w:1, o:259, a:1, s:1, b:1),
% 1.26/1.66 alpha11 [240, 2] (w:1, o:260, a:1, s:1, b:1),
% 1.26/1.66 alpha12 [241, 2] (w:1, o:261, a:1, s:1, b:1),
% 1.26/1.66 alpha13 [242, 2] (w:1, o:262, a:1, s:1, b:1),
% 1.26/1.66 alpha14 [243, 4] (w:1, o:355, a:1, s:1, b:1),
% 1.26/1.66 alpha15 [244, 2] (w:1, o:263, a:1, s:1, b:1),
% 1.26/1.66 alpha16 [245, 3] (w:1, o:307, a:1, s:1, b:1),
% 1.26/1.66 alpha17 [246, 4] (w:1, o:356, a:1, s:1, b:1),
% 1.26/1.66 alpha18 [247, 3] (w:1, o:308, a:1, s:1, b:1),
% 1.26/1.66 alpha19 [248, 3] (w:1, o:309, a:1, s:1, b:1),
% 1.26/1.66 alpha20 [249, 3] (w:1, o:279, a:1, s:1, b:1),
% 1.26/1.66 alpha21 [250, 3] (w:1, o:280, a:1, s:1, b:1),
% 1.26/1.66 alpha22 [251, 3] (w:1, o:281, a:1, s:1, b:1),
% 1.26/1.66 alpha23 [252, 3] (w:1, o:282, a:1, s:1, b:1),
% 1.26/1.66 alpha24 [253, 3] (w:1, o:283, a:1, s:1, b:1),
% 1.26/1.66 alpha25 [254, 3] (w:1, o:284, a:1, s:1, b:1),
% 1.26/1.66 alpha26 [255, 3] (w:1, o:285, a:1, s:1, b:1),
% 1.26/1.66 alpha27 [256, 3] (w:1, o:286, a:1, s:1, b:1),
% 2.38/2.76 alpha28 [257, 3] (w:1, o:287, a:1, s:1, b:1),
% 2.38/2.76 alpha29 [258, 4] (w:1, o:358, a:1, s:1, b:1),
% 2.38/2.76 alpha30 [259, 4] (w:1, o:359, a:1, s:1, b:1),
% 2.38/2.76 alpha31 [260, 3] (w:1, o:289, a:1, s:1, b:1),
% 2.38/2.76 alpha32 [261, 3] (w:1, o:290, a:1, s:1, b:1),
% 2.38/2.76 alpha33 [262, 3] (w:1, o:291, a:1, s:1, b:1),
% 2.38/2.76 alpha34 [263, 3] (w:1, o:292, a:1, s:1, b:1),
% 2.38/2.76 alpha35 [264, 2] (w:1, o:264, a:1, s:1, b:1),
% 2.38/2.76 alpha36 [265, 2] (w:1, o:265, a:1, s:1, b:1),
% 2.38/2.76 alpha37 [266, 2] (w:1, o:266, a:1, s:1, b:1),
% 2.38/2.76 alpha38 [267, 3] (w:1, o:293, a:1, s:1, b:1),
% 2.38/2.76 alpha39 [268, 3] (w:1, o:294, a:1, s:1, b:1),
% 2.38/2.76 alpha40 [269, 3] (w:1, o:296, a:1, s:1, b:1),
% 2.38/2.76 alpha41 [270, 4] (w:1, o:360, a:1, s:1, b:1),
% 2.38/2.76 alpha42 [271, 2] (w:1, o:267, a:1, s:1, b:1),
% 2.38/2.76 alpha43 [272, 3] (w:1, o:297, a:1, s:1, b:1),
% 2.38/2.76 alpha44 [273, 4] (w:1, o:361, a:1, s:1, b:1),
% 2.38/2.76 alpha45 [274, 3] (w:1, o:298, a:1, s:1, b:1),
% 2.38/2.76 alpha46 [275, 3] (w:1, o:299, a:1, s:1, b:1),
% 2.38/2.76 alpha47 [276, 3] (w:1, o:300, a:1, s:1, b:1),
% 2.38/2.76 alpha48 [277, 3] (w:1, o:301, a:1, s:1, b:1),
% 2.38/2.76 alpha49 [278, 3] (w:1, o:302, a:1, s:1, b:1),
% 2.38/2.76 alpha50 [279, 4] (w:1, o:362, a:1, s:1, b:1),
% 2.38/2.76 alpha51 [280, 4] (w:1, o:363, a:1, s:1, b:1),
% 2.38/2.76 alpha52 [281, 4] (w:1, o:364, a:1, s:1, b:1),
% 2.38/2.76 alpha53 [282, 4] (w:1, o:365, a:1, s:1, b:1),
% 2.38/2.76 alpha54 [283, 4] (w:1, o:366, a:1, s:1, b:1),
% 2.38/2.76 alpha55 [284, 4] (w:1, o:367, a:1, s:1, b:1),
% 2.38/2.76 alpha56 [285, 2] (w:1, o:268, a:1, s:1, b:1),
% 2.38/2.76 alpha57 [286, 3] (w:1, o:304, a:1, s:1, b:1),
% 2.38/2.76 alpha58 [287, 3] (w:1, o:305, a:1, s:1, b:1),
% 2.38/2.76 alpha59 [288, 4] (w:1, o:368, a:1, s:1, b:1),
% 2.38/2.76 alpha60 [289, 3] (w:1, o:310, a:1, s:1, b:1),
% 2.38/2.76 alpha61 [290, 3] (w:1, o:311, a:1, s:1, b:1),
% 2.38/2.76 alpha62 [291, 4] (w:1, o:369, a:1, s:1, b:1),
% 2.38/2.76 alpha63 [292, 4] (w:1, o:370, a:1, s:1, b:1),
% 2.38/2.76 alpha64 [293, 4] (w:1, o:371, a:1, s:1, b:1),
% 2.38/2.76 alpha65 [294, 4] (w:1, o:372, a:1, s:1, b:1),
% 2.38/2.76 alpha66 [295, 3] (w:1, o:312, a:1, s:1, b:1),
% 2.38/2.76 alpha67 [296, 3] (w:1, o:313, a:1, s:1, b:1),
% 2.38/2.76 alpha68 [297, 4] (w:1, o:373, a:1, s:1, b:1),
% 2.38/2.76 alpha69 [298, 3] (w:1, o:314, a:1, s:1, b:1),
% 2.38/2.76 alpha70 [299, 3] (w:1, o:315, a:1, s:1, b:1),
% 2.38/2.76 alpha71 [300, 4] (w:1, o:374, a:1, s:1, b:1),
% 2.38/2.76 alpha72 [301, 4] (w:1, o:375, a:1, s:1, b:1),
% 2.38/2.76 alpha73 [302, 4] (w:1, o:376, a:1, s:1, b:1),
% 2.38/2.76 alpha74 [303, 4] (w:1, o:377, a:1, s:1, b:1),
% 2.38/2.76 alpha75 [304, 4] (w:1, o:378, a:1, s:1, b:1),
% 2.38/2.76 alpha76 [305, 3] (w:1, o:316, a:1, s:1, b:1),
% 2.38/2.76 alpha77 [306, 3] (w:1, o:317, a:1, s:1, b:1),
% 2.38/2.76 alpha78 [307, 3] (w:1, o:318, a:1, s:1, b:1),
% 2.38/2.76 alpha79 [308, 3] (w:1, o:319, a:1, s:1, b:1),
% 2.38/2.76 alpha80 [309, 4] (w:1, o:379, a:1, s:1, b:1),
% 2.38/2.76 alpha81 [310, 4] (w:1, o:380, a:1, s:1, b:1),
% 2.38/2.76 alpha82 [311, 4] (w:1, o:381, a:1, s:1, b:1),
% 2.38/2.76 alpha83 [312, 4] (w:1, o:382, a:1, s:1, b:1),
% 2.38/2.76 alpha84 [313, 3] (w:1, o:320, a:1, s:1, b:1),
% 2.38/2.76 alpha85 [314, 4] (w:1, o:383, a:1, s:1, b:1),
% 2.38/2.76 alpha86 [315, 3] (w:1, o:321, a:1, s:1, b:1),
% 2.38/2.76 alpha87 [316, 3] (w:1, o:322, a:1, s:1, b:1),
% 2.38/2.76 alpha88 [317, 4] (w:1, o:384, a:1, s:1, b:1),
% 2.38/2.76 alpha89 [318, 3] (w:1, o:323, a:1, s:1, b:1),
% 2.38/2.76 alpha90 [319, 3] (w:1, o:324, a:1, s:1, b:1),
% 2.38/2.76 alpha91 [320, 2] (w:1, o:269, a:1, s:1, b:1),
% 2.38/2.76 alpha92 [321, 2] (w:1, o:270, a:1, s:1, b:1),
% 2.38/2.76 alpha93 [322, 3] (w:1, o:325, a:1, s:1, b:1),
% 2.38/2.76 skol1 [323, 2] (w:1, o:219, a:1, s:1, b:1),
% 2.38/2.76 skol2 [324, 2] (w:1, o:226, a:1, s:1, b:1),
% 2.38/2.76 skol3 [325, 2] (w:1, o:234, a:1, s:1, b:1),
% 2.38/2.76 skol4 [326, 2] (w:1, o:235, a:1, s:1, b:1),
% 2.38/2.76 skol5 [327, 3] (w:1, o:333, a:1, s:1, b:1),
% 2.38/2.76 skol6 [328, 3] (w:1, o:338, a:1, s:1, b:1),
% 2.38/2.76 skol7 [329, 3] (w:1, o:343, a:1, s:1, b:1),
% 2.38/2.76 skol8 [330, 2] (w:1, o:236, a:1, s:1, b:1),
% 2.38/2.76 skol9 [331, 2] (w:1, o:237, a:1, s:1, b:1),
% 2.38/2.76 skol10 [332, 2] (w:1, o:220, a:1, s:1, b:1),
% 2.38/2.76 skol11 [333, 1] (w:1, o:188, a:1, s:1, b:1),
% 2.38/2.76 skol12 [334, 2] (w:1, o:221, a:1, s:1, b:1),
% 23.32/23.72 skol13 [335, 1] (w:1, o:189, a:1, s:1, b:1),
% 23.32/23.72 skol14 [336, 2] (w:1, o:222, a:1, s:1, b:1),
% 23.32/23.72 skol15 [337, 2] (w:1, o:223, a:1, s:1, b:1),
% 23.32/23.72 skol16 [338, 1] (w:1, o:190, a:1, s:1, b:1),
% 23.32/23.72 skol17 [339, 4] (w:1, o:385, a:1, s:1, b:1),
% 23.32/23.72 skol18 [340, 2] (w:1, o:224, a:1, s:1, b:1),
% 23.32/23.72 skol19 [341, 2] (w:1, o:225, a:1, s:1, b:1),
% 23.32/23.72 skol20 [342, 2] (w:1, o:227, a:1, s:1, b:1),
% 23.32/23.72 skol21 [343, 3] (w:1, o:344, a:1, s:1, b:1),
% 23.32/23.72 skol22 [344, 2] (w:1, o:228, a:1, s:1, b:1),
% 23.32/23.72 skol23 [345, 2] (w:1, o:229, a:1, s:1, b:1),
% 23.32/23.72 skol24 [346, 2] (w:1, o:230, a:1, s:1, b:1),
% 23.32/23.72 skol25 [347, 1] (w:1, o:191, a:1, s:1, b:1),
% 23.32/23.72 skol26 [348, 2] (w:1, o:231, a:1, s:1, b:1),
% 23.32/23.72 skol27 [349, 3] (w:1, o:345, a:1, s:1, b:1),
% 23.32/23.72 skol28 [350, 2] (w:1, o:232, a:1, s:1, b:1),
% 23.32/23.72 skol29 [351, 2] (w:1, o:233, a:1, s:1, b:1),
% 23.32/23.72 skol30 [352, 3] (w:1, o:346, a:1, s:1, b:1),
% 23.32/23.72 skol31 [353, 3] (w:1, o:347, a:1, s:1, b:1),
% 23.32/23.72 skol32 [354, 3] (w:1, o:348, a:1, s:1, b:1),
% 23.32/23.72 skol33 [355, 3] (w:1, o:349, a:1, s:1, b:1),
% 23.32/23.72 skol34 [356, 3] (w:1, o:350, a:1, s:1, b:1),
% 23.32/23.72 skol35 [357, 1] (w:1, o:192, a:1, s:1, b:1),
% 23.32/23.72 skol36 [358, 3] (w:1, o:351, a:1, s:1, b:1),
% 23.32/23.72 skol37 [359, 4] (w:1, o:386, a:1, s:1, b:1),
% 23.32/23.72 skol38 [360, 3] (w:1, o:352, a:1, s:1, b:1),
% 23.32/23.72 skol39 [361, 3] (w:1, o:353, a:1, s:1, b:1),
% 23.32/23.72 skol40 [362, 2] (w:1, o:238, a:1, s:1, b:1),
% 23.32/23.72 skol41 [363, 3] (w:1, o:326, a:1, s:1, b:1),
% 23.32/23.72 skol42 [364, 3] (w:1, o:327, a:1, s:1, b:1),
% 23.32/23.72 skol43 [365, 3] (w:1, o:328, a:1, s:1, b:1),
% 23.32/23.72 skol44 [366, 3] (w:1, o:329, a:1, s:1, b:1),
% 23.32/23.72 skol45 [367, 3] (w:1, o:330, a:1, s:1, b:1),
% 23.32/23.72 skol46 [368, 2] (w:1, o:239, a:1, s:1, b:1),
% 23.32/23.72 skol47 [369, 3] (w:1, o:331, a:1, s:1, b:1),
% 23.32/23.72 skol48 [370, 3] (w:1, o:332, a:1, s:1, b:1),
% 23.32/23.72 skol49 [371, 2] (w:1, o:240, a:1, s:1, b:1),
% 23.32/23.72 skol50 [372, 2] (w:1, o:241, a:1, s:1, b:1),
% 23.32/23.72 skol51 [373, 3] (w:1, o:334, a:1, s:1, b:1),
% 23.32/23.72 skol52 [374, 4] (w:1, o:387, a:1, s:1, b:1),
% 23.32/23.72 skol53 [375, 2] (w:1, o:242, a:1, s:1, b:1),
% 23.32/23.72 skol54 [376, 3] (w:1, o:335, a:1, s:1, b:1),
% 23.32/23.72 skol55 [377, 2] (w:1, o:243, a:1, s:1, b:1),
% 23.32/23.72 skol56 [378, 2] (w:1, o:244, a:1, s:1, b:1),
% 23.32/23.72 skol57 [379, 3] (w:1, o:336, a:1, s:1, b:1),
% 23.32/23.72 skol58 [380, 3] (w:1, o:337, a:1, s:1, b:1),
% 23.32/23.72 skol59 [381, 2] (w:1, o:245, a:1, s:1, b:1),
% 23.32/23.72 skol60 [382, 3] (w:1, o:339, a:1, s:1, b:1),
% 23.32/23.72 skol61 [383, 3] (w:1, o:340, a:1, s:1, b:1),
% 23.32/23.72 skol62 [384, 3] (w:1, o:341, a:1, s:1, b:1),
% 23.32/23.72 skol63 [385, 3] (w:1, o:342, a:1, s:1, b:1),
% 23.32/23.72 skol64 [386, 2] (w:1, o:246, a:1, s:1, b:1),
% 23.32/23.72 skol65 [387, 2] (w:1, o:247, a:1, s:1, b:1).
% 23.32/23.72
% 23.32/23.72
% 23.32/23.72 Starting Search:
% 23.32/23.72
% 23.32/23.72 *** allocated 170857 integers for clauses
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72
% 23.32/23.72 Intermediate Status:
% 23.32/23.72 Generated: 2761
% 23.32/23.72 Kept: 2000
% 23.32/23.72 Inuse: 20
% 23.32/23.72 Deleted: 0
% 23.32/23.72 Deletedinuse: 0
% 23.32/23.72
% 23.32/23.72 *** allocated 256285 integers for clauses
% 23.32/23.72 *** allocated 170857 integers for termspace/termends
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72 *** allocated 384427 integers for clauses
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72
% 23.32/23.72 Intermediate Status:
% 23.32/23.72 Generated: 7667
% 23.32/23.72 Kept: 4006
% 23.32/23.72 Inuse: 144
% 23.32/23.72 Deleted: 2
% 23.32/23.72 Deletedinuse: 0
% 23.32/23.72
% 23.32/23.72 *** allocated 256285 integers for termspace/termends
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72
% 23.32/23.72 Intermediate Status:
% 23.32/23.72 Generated: 11423
% 23.32/23.72 Kept: 6172
% 23.32/23.72 Inuse: 207
% 23.32/23.72 Deleted: 4
% 23.32/23.72 Deletedinuse: 0
% 23.32/23.72
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72 *** allocated 576640 integers for clauses
% 23.32/23.72 *** allocated 384427 integers for termspace/termends
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72
% 23.32/23.72 Intermediate Status:
% 23.32/23.72 Generated: 21229
% 23.32/23.72 Kept: 8266
% 23.32/23.72 Inuse: 252
% 23.32/23.72 Deleted: 4
% 23.32/23.72 Deletedinuse: 0
% 23.32/23.72
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72 *** allocated 576640 integers for termspace/termends
% 23.32/23.72 *** allocated 864960 integers for clauses
% 23.32/23.72
% 23.32/23.72 Intermediate Status:
% 23.32/23.72 Generated: 35963
% 23.32/23.72 Kept: 10643
% 23.32/23.72 Inuse: 313
% 23.32/23.72 Deleted: 8
% 23.32/23.72 Deletedinuse: 0
% 23.32/23.72
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72 Resimplifying inuse:
% 23.32/23.72 Done
% 23.32/23.72
% 23.32/23.72
% 23.32/23.72 Intermediate Status:
% 23.32/23.72 Generated: 44895
% 23.32/23.72 Kept: 12666
% 23.32/23.72 Inuse: 366
% 92.43/92.84 Deleted: 8
% 92.43/92.84 Deletedinuse: 0
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 51401
% 92.43/92.84 Kept: 15081
% 92.43/92.84 Inuse: 396
% 92.43/92.84 Deleted: 10
% 92.43/92.84 Deletedinuse: 0
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 *** allocated 864960 integers for termspace/termends
% 92.43/92.84 *** allocated 1297440 integers for clauses
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 58283
% 92.43/92.84 Kept: 17484
% 92.43/92.84 Inuse: 431
% 92.43/92.84 Deleted: 10
% 92.43/92.84 Deletedinuse: 0
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 66704
% 92.43/92.84 Kept: 19970
% 92.43/92.84 Inuse: 466
% 92.43/92.84 Deleted: 10
% 92.43/92.84 Deletedinuse: 0
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying clauses:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 75738
% 92.43/92.84 Kept: 22000
% 92.43/92.84 Inuse: 511
% 92.43/92.84 Deleted: 315
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 88904
% 92.43/92.84 Kept: 25022
% 92.43/92.84 Inuse: 526
% 92.43/92.84 Deleted: 315
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 *** allocated 1297440 integers for termspace/termends
% 92.43/92.84 *** allocated 1946160 integers for clauses
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 100172
% 92.43/92.84 Kept: 27265
% 92.43/92.84 Inuse: 560
% 92.43/92.84 Deleted: 316
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 110842
% 92.43/92.84 Kept: 29306
% 92.43/92.84 Inuse: 580
% 92.43/92.84 Deleted: 316
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 123266
% 92.43/92.84 Kept: 32144
% 92.43/92.84 Inuse: 594
% 92.43/92.84 Deleted: 317
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 140186
% 92.43/92.84 Kept: 34152
% 92.43/92.84 Inuse: 606
% 92.43/92.84 Deleted: 317
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 157865
% 92.43/92.84 Kept: 36152
% 92.43/92.84 Inuse: 616
% 92.43/92.84 Deleted: 317
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 171983
% 92.43/92.84 Kept: 38280
% 92.43/92.84 Inuse: 629
% 92.43/92.84 Deleted: 317
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 178562
% 92.43/92.84 Kept: 41015
% 92.43/92.84 Inuse: 639
% 92.43/92.84 Deleted: 317
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying clauses:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 *** allocated 1946160 integers for termspace/termends
% 92.43/92.84 *** allocated 2919240 integers for clauses
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 187827
% 92.43/92.84 Kept: 44438
% 92.43/92.84 Inuse: 669
% 92.43/92.84 Deleted: 561
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 195627
% 92.43/92.84 Kept: 46560
% 92.43/92.84 Inuse: 719
% 92.43/92.84 Deleted: 561
% 92.43/92.84 Deletedinuse: 1
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 204295
% 92.43/92.84 Kept: 48601
% 92.43/92.84 Inuse: 739
% 92.43/92.84 Deleted: 565
% 92.43/92.84 Deletedinuse: 5
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 219992
% 92.43/92.84 Kept: 51006
% 92.43/92.84 Inuse: 754
% 92.43/92.84 Deleted: 565
% 92.43/92.84 Deletedinuse: 5
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 237252
% 92.43/92.84 Kept: 53511
% 92.43/92.84 Inuse: 768
% 92.43/92.84 Deleted: 566
% 92.43/92.84 Deletedinuse: 5
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 245490
% 92.43/92.84 Kept: 55551
% 92.43/92.84 Inuse: 793
% 92.43/92.84 Deleted: 566
% 92.43/92.84 Deletedinuse: 5
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 253708
% 92.43/92.84 Kept: 57627
% 92.43/92.84 Inuse: 833
% 92.43/92.84 Deleted: 566
% 92.43/92.84 Deletedinuse: 5
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 263456
% 92.43/92.84 Kept: 59735
% 92.43/92.84 Inuse: 868
% 92.43/92.84 Deleted: 566
% 92.43/92.84 Deletedinuse: 5
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying clauses:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 269675
% 92.43/92.84 Kept: 61752
% 92.43/92.84 Inuse: 882
% 92.43/92.84 Deleted: 1110
% 92.43/92.84 Deletedinuse: 5
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 278701
% 92.43/92.84 Kept: 63756
% 92.43/92.84 Inuse: 916
% 92.43/92.84 Deleted: 1113
% 92.43/92.84 Deletedinuse: 7
% 92.43/92.84
% 92.43/92.84 Resimplifying inuse:
% 92.43/92.84 Done
% 92.43/92.84
% 92.43/92.84 *** allocated 2919240 integers for termspace/termends
% 92.43/92.84
% 92.43/92.84 Intermediate Status:
% 92.43/92.84 Generated: 283705
% 92.43/92.84 Kept: 65992
% 92.43/92.84 Inuse: 967
% 184.71/185.15 Deleted: 1115
% 184.71/185.15 Deletedinuse: 9
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 *** allocated 4378860 integers for clauses
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 289527
% 184.71/185.15 Kept: 68084
% 184.71/185.15 Inuse: 1017
% 184.71/185.15 Deleted: 1121
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 297951
% 184.71/185.15 Kept: 70297
% 184.71/185.15 Inuse: 1047
% 184.71/185.15 Deleted: 1121
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 305783
% 184.71/185.15 Kept: 72601
% 184.71/185.15 Inuse: 1062
% 184.71/185.15 Deleted: 1121
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 317276
% 184.71/185.15 Kept: 75724
% 184.71/185.15 Inuse: 1092
% 184.71/185.15 Deleted: 1121
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 325290
% 184.71/185.15 Kept: 77756
% 184.71/185.15 Inuse: 1102
% 184.71/185.15 Deleted: 1121
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 336716
% 184.71/185.15 Kept: 80708
% 184.71/185.15 Inuse: 1122
% 184.71/185.15 Deleted: 1121
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying clauses:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 347192
% 184.71/185.15 Kept: 82961
% 184.71/185.15 Inuse: 1157
% 184.71/185.15 Deleted: 1445
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 373716
% 184.71/185.15 Kept: 85952
% 184.71/185.15 Inuse: 1167
% 184.71/185.15 Deleted: 1445
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 409326
% 184.71/185.15 Kept: 90169
% 184.71/185.15 Inuse: 1177
% 184.71/185.15 Deleted: 1445
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 421587
% 184.71/185.15 Kept: 92197
% 184.71/185.15 Inuse: 1187
% 184.71/185.15 Deleted: 1445
% 184.71/185.15 Deletedinuse: 15
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 432216
% 184.71/185.15 Kept: 94313
% 184.71/185.15 Inuse: 1212
% 184.71/185.15 Deleted: 1446
% 184.71/185.15 Deletedinuse: 16
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 *** allocated 4378860 integers for termspace/termends
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 445345
% 184.71/185.15 Kept: 96701
% 184.71/185.15 Inuse: 1222
% 184.71/185.15 Deleted: 1450
% 184.71/185.15 Deletedinuse: 20
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 454760
% 184.71/185.15 Kept: 98760
% 184.71/185.15 Inuse: 1242
% 184.71/185.15 Deleted: 1451
% 184.71/185.15 Deletedinuse: 21
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 *** allocated 6568290 integers for clauses
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 467434
% 184.71/185.15 Kept: 101737
% 184.71/185.15 Inuse: 1262
% 184.71/185.15 Deleted: 1451
% 184.71/185.15 Deletedinuse: 21
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying clauses:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 476527
% 184.71/185.15 Kept: 103916
% 184.71/185.15 Inuse: 1272
% 184.71/185.15 Deleted: 1675
% 184.71/185.15 Deletedinuse: 21
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 488902
% 184.71/185.15 Kept: 107367
% 184.71/185.15 Inuse: 1311
% 184.71/185.15 Deleted: 1675
% 184.71/185.15 Deletedinuse: 21
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 503805
% 184.71/185.15 Kept: 109496
% 184.71/185.15 Inuse: 1327
% 184.71/185.15 Deleted: 1675
% 184.71/185.15 Deletedinuse: 21
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 517660
% 184.71/185.15 Kept: 112715
% 184.71/185.15 Inuse: 1352
% 184.71/185.15 Deleted: 1675
% 184.71/185.15 Deletedinuse: 21
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 527404
% 184.71/185.15 Kept: 114730
% 184.71/185.15 Inuse: 1364
% 184.71/185.15 Deleted: 1675
% 184.71/185.15 Deletedinuse: 21
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 538361
% 184.71/185.15 Kept: 116876
% 184.71/185.15 Inuse: 1406
% 184.71/185.15 Deleted: 1677
% 184.71/185.15 Deletedinuse: 22
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 544495
% 184.71/185.15 Kept: 119086
% 184.71/185.15 Inuse: 1421
% 184.71/185.15 Deleted: 1677
% 184.71/185.15 Deletedinuse: 22
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 549931
% 184.71/185.15 Kept: 121092
% 184.71/185.15 Inuse: 1433
% 184.71/185.15 Deleted: 1677
% 184.71/185.15 Deletedinuse: 22
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 184.71/185.15 Generated: 563261
% 184.71/185.15 Kept: 123857
% 184.71/185.15 Inuse: 1441
% 184.71/185.15 Deleted: 1677
% 184.71/185.15 Deletedinuse: 22
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying clauses:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15 Resimplifying inuse:
% 184.71/185.15 Done
% 184.71/185.15
% 184.71/185.15
% 184.71/185.15 Intermediate Status:
% 287.93/288.41 Generated: 573279
% 287.93/288.41 Kept: 125927
% 287.93/288.41 Inuse: 1451
% 287.93/288.41 Deleted: 2367
% 287.93/288.41 Deletedinuse: 22
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 584443
% 287.93/288.41 Kept: 128775
% 287.93/288.41 Inuse: 1466
% 287.93/288.41 Deleted: 2367
% 287.93/288.41 Deletedinuse: 22
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 *** allocated 6568290 integers for termspace/termends
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 596468
% 287.93/288.41 Kept: 134903
% 287.93/288.41 Inuse: 1476
% 287.93/288.41 Deleted: 2367
% 287.93/288.41 Deletedinuse: 22
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 609311
% 287.93/288.41 Kept: 141107
% 287.93/288.41 Inuse: 1491
% 287.93/288.41 Deleted: 2367
% 287.93/288.41 Deletedinuse: 22
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 617407
% 287.93/288.41 Kept: 143129
% 287.93/288.41 Inuse: 1516
% 287.93/288.41 Deleted: 2369
% 287.93/288.41 Deletedinuse: 24
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 630620
% 287.93/288.41 Kept: 145227
% 287.93/288.41 Inuse: 1531
% 287.93/288.41 Deleted: 2369
% 287.93/288.41 Deletedinuse: 24
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying clauses:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 642597
% 287.93/288.41 Kept: 147349
% 287.93/288.41 Inuse: 1566
% 287.93/288.41 Deleted: 2864
% 287.93/288.41 Deletedinuse: 25
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 651347
% 287.93/288.41 Kept: 149458
% 287.93/288.41 Inuse: 1596
% 287.93/288.41 Deleted: 2864
% 287.93/288.41 Deletedinuse: 25
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 *** allocated 9852435 integers for clauses
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 667115
% 287.93/288.41 Kept: 153525
% 287.93/288.41 Inuse: 1625
% 287.93/288.41 Deleted: 2868
% 287.93/288.41 Deletedinuse: 28
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 678685
% 287.93/288.41 Kept: 159228
% 287.93/288.41 Inuse: 1630
% 287.93/288.41 Deleted: 2868
% 287.93/288.41 Deletedinuse: 28
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 684225
% 287.93/288.41 Kept: 161294
% 287.93/288.41 Inuse: 1635
% 287.93/288.41 Deleted: 2870
% 287.93/288.41 Deletedinuse: 30
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 695241
% 287.93/288.41 Kept: 167445
% 287.93/288.41 Inuse: 1640
% 287.93/288.41 Deleted: 2870
% 287.93/288.41 Deletedinuse: 30
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying clauses:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 704411
% 287.93/288.41 Kept: 169513
% 287.93/288.41 Inuse: 1670
% 287.93/288.41 Deleted: 4298
% 287.93/288.41 Deletedinuse: 46
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 712358
% 287.93/288.41 Kept: 171529
% 287.93/288.41 Inuse: 1699
% 287.93/288.41 Deleted: 4298
% 287.93/288.41 Deletedinuse: 46
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 721181
% 287.93/288.41 Kept: 173798
% 287.93/288.41 Inuse: 1715
% 287.93/288.41 Deleted: 4298
% 287.93/288.41 Deletedinuse: 46
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 727218
% 287.93/288.41 Kept: 176102
% 287.93/288.41 Inuse: 1730
% 287.93/288.41 Deleted: 4298
% 287.93/288.41 Deletedinuse: 46
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 744749
% 287.93/288.41 Kept: 180205
% 287.93/288.41 Inuse: 1761
% 287.93/288.41 Deleted: 4302
% 287.93/288.41 Deletedinuse: 46
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 755423
% 287.93/288.41 Kept: 182461
% 287.93/288.41 Inuse: 1776
% 287.93/288.41 Deleted: 4302
% 287.93/288.41 Deletedinuse: 46
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 768096
% 287.93/288.41 Kept: 184480
% 287.93/288.41 Inuse: 1794
% 287.93/288.41 Deleted: 4305
% 287.93/288.41 Deletedinuse: 47
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 781540
% 287.93/288.41 Kept: 186587
% 287.93/288.41 Inuse: 1809
% 287.93/288.41 Deleted: 4305
% 287.93/288.41 Deletedinuse: 47
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying clauses:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 799767
% 287.93/288.41 Kept: 188608
% 287.93/288.41 Inuse: 1820
% 287.93/288.41 Deleted: 17507
% 287.93/288.41 Deletedinuse: 47
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 808233
% 287.93/288.41 Kept: 190961
% 287.93/288.41 Inuse: 1839
% 287.93/288.41 Deleted: 17507
% 287.93/288.41 Deletedinuse: 47
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 814329
% 287.93/288.41 Kept: 192983
% 287.93/288.41 Inuse: 1868
% 287.93/288.41 Deleted: 17507
% 287.93/288.41 Deletedinuse: 47
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41 Resimplifying inuse:
% 287.93/288.41 Done
% 287.93/288.41
% 287.93/288.41
% 287.93/288.41 Intermediate Status:
% 287.93/288.41 Generated: 819725
% 287.93/288.41 Kept: 195062
% 287.93/288.41 Inuse: 1894
% 287.93/288.41 Deleted: 17507
% 287.93/288.41 Deletedinuse: 47
% 287.93/288.41
% 287.93/288.41 ResimpliCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------