TSTP Solution File: SWW266+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW266+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 23:21:41 EDT 2022
% Result : Timeout 300.07s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW266+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sun Jun 5 01:37:02 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.02/1.63 *** allocated 10000 integers for termspace/termends
% 1.02/1.63 *** allocated 10000 integers for clauses
% 1.02/1.63 *** allocated 10000 integers for justifications
% 1.02/1.63 *** allocated 15000 integers for termspace/termends
% 1.02/1.63 *** allocated 22500 integers for termspace/termends
% 1.02/1.63 *** allocated 33750 integers for termspace/termends
% 1.02/1.63 Bliksem 1.12
% 1.02/1.63
% 1.02/1.63
% 1.02/1.63 Automatic Strategy Selection
% 1.02/1.63
% 1.02/1.63 *** allocated 50625 integers for termspace/termends
% 1.02/1.63 *** allocated 75937 integers for termspace/termends
% 1.02/1.63 *** allocated 113905 integers for termspace/termends
% 1.02/1.63
% 1.02/1.63 Clauses:
% 1.02/1.63
% 1.02/1.63 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.02/1.63 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.63 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.63 tc_Complex_Ocomplex, v_p ) ) }.
% 1.02/1.63 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_t____ ) }.
% 1.02/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_t____,
% 1.02/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.02/1.63 c_RealVector_Oof__real( tc_Complex_Ocomplex, Y ) ), X ) =
% 1.02/1.63 c_RealVector_Oof__real( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.63 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ) }.
% 1.02/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.63 }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 1.02/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) )
% 1.02/1.63 = hAPP( hAPP( c_Power_Opower__class_Opower( X ), c_RealVector_Oof__real(
% 1.02/1.63 X, Z ) ), Y ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.02/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.02/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.63 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), v_m____ ) }.
% 1.02/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.63 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.02/1.63 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.02/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.02/1.63 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.63 ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 1.02/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) )
% 1.02/1.63 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), c_RealVector_Oof__real
% 1.02/1.63 ( X, Z ) ), c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_m____ ) }.
% 1.02/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_t____ ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ), hAPP(
% 1.02/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ) ) }.
% 1.02/1.63 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.63 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.63 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 1.02/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.02/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.63 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.02/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.63 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.63 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Y
% 1.02/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.63 tc_RealDef_Oreal ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), ! Y =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 1.02/1.63 X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.63 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.02/1.63 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.63 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.63 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.63 .
% 1.02/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.63 tc_Nat_Onat ) }.
% 1.02/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.63 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.02/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.02/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.02/1.63 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.02/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.02/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.63 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.02/1.63 ( X ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.02/1.63 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.63 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.63 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.02/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.02/1.63 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.02/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.02/1.63 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.63 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.02/1.63 X, T ) = hAPP( X, U ) }.
% 1.02/1.63 { ! hAPP( X, skol2( X ) ) = hAPP( X, skol33( X ) ),
% 1.02/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.63 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.63 tc_RealDef_Oreal ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.63 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.02/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Z
% 1.02/1.63 ) = c_RealVector_Oof__real( X, Y ), Z = Y }.
% 1.02/1.63 { ! class_RealVector_Oreal__algebra__1( X ), ! Z = Y,
% 1.02/1.63 c_RealVector_Oof__real( X, Z ) = c_RealVector_Oof__real( X, Y ) }.
% 1.02/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.64 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.02/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.02/1.64 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.64 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_RealDef_Oreal ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.64 tc_RealDef_Oreal ), v_t____ ), v_k____ ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_t____ ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_t____
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.02/1.64 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.64 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol3 ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), skol3 ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4( Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol4( Y ),
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol4( X ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.02/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.02/1.64 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! v_a____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { ! v_w____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 1.02/1.64 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 1.02/1.64 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_t____ ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ),
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.64 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.64 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( tc_RealDef_Oreal ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.64 tc_RealDef_Oreal ), v_t____ ), v_k____ ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), v_t____ ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 1.02/1.64 ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, v_t____,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 1.02/1.64 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.64 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 1.02/1.64 c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 1.02/1.64 c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.02/1.64 ) ), T ), Y ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.02/1.64 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.64 ( X, Y ) ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.02/1.64 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.64 ), X ) ) }.
% 1.02/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.64 tc_Nat_Onat ) ) = Y }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.64 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.02/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.02/1.64 ), Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, Y, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.02/1.64 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.02/1.64 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.02/1.64 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.02/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.02/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.02/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.02/1.64 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ), alpha1( X, Y, Z ), alpha8( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ), Y ), alpha8( X, Y, Z ) }.
% 1.02/1.64 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.64 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 1.02/1.64 , Z ), alpha9( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha9( X, Y, Z ) }.
% 1.02/1.64 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.64 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha3( X, Y, Z, T ),
% 1.02/1.64 alpha10( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha10( X, Y, Z, T ) }.
% 1.02/1.64 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.64 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha3( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha4( X, Y, Z, T ),
% 1.02/1.64 alpha11( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha11( X, Y, Z, T ) }.
% 1.02/1.64 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.02/1.64 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha4( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.64 v_pa____ ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.64 ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.02/1.64 ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.02/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.64 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 1.02/1.64 ), v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 1.02/1.64 ) ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_k____ ) ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 1.02/1.64 v_k____ ) ), v_a____ ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.64 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ), v_k____ ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ) ) = Y }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.02/1.64 class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.64 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__div__algebra( X ), !
% 1.02/1.64 class_Rings_Odivision__ring__inverse__zero( X ), c_RealVector_Oof__real(
% 1.02/1.64 X, c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) =
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__div__algebra( X ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 1.02/1.64 X, c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) =
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 X, Y ) ) = Y }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 = Y }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.02/1.64 ) ), Y ) }.
% 1.02/1.64 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.64 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.64 ) ), Z ) }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.64 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.64 { alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.64 { alpha14( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.02/1.64 ( X, Y ), Z ) ) }.
% 1.02/1.64 { ! alpha14( X, Y, Z ), alpha16( X, Y, Z ), Z = Y }.
% 1.02/1.64 { ! alpha14( X, Y, Z ), alpha16( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! alpha16( X, Y, Z ), alpha14( X, Y, Z ) }.
% 1.02/1.64 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha14( X, Y, Z ) }.
% 1.02/1.64 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.02/1.64 }.
% 1.02/1.64 { ! alpha16( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.02/1.64 X, Y ), Z ) ), alpha16( X, Y, Z ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.02/1.64 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.02/1.64 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), !
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.02/1.64 .
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), X ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), X ) = X }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ) ) = X }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.64 .
% 1.02/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.02/1.64 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.64 .
% 1.02/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.02/1.64 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.64 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.02/1.64 .
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.02/1.64 , X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) }.
% 1.02/1.64 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.02/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.02/1.64 tc_Nat_Onat ) }.
% 1.02/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.02/1.64 tc_Nat_Onat ) }.
% 1.02/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.64 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.02/1.64 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.64 , Y ), X ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 Y ), X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.02/1.64 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7 ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol7,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol7,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, c_RealVector_Oof__real
% 1.02/1.64 ( tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.64 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ) ) ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.64 ) ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.64 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ) ) ) ) }.
% 1.02/1.64 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 1.02/1.64 ) ) ) = c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, c_RealVector_Oof__real
% 1.02/1.64 ( tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.64 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ) ) ) }.
% 1.02/1.64 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_k____ ) ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 1.02/1.64 v_k____ ) ), v_a____ ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.64 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ), v_k____ ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 1.02/1.64 = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.64 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ) ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 1.02/1.64 ) ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.64 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 1.02/1.64 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.64 tc_Complex_Ocomplex, v_pa____ ) ),
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 1.02/1.64 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol8( X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol9 ), v_k____ ) )
% 1.02/1.64 , v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.64 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.02/1.64 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.64 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.64 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.02/1.64 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.64 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.64 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 1.02/1.64 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 1.02/1.64 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.64 tc_Complex_Ocomplex, v_s____ ), v_k____ ), c_Groups_Oone__class_Oone(
% 1.02/1.64 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.64 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 1.02/1.64 c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.64 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 1.02/1.64 c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.64 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.64 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.64 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.64 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.64 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.64 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( X, Y, Z ) ) }.
% 1.02/1.64 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.64 Z ) ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.64 W ) ), U ), Y ) }.
% 1.02/1.64 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), U ), Y ) }.
% 1.02/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.64 Z ) ), U ), T ) = Y }.
% 1.02/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.64 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), U ), Y ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.64 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.64 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), U ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.02/1.64 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.64 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.64 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.64 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.64 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.64 ( X, Y ) ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.64 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.64 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( X, T, Y ) ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_a____,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ) ) )
% 1.02/1.64 ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_t____ ), v_k____ ) )
% 1.02/1.64 ), c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.64 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.64 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.64 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.64 v_t____ ) ), v_w____ ) ) ) ) ) ) }.
% 1.02/1.64 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.64 skol10 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.64 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.02/1.64 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol10 ), X ) = hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.02/1.64 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol11 ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 1.02/1.64 ), v_a____ ) ), c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.64 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 1.02/1.64 v_k____ ) ), v_a____ ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.64 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.02/1.64 ( tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y ) ), X ),
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.64 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 1.02/1.64 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.02/1.64 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.02/1.64 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.02/1.64 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.64 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.02/1.64 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.64 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.64 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.64 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 1.02/1.64 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.02/1.64 tc_Complex_Ocomplex, v_a____, v_s____ ) ), X ) ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.64 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.64 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.64 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.02/1.64 ( hAPP( c_Power_Opower__class_Opower( X ),
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 1.02/1.64 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.64 ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.02/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.64 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.64 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.64 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.64 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.64 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.64 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.64 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.64 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.64 ( X, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.64 ) ), Y ) }.
% 1.02/1.64 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.64 ( X, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 1.02/1.64 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.02/1.64 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.02/1.64 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.64 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.64 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.64 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.64 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.64 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.02/1.64 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.64 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.02/1.64 ( X, Z ) }.
% 1.02/1.64 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.64 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.64 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.64 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ) =
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.02/1.64 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.64 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.64 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.02/1.64 , Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.02/1.64 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring__abs( X ), alpha15( X, Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring__abs( X ), alpha15( X, Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.64 { ! alpha15( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! alpha15( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ), alpha15( X, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.64 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.02/1.64 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.02/1.64 , X ) }.
% 1.02/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.64 , alpha5( X, Y, Z ) }.
% 1.02/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.64 , alpha12( X, Y, Z ) }.
% 1.02/1.64 { ! alpha5( X, Y, Z ), ! alpha12( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.64 { ! alpha12( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.64 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.02/1.64 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha12( X, Y, Z ) }.
% 1.02/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol12( X, Y, Z ) ),
% 1.02/1.64 alpha12( X, Y, Z ) }.
% 1.02/1.64 { ! alpha5( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.02/1.64 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha5( X, Y, Z ) }.
% 1.02/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha5
% 1.02/1.64 ( X, Y, Z ) }.
% 1.02/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.64 , ! alpha6( X, Y, Z ) }.
% 1.02/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.64 , ! alpha13( X, Y, Z ) }.
% 1.02/1.64 { alpha6( X, Y, Z ), alpha13( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.64 { ! alpha13( X, Y, Z ), ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ) }.
% 1.02/1.64 { ! alpha13( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.64 skol13( X, Y, Z ) ) }.
% 1.02/1.64 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.02/1.64 ) ), alpha13( X, Y, Z ) }.
% 1.02/1.64 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.02/1.64 .
% 1.02/1.64 { ! alpha6( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Nat_Onat ) ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6( X, Y, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.64 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.64 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.02/1.64 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.64 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.02/1.64 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.02/1.64 ( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.64 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.02/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.02/1.64 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 1.02/1.64 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.02/1.64 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), skol14 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.02/1.64 }.
% 1.02/1.64 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.64 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.64 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.64 v_q____ ) ), skol15 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.64 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 1.02/1.64 skol34 ) }.
% 1.02/1.64 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.02/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.64 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.64 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.64 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.64 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.64 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.64 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.02/1.64 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 Y ) ) }.
% 1.02/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 1.02/1.64 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.64 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 1.02/1.64 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.64 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.02/1.64 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.02/1.64 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 1.02/1.64 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 1.02/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.02/1.64 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.02/1.64 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 1.02/1.64 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 1.02/1.64 , X ) ) ) ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.02/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.64 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.02/1.64 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.64 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.02/1.64 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.64 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.02/1.64 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.02/1.64 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.02/1.64 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y ) )
% 1.02/1.64 = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X, Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.64 ) ) = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X
% 1.02/1.64 , Y ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.64 , Y ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.02/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 1.02/1.64 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.64 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.64 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.64 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.64 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.64 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.64 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.65 tc_Complex_Ocomplex, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), c_Polynomial_Omonom(
% 1.02/1.65 tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.02/1.65 , v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.65 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Complex_Ocomplex ), c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____
% 1.02/1.65 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) }.
% 1.02/1.65 { c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.65 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.65 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.65 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.65 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.65 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.65 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.65 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.65 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.02/1.65 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.02/1.65 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.02/1.65 X, Z ), Y ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 1.02/1.65 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.02/1.65 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.02/1.65 c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), skol16 ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.02/1.65 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), T ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.02/1.65 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.02/1.65 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 1.02/1.65 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.65 Y ) ) ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.02/1.65 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 Y, T ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 T, Y ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 T, Y ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 Y, Z ), T = Y }.
% 1.02/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 Y, Z ) }.
% 1.02/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 T, Y ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 T, Y ) }.
% 1.02/1.65 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.65 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.65 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.65 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.65 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.65 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.65 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.65 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.65 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, T, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , Y, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , T, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , Y, T ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , T, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.65 , T ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.02/1.65 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( X ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.65 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ), Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 Z, Y ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 Y ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.65 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.02/1.65 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.02/1.65 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 Z, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 Y, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.65 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.65 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.65 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.65 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , Y, T ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.65 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 Z ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 X, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.65 X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.65 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.02/1.65 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.65 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.65 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.65 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.65 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.65 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 X, Y ) }.
% 1.02/1.65 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.02/1.65 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol17( X, Y ) ), Y
% 1.02/1.65 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.65 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Y ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.65 ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.65 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.02/1.65 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.65 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.65 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.02/1.65 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.02/1.65 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.02/1.65 , Y ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.65 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.65 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.65 ), ! U = T }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.65 ), ! Z = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.65 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.02/1.65 ) ), Z ) }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.65 ), U = Z, T = Y }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) ) = Y }.
% 1.02/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.65 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.65 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.65 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.65 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.65 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.65 class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18( Y ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.65 class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol18( X ) ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.65 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.02/1.65 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.02/1.65 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.02/1.65 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.02/1.65 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.65 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), X ) = X }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ) ) = X }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.02/1.65 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.02/1.65 }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.02/1.65 = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ) }.
% 1.02/1.65 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.02/1.65 }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.02/1.65 tc_Int_Oint, Y ) ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 1.02/1.65 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 1.02/1.65 tc_Int_Oint, X ) = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_Int_Oint ) ) ) }.
% 1.02/1.65 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.02/1.65 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.02/1.65 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.02/1.65 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.65 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 1.02/1.65 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Oii ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.65 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.02/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_Int_Oint ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.65 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.65 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.02/1.65 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.65 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.02/1.65 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.65 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), skol19 ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.65 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.65 hAPP( Y, U ) ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.65 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.02/1.65 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.65 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.65 hAPP( Y, U ) ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.65 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.65 hAPP( Y, U ) ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.02/1.65 ( Z, skol20( X, Y, Z ) ), hAPP( Y, skol20( X, Y, Z ) ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 Y ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), ! Z = Y }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 Z ), ! Z = Y }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , ! Z = Y }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , ! Z = Y }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , ! Y = Z }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.65 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.65 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , ! Z = Y }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.65 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.65 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.65 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.65 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.65 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.65 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.65 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.65 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.65 { ! skol21 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { ! skol35 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.65 tc_Complex_Ocomplex, skol38 ), skol35 ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.65 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.65 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.02/1.65 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.65 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.65 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.65 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.65 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 1.02/1.65 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.65 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.65 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.65 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.65 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), skol35 ) ),
% 1.02/1.65 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.02/1.65 tc_Complex_Ocomplex, skol21, skol38 ) ), X ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.02/1.65 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.02/1.65 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.02/1.65 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.65 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.02/1.65 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.02/1.65 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.02/1.65 Y ), c_RComplete_Onatceiling( X ) ) }.
% 1.02/1.65 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.02/1.65 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.65 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.65 }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 1.02/1.65 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.02/1.65 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.02/1.65 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.65 class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22( Y ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.65 class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol22( X ) ) )
% 1.02/1.65 }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, T, skol23( X, U, W, T ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.02/1.65 hAPP( Z, T ), hAPP( Z, skol23( X, Y, Z, T ) ) ) ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Y ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol24( X ) ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol25( X, Y ) ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( Z, T ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol26( X, Y ) ) ) }.
% 1.02/1.65 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.65 skol27 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.65 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.02/1.65 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol27 ), X ) = hAPP(
% 1.02/1.65 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.65 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 1.02/1.65 ), c_RComplete_Onatfloor( X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 1.02/1.65 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.02/1.65 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.02/1.65 tc_Int_Oint, X, Y ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.02/1.65 tc_Int_Oint, X, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.02/1.65 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.65 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 1.02/1.65 ( X, Y, Z ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.65 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 1.02/1.65 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.65 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.02/1.65 ( X ) ) }.
% 1.02/1.65 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.65 alpha7( X, Y, Z ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 1.02/1.65 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.65 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.65 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.65 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.02/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.65 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.65 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.02/1.65 ( tc_Nat_Onat, X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.65 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 1.02/1.65 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.65 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.02/1.65 Y = X }.
% 1.02/1.65 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.02/1.65 , X ) }.
% 1.02/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 1.02/1.65 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 1.02/1.65 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.02/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.02/1.65 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.65 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.65 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.02/1.65 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.02/1.65 , c_RComplete_Onatfloor( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 1.02/1.65 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_RComplete_Onatceiling( Y ), X ) }.
% 1.02/1.65 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.02/1.65 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.65 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.02/1.65 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_RealDef_Oreal ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.02/1.65 , X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.02/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.02/1.65 , c_RComplete_Onatfloor( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.65 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.02/1.65 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_RComplete_Onatceiling( X ), Y ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_RealDef_Oreal ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor(
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.65 c_RComplete_Onatfloor( X ), Y ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling(
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.65 c_RComplete_Onatceiling( X ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_RComplete_Onatfloor( X ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.02/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.02/1.65 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.02/1.65 c_RComplete_Onatfloor( X ) = Y }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.02/1.65 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.02/1.65 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol28( X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.02/1.65 tc_Nat_Onat, skol28( X ) ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.65 tc_Nat_Onat, skol29( X, Y ), skol36( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 hAPP( Y, skol36( X, Y ) ), hAPP( Y, skol29( X, Y ) ) ), c_SEQ_Odecseq( X
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( T, U, W ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, T, Z ) ), skol30( X,
% 1.02/1.65 Y, Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, hAPP(
% 1.02/1.65 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), T ), hAPP(
% 1.02/1.65 c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), Z ) ) ), X ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.02/1.65 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.02/1.65 hAPP( Z, Y ) ) }.
% 1.02/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.02/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ), Z = Y }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.02/1.65 { ! class_RealVector_Oreal__algebra__1( X ), !
% 1.02/1.65 class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, Y ) ), skol31( X ) ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 1.02/1.65 ( X ) ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.02/1.65 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, c_RealVector_Oof__real( X, Y ) ) =
% 1.02/1.65 c_RealVector_Oof__real( X, c_Groups_Osgn__class_Osgn( tc_RealDef_Oreal, Y
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.02/1.65 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.02/1.65 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.02/1.65 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.02/1.65 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.02/1.65 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.02/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.02/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_RealDef_Oreal ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.65 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_RealDef_Oreal ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.02/1.65 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.02/1.65 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.02/1.65 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.65 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.02/1.65 c_Polynomial_OpCons( X, T,
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.65 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.65 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.02/1.65 , Z, Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.65 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.65 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.65 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.02/1.65 hAPP( Z, skol32( U, W, Z ) ) ) }.
% 1.02/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.65 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol32( X
% 1.02/1.65 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.02/1.65 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.02/1.65 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol37( X,
% 1.02/1.65 Y, Z ) ) ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.65 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.65 Z, T ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.65 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.02/1.65 ( tc_fun( Y, X ) ) }.
% 1.02/1.65 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.02/1.65 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.02/1.65 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.02/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.65 tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.02/1.65 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.02/1.65 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.02/1.65 { class_Power_Opower( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.02/1.65 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.02/1.65 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.02/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.65 tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.02/1.65 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.02/1.65 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.02/1.65 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.02/1.65 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.02/1.65 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.02/1.65 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.02/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.65 tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.02/1.65 .
% 1.02/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_RealVector_Oreal__div__algebra( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_RealVector_Oreal__algebra__1( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Osgn__if( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 1.02/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.65 tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_RealVector_Oreal__div__algebra( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_RealVector_Oreal__algebra__1( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ),
% 1.02/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.02/1.65 X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.65 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.65 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.65 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.02/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.02/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.65 c_RealVector_Oof__real( tc_Complex_Ocomplex, v_t____ ) ), v_w____ ) ),
% 1.02/1.65 v_k____ ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.65 v_t____ ) ), v_w____ ) ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex
% 1.02/1.65 , v_s____ ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Complex_Ocomplex ), c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 1.02/1.65 v_t____ ) ), v_w____ ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.65 tc_RealDef_Oreal ), v_t____ ), v_k____ ) ) }.
% 1.02/1.65
% 1.02/1.65 *** allocated 15000 integers for clauses
% 1.02/1.65 *** allocated 22500 integers for clauses
% 1.02/1.65 *** allocated 33750 integers for clauses
% 1.02/1.65 *** allocated 50625 integers for clauses
% 1.02/1.65 *** allocated 75937 integers for clauses
% 1.02/1.65 *** allocated 113905 integers for clauses
% 1.02/1.65 percentage equality = 0.260757, percentage horn = 0.930079
% 1.02/1.65 This is a problem with some equality
% 1.02/1.65
% 1.02/1.65
% 1.02/1.65
% 1.02/1.65 Options Used:
% 1.02/1.65
% 1.02/1.65 useres = 1
% 1.02/1.65 useparamod = 1
% 1.02/1.65 useeqrefl = 1
% 1.02/1.65 useeqfact = 1
% 1.02/1.65 usefactor = 1
% 1.02/1.65 usesimpsplitting = 0
% 1.02/1.65 usesimpdemod = 5
% 1.02/1.65 usesimpres = 3
% 1.02/1.65
% 1.02/1.65 resimpinuse = 1000
% 1.02/1.65 resimpclauses = 20000
% 1.02/1.65 substype = eqrewr
% 1.02/1.65 backwardsubs = 1
% 1.02/1.65 selectoldest = 5
% 1.02/1.65
% 1.02/1.65 litorderings [0] = split
% 1.02/1.65 litorderings [1] = extend the termordering, first sorting on arguments
% 1.02/1.65
% 1.02/1.65 termordering = kbo
% 1.02/1.65
% 1.02/1.65 litapriori = 0
% 1.02/1.65 termapriori = 1
% 1.02/1.65 litaposteriori = 0
% 1.02/1.65 termaposteriori = 0
% 1.02/1.65 demodaposteriori = 0
% 1.02/1.65 ordereqreflfact = 0
% 1.02/1.65
% 1.02/1.65 litselect = negord
% 1.02/1.65
% 1.02/1.65 maxweight = 15
% 1.02/1.65 maxdepth = 30000
% 1.02/1.65 maxlength = 115
% 1.02/1.65 maxnrvars = 195
% 1.02/1.65 excuselevel = 1
% 1.02/1.65 increasemaxweight = 1
% 1.02/1.65
% 1.02/1.65 maxselected = 10000000
% 1.02/1.65 maxnrclauses = 10000000
% 1.02/1.65
% 1.02/1.65 showgenerated = 0
% 1.02/1.65 showkept = 0
% 1.02/1.65 showselected = 0
% 1.02/1.65 showdeleted = 0
% 1.02/1.65 showresimp = 1
% 1.02/1.65 showstatus = 2000
% 1.02/1.65
% 1.02/1.65 prologoutput = 0
% 1.02/1.65 nrgoals = 5000000
% 1.02/1.65 totalproof = 1
% 1.02/1.65
% 1.02/1.65 Symbols occurring in the translation:
% 1.02/1.65
% 1.02/1.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.02/1.65 . [1, 2] (w:1, o:223, a:1, s:1, b:0),
% 1.02/1.65 ! [4, 1] (w:0, o:126, a:1, s:1, b:0),
% 1.02/1.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.65 hAPP [38, 2] (w:1, o:247, a:1, s:1, b:0),
% 1.02/1.65 tc_Complex_Ocomplex [39, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.02/1.65 v_p [40, 0] (w:1, o:29, a:1, s:1, b:0),
% 1.02/1.65 c_Polynomial_Opoly [41, 2] (w:1, o:248, a:1, s:1, b:0),
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [42, 3] (w:1, o:
% 1.02/1.65 270, a:1, s:1, b:0),
% 1.02/1.65 v_k____ [43, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.02/1.65 tc_Nat_Onat [44, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.02/1.65 c_Groups_Ozero__class_Ozero [45, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.02/1.65 tc_RealDef_Oreal [46, 0] (w:1, o:32, a:1, s:1, b:0),
% 1.02/1.65 v_t____ [47, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.02/1.65 c_Orderings_Oord__class_Oless [48, 3] (w:1, o:271, a:1, s:1, b:0),
% 1.02/1.65 c_Groups_Oone__class_Oone [49, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.02/1.65 c_Power_Opower__class_Opower [52, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.02/1.65 c_RealVector_Oof__real [53, 2] (w:1, o:250, a:1, s:1, b:0),
% 1.02/1.65 c_Groups_Otimes__class_Otimes [54, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.02/1.65 v_w____ [55, 0] (w:1, o:48, a:1, s:1, b:0),
% 1.02/1.65 c_RealVector_Onorm__class_Onorm [56, 2] (w:1, o:249, a:1, s:1, b:0),
% 1.02/1.65
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq [57, 3] (w:1, o:272, a:1, s:1, b:0)
% 1.02/1.65 ,
% 1.02/1.65 class_RealVector_Oreal__algebra__1 [59, 1] (w:1, o:135, a:1, s:1, b:0
% 1.02/1.65 ),
% 1.02/1.65 class_RealVector_Oreal__normed__div__algebra [60, 1] (w:1, o:136, a:1
% 1.02/1.65 , s:1, b:0),
% 1.02/1.65 class_RealVector_Oreal__normed__algebra [64, 1] (w:1, o:137, a:1, s:1
% 1.02/1.65 , b:0),
% 1.02/1.65 v_s____ [66, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.02/1.65 v_m____ [67, 0] (w:1, o:67, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Ocomm__semiring__1 [69, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.02/1.65 tc_Polynomial_Opoly [70, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Ocomm__semiring__0 [72, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.02/1.65 class_Groups_Omonoid__mult [74, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.02/1.65 class_Groups_Ocomm__monoid__mult [76, 1] (w:1, o:158, a:1, s:1, b:0)
% 1.02/1.65 ,
% 1.02/1.65 v_pa____ [77, 0] (w:1, o:73, a:1, s:1, b:0),
% 1.02/1.65 class_RealVector_Oreal__normed__vector [78, 1] (w:1, o:159, a:1, s:1
% 1.02/1.65 , b:0),
% 1.02/1.65 class_RealVector_Oreal__normed__algebra__1 [79, 1] (w:1, o:160, a:1
% 1.02/1.65 , s:1, b:0),
% 1.02/1.65 class_Power_Opower [80, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Osemiring__0 [81, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Omult__zero [85, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Ono__zero__divisors [86, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.02/1.65
% 1.02/1.65 class_Rings_Ozero__neq__one [87, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Olinordered__semidom [88, 1] (w:1, o:173, a:1, s:1, b:0)
% 1.02/1.65 ,
% 1.02/1.65 class_Rings_Oring__1__no__zero__divisors [93, 1] (w:1, o:166, a:1, s:
% 1.02/1.65 1, b:0),
% 1.02/1.65 class_Int_Oring__char__0 [99, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Oidom [100, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.02/1.65 c_Groups_Oplus__class_Oplus [101, 3] (w:1, o:274, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Olinordered__idom [107, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Olinordered__semiring__strict [108, 1] (w:1, o:175, a:1
% 1.02/1.65 , s:1, b:0),
% 1.02/1.65 v_a____ [109, 0] (w:1, o:89, a:1, s:1, b:0),
% 1.02/1.65 v_c____ [110, 0] (w:1, o:90, a:1, s:1, b:0),
% 1.02/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [112, 2] (w:1, o:
% 1.02/1.65 251, a:1, s:1, b:0),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse [113, 2] (w:1, o:252, a:1, s:1, b:0)
% 1.02/1.65 ,
% 1.02/1.65 class_Rings_Ocomm__semiring [117, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Osemiring [119, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Olinordered__semiring__1 [127, 1] (w:1, o:176, a:1, s:1
% 1.02/1.65 , b:0),
% 1.02/1.65 class_Rings_Olinordered__semiring__1__strict [135, 1] (w:1, o:177, a:
% 1.02/1.65 1, s:1, b:0),
% 1.02/1.65 class_Rings_Oring__no__zero__divisors [136, 1] (w:1, o:167, a:1, s:1
% 1.02/1.65 , b:0),
% 1.02/1.65 class_Rings_Oordered__cancel__semiring [138, 1] (w:1, o:187, a:1, s:1
% 1.02/1.65 , b:0),
% 1.02/1.65 class_Rings_Oordered__ring [139, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Oordered__semiring [141, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.02/1.65
% 1.02/1.65 class_Rings_Oordered__comm__semiring [142, 1] (w:1, o:191, a:1, s:1
% 1.02/1.65 , b:0),
% 1.02/1.65 class_Rings_Olinordered__ring__strict [143, 1] (w:1, o:171, a:1, s:1
% 1.02/1.65 , b:0),
% 1.02/1.65 class_Rings_Olinordered__ring [144, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Olinordered__comm__semiring__strict [145, 1] (w:1, o:178
% 1.02/1.65 , a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Olinordered__semiring [146, 1] (w:1, o:179, a:1, s:1, b:0
% 1.02/1.65 ),
% 1.02/1.65 class_Rings_Odivision__ring__inverse__zero [147, 1] (w:1, o:192, a:1
% 1.02/1.65 , s:1, b:0),
% 1.02/1.65 class_RealVector_Oreal__div__algebra [148, 1] (w:1, o:193, a:1, s:1
% 1.02/1.65 , b:0),
% 1.02/1.65 class_Rings_Odivision__ring [149, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.02/1.65 class_Groups_Ocomm__monoid__add [150, 1] (w:1, o:195, a:1, s:1, b:0)
% 1.02/1.65 ,
% 1.02/1.65 hBOOL [153, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.02/1.65 class_Groups_Ozero [154, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.02/1.65 c_Groups_Ominus__class_Ominus [158, 3] (w:1, o:275, a:1, s:1, b:0),
% 1.02/1.65 v_q____ [159, 0] (w:1, o:111, a:1, s:1, b:0),
% 1.02/1.65 c_Polynomial_Osmult [160, 3] (w:1, o:276, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Ocomm__ring [161, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.02/1.65 class_Rings_Oring [162, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.62/2.01 class_Rings_Oring__1 [165, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.62/2.01 c_Groups_Oabs__class_Oabs [166, 2] (w:1, o:253, a:1, s:1, b:0),
% 1.62/2.01 c_Groups_Ouminus__class_Ouminus [168, 2] (w:1, o:254, a:1, s:1, b:0)
% 1.62/2.01 ,
% 1.62/2.01 c_Polynomial_OpCons [170, 3] (w:1, o:278, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Oab__group__add [171, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Ogroup__add [172, 1] (w:1, o:199, a:1, s:1, b:0),
% 1.62/2.01 class_Rings_Oordered__ring__abs [175, 1] (w:1, o:189, a:1, s:1, b:0)
% 1.62/2.01 ,
% 1.62/2.01 class_Fields_Olinordered__field__inverse__zero [178, 1] (w:1, o:152
% 1.62/2.01 , a:1, s:1, b:0),
% 1.62/2.01 class_Fields_Ofield__inverse__zero [180, 1] (w:1, o:153, a:1, s:1, b:
% 1.62/2.01 0),
% 1.62/2.01 class_Fields_Olinordered__field [181, 1] (w:1, o:154, a:1, s:1, b:0)
% 1.62/2.01 ,
% 1.62/2.01 class_Fields_Ofield [182, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.62/2.01 c_Polynomial_Omonom [184, 3] (w:1, o:279, a:1, s:1, b:0),
% 1.62/2.01 class_Rings_Ocomm__ring__1 [185, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Oordered__ab__group__add__abs [186, 1] (w:1, o:200, a:1
% 1.62/2.01 , s:1, b:0),
% 1.62/2.01 class_Groups_Oab__semigroup__mult [187, 1] (w:1, o:201, a:1, s:1, b:0
% 1.62/2.01 ),
% 1.62/2.01 class_Groups_Ocancel__semigroup__add [188, 1] (w:1, o:202, a:1, s:1
% 1.62/2.01 , b:0),
% 1.62/2.01 class_Groups_Ocancel__ab__semigroup__add [189, 1] (w:1, o:203, a:1
% 1.62/2.01 , s:1, b:0),
% 1.62/2.01 class_Groups_Oab__semigroup__add [190, 1] (w:1, o:204, a:1, s:1, b:0)
% 1.62/2.01 ,
% 1.62/2.01 class_Groups_Oone [191, 1] (w:1, o:205, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Omonoid__add [192, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Olinordered__ab__group__add [193, 1] (w:1, o:156, a:1
% 1.62/2.01 , s:1, b:0),
% 1.62/2.01 class_Groups_Oordered__ab__semigroup__add__imp__le [194, 1] (w:1, o:
% 1.62/2.01 207, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Oordered__ab__semigroup__add [195, 1] (w:1, o:208, a:1
% 1.62/2.01 , s:1, b:0),
% 1.62/2.01 class_Groups_Oordered__cancel__ab__semigroup__add [196, 1] (w:1, o:
% 1.62/2.01 209, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Oordered__ab__group__add [197, 1] (w:1, o:210, a:1, s:1
% 1.62/2.01 , b:0),
% 1.62/2.01 class_Groups_Oordered__comm__monoid__add [198, 1] (w:1, o:211, a:1
% 1.62/2.01 , s:1, b:0),
% 1.62/2.01 class_Groups_Oabs__if [199, 1] (w:1, o:212, a:1, s:1, b:0),
% 1.62/2.01 c_Polynomial_Osynthetic__div [200, 3] (w:1, o:280, a:1, s:1, b:0),
% 1.62/2.01 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.62/2.01 205, 1] (w:1, o:214, a:1, s:1, b:0),
% 1.62/2.01 c_Polynomial_Opcompose [206, 3] (w:1, o:281, a:1, s:1, b:0),
% 1.62/2.01 tc_Int_Oint [208, 0] (w:1, o:115, a:1, s:1, b:0),
% 1.62/2.01 c_Complex_Oii [209, 0] (w:1, o:116, a:1, s:1, b:0),
% 1.62/2.01 c_Polynomial_Oorder [210, 3] (w:1, o:277, a:1, s:1, b:0),
% 1.62/2.01 class_Orderings_Opreorder [215, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.62/2.01 class_Orderings_Olinorder [216, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.62/2.01 class_Orderings_Oord [217, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.62/2.01 tc_fun [218, 2] (w:1, o:263, a:1, s:1, b:0),
% 1.62/2.01 class_Orderings_Oorder [219, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.62/2.01 c_RComplete_Onatceiling [221, 1] (w:1, o:215, a:1, s:1, b:0),
% 1.62/2.01 c_Power_Opower_Opower [222, 3] (w:1, o:282, a:1, s:1, b:0),
% 1.62/2.01 c_RComplete_Onatfloor [228, 1] (w:1, o:216, a:1, s:1, b:0),
% 1.62/2.01 c_Nat__Transfer_Otsub [229, 2] (w:1, o:264, a:1, s:1, b:0),
% 1.62/2.01 c_RealDef_Oreal [230, 2] (w:1, o:265, a:1, s:1, b:0),
% 1.62/2.01 c_Polynomial_Opos__poly [231, 2] (w:1, o:266, a:1, s:1, b:0),
% 1.62/2.01 c_SEQ_Odecseq [232, 2] (w:1, o:267, a:1, s:1, b:0),
% 1.62/2.01 class_Lattices_Oboolean__algebra [233, 1] (w:1, o:218, a:1, s:1, b:0)
% 1.62/2.01 ,
% 1.62/2.01 class_Groups_Ominus [236, 1] (w:1, o:219, a:1, s:1, b:0),
% 1.62/2.01 class_Lattices_Oab__semigroup__idem__mult [237, 1] (w:1, o:217, a:1
% 1.62/2.01 , s:1, b:0),
% 1.62/2.01 class_Groups_Ouminus [238, 1] (w:1, o:220, a:1, s:1, b:0),
% 1.62/2.01 c_Groups_Osgn__class_Osgn [239, 2] (w:1, o:268, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Osgn__if [240, 1] (w:1, o:221, a:1, s:1, b:0),
% 1.62/2.01 c_Rings_Odvd__class_Odvd [241, 3] (w:1, o:283, a:1, s:1, b:0),
% 1.62/2.01 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [243, 3] (w:
% 1.62/2.01 1, o:273, a:1, s:1, b:0),
% 1.62/2.01 class_Rings_Odvd [246, 1] (w:1, o:213, a:1, s:1, b:0),
% 1.62/2.01 class_Groups_Ocancel__comm__monoid__add [249, 1] (w:1, o:222, a:1, s:
% 16.34/16.79 1, b:0),
% 16.34/16.79 tc_HOL_Obool [251, 0] (w:1, o:114, a:1, s:1, b:0),
% 16.34/16.79 alpha1 [252, 3] (w:1, o:284, a:1, s:1, b:1),
% 16.34/16.79 alpha2 [253, 3] (w:1, o:289, a:1, s:1, b:1),
% 16.34/16.79 alpha3 [254, 4] (w:1, o:301, a:1, s:1, b:1),
% 16.34/16.79 alpha4 [255, 4] (w:1, o:302, a:1, s:1, b:1),
% 16.34/16.79 alpha5 [256, 3] (w:1, o:290, a:1, s:1, b:1),
% 16.34/16.79 alpha6 [257, 3] (w:1, o:291, a:1, s:1, b:1),
% 16.34/16.79 alpha7 [258, 3] (w:1, o:292, a:1, s:1, b:1),
% 16.34/16.79 alpha8 [259, 3] (w:1, o:293, a:1, s:1, b:1),
% 16.34/16.79 alpha9 [260, 3] (w:1, o:294, a:1, s:1, b:1),
% 16.34/16.79 alpha10 [261, 4] (w:1, o:303, a:1, s:1, b:1),
% 16.34/16.79 alpha11 [262, 4] (w:1, o:304, a:1, s:1, b:1),
% 16.34/16.79 alpha12 [263, 3] (w:1, o:285, a:1, s:1, b:1),
% 16.34/16.79 alpha13 [264, 3] (w:1, o:286, a:1, s:1, b:1),
% 16.34/16.79 alpha14 [265, 3] (w:1, o:287, a:1, s:1, b:1),
% 16.34/16.79 alpha15 [266, 2] (w:1, o:269, a:1, s:1, b:1),
% 16.34/16.79 alpha16 [267, 3] (w:1, o:288, a:1, s:1, b:1),
% 16.34/16.79 skol1 [268, 2] (w:1, o:255, a:1, s:1, b:1),
% 16.34/16.79 skol2 [269, 1] (w:1, o:143, a:1, s:1, b:1),
% 16.34/16.79 skol3 [270, 0] (w:1, o:16, a:1, s:1, b:1),
% 16.34/16.79 skol4 [271, 1] (w:1, o:146, a:1, s:1, b:1),
% 16.34/16.79 skol5 [272, 2] (w:1, o:256, a:1, s:1, b:1),
% 16.34/16.79 skol6 [273, 2] (w:1, o:257, a:1, s:1, b:1),
% 16.34/16.79 skol7 [274, 0] (w:1, o:17, a:1, s:1, b:1),
% 16.34/16.79 skol8 [275, 1] (w:1, o:147, a:1, s:1, b:1),
% 16.34/16.79 skol9 [276, 0] (w:1, o:18, a:1, s:1, b:1),
% 16.34/16.79 skol10 [277, 0] (w:1, o:19, a:1, s:1, b:1),
% 16.34/16.79 skol11 [278, 0] (w:1, o:20, a:1, s:1, b:1),
% 16.34/16.79 skol12 [279, 3] (w:1, o:295, a:1, s:1, b:1),
% 16.34/16.79 skol13 [280, 3] (w:1, o:296, a:1, s:1, b:1),
% 16.34/16.79 skol14 [281, 0] (w:1, o:21, a:1, s:1, b:1),
% 16.34/16.79 skol15 [282, 0] (w:1, o:22, a:1, s:1, b:1),
% 16.34/16.79 skol16 [283, 0] (w:1, o:23, a:1, s:1, b:1),
% 16.34/16.79 skol17 [284, 2] (w:1, o:258, a:1, s:1, b:1),
% 16.34/16.79 skol18 [285, 1] (w:1, o:142, a:1, s:1, b:1),
% 16.34/16.79 skol19 [286, 0] (w:1, o:24, a:1, s:1, b:1),
% 16.34/16.79 skol20 [287, 3] (w:1, o:297, a:1, s:1, b:1),
% 16.34/16.79 skol21 [288, 0] (w:1, o:14, a:1, s:1, b:1),
% 16.34/16.79 skol22 [289, 1] (w:1, o:148, a:1, s:1, b:1),
% 16.34/16.79 skol23 [290, 4] (w:1, o:305, a:1, s:1, b:1),
% 16.34/16.79 skol24 [291, 1] (w:1, o:149, a:1, s:1, b:1),
% 16.34/16.79 skol25 [292, 2] (w:1, o:259, a:1, s:1, b:1),
% 16.34/16.79 skol26 [293, 2] (w:1, o:260, a:1, s:1, b:1),
% 16.34/16.79 skol27 [294, 0] (w:1, o:15, a:1, s:1, b:1),
% 16.34/16.79 skol28 [295, 1] (w:1, o:150, a:1, s:1, b:1),
% 16.34/16.79 skol29 [296, 2] (w:1, o:261, a:1, s:1, b:1),
% 16.34/16.79 skol30 [297, 3] (w:1, o:298, a:1, s:1, b:1),
% 16.34/16.79 skol31 [298, 1] (w:1, o:144, a:1, s:1, b:1),
% 16.34/16.79 skol32 [299, 3] (w:1, o:299, a:1, s:1, b:1),
% 16.34/16.79 skol33 [300, 1] (w:1, o:145, a:1, s:1, b:1),
% 16.34/16.79 skol34 [301, 0] (w:1, o:25, a:1, s:1, b:1),
% 16.34/16.79 skol35 [302, 0] (w:1, o:26, a:1, s:1, b:1),
% 16.34/16.79 skol36 [303, 2] (w:1, o:262, a:1, s:1, b:1),
% 16.34/16.79 skol37 [304, 3] (w:1, o:300, a:1, s:1, b:1),
% 16.34/16.79 skol38 [305, 0] (w:1, o:27, a:1, s:1, b:1).
% 16.34/16.79
% 16.34/16.79
% 16.34/16.79 Starting Search:
% 16.34/16.79
% 16.34/16.79 *** allocated 170857 integers for clauses
% 16.34/16.79 Resimplifying inuse:
% 16.34/16.79 Done
% 16.34/16.79
% 16.34/16.79
% 16.34/16.79 Intermediate Status:
% 16.34/16.79 Generated: 3001
% 16.34/16.79 Kept: 2003
% 16.34/16.79 Inuse: 61
% 16.34/16.79 Deleted: 0
% 16.34/16.79 Deletedinuse: 0
% 16.34/16.79
% 16.34/16.79 *** allocated 256285 integers for clauses
% 16.34/16.79 *** allocated 170857 integers for termspace/termends
% 16.34/16.79 Resimplifying inuse:
% 16.34/16.79 Done
% 16.34/16.79
% 16.34/16.79 *** allocated 384427 integers for clauses
% 16.34/16.79
% 16.34/16.79 Intermediate Status:
% 16.34/16.79 Generated: 6076
% 16.34/16.79 Kept: 4050
% 16.34/16.79 Inuse: 187
% 16.34/16.79 Deleted: 4
% 16.34/16.79 Deletedinuse: 0
% 16.34/16.79
% 16.34/16.79 Resimplifying inuse:
% 16.34/16.79 Done
% 16.34/16.79
% 16.34/16.79 *** allocated 256285 integers for termspace/termends
% 16.34/16.79 Resimplifying inuse:
% 16.34/16.79 Done
% 16.34/16.79
% 16.34/16.79
% 16.34/16.79 Intermediate Status:
% 16.34/16.79 Generated: 10446
% 16.34/16.79 Kept: 6198
% 16.34/16.79 Inuse: 261
% 16.34/16.79 Deleted: 5
% 16.34/16.79 Deletedinuse: 0
% 16.34/16.79
% 16.34/16.79 Resimplifying inuse:
% 16.34/16.79 Done
% 16.34/16.79
% 16.34/16.79 *** allocated 576640 integers for clauses
% 16.34/16.79 Resimplifying inuse:
% 16.34/16.79 Done
% 16.34/16.79
% 16.34/16.79 *** allocated 384427 integers for termspace/termends
% 16.34/16.79
% 16.34/16.79 Intermediate Status:
% 16.34/16.79 Generated: 16361
% 16.34/16.79 Kept: 8778
% 16.34/16.79 Inuse: 315
% 16.34/16.79 Deleted: 6
% 16.34/16.79 Deletedinuse: 0
% 16.34/16.79
% 16.34/16.79 Resimplifying inuse:
% 16.34/16.79 Done
% 16.34/16.79
% 16.34/16.79 Resimplifying inuse:
% 16.34/16.79 Done
% 16.34/16.79
% 16.34/16.79 *** allocated 864960 integers for clauses
% 16.34/16.79
% 16.34/16.79 Intermediate Status:
% 16.34/16.79 Generated: 23903
% 16.34/16.79 Kept: 11416
% 16.34/16.79 Inuse: 365
% 16.34/16.79 Deleted: 7
% 16.34/16.79 Deletedinuse: 1
% 16.34/16.79
% 16.34/16.79 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 *** allocated 576640 integers for termspace/termends
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 28631
% 83.75/84.17 Kept: 13468
% 83.75/84.17 Inuse: 413
% 83.75/84.17 Deleted: 9
% 83.75/84.17 Deletedinuse: 1
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 34213
% 83.75/84.17 Kept: 15704
% 83.75/84.17 Inuse: 475
% 83.75/84.17 Deleted: 14
% 83.75/84.17 Deletedinuse: 3
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 *** allocated 1297440 integers for clauses
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 41260
% 83.75/84.17 Kept: 18566
% 83.75/84.17 Inuse: 539
% 83.75/84.17 Deleted: 15
% 83.75/84.17 Deletedinuse: 3
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 *** allocated 864960 integers for termspace/termends
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying clauses:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 52216
% 83.75/84.17 Kept: 21808
% 83.75/84.17 Inuse: 593
% 83.75/84.17 Deleted: 428
% 83.75/84.17 Deletedinuse: 3
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 58964
% 83.75/84.17 Kept: 23819
% 83.75/84.17 Inuse: 614
% 83.75/84.17 Deleted: 430
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 *** allocated 1946160 integers for clauses
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 68859
% 83.75/84.17 Kept: 25825
% 83.75/84.17 Inuse: 641
% 83.75/84.17 Deleted: 430
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 77233
% 83.75/84.17 Kept: 27836
% 83.75/84.17 Inuse: 646
% 83.75/84.17 Deleted: 430
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 *** allocated 1297440 integers for termspace/termends
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 87503
% 83.75/84.17 Kept: 30223
% 83.75/84.17 Inuse: 658
% 83.75/84.17 Deleted: 430
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 93660
% 83.75/84.17 Kept: 33831
% 83.75/84.17 Inuse: 678
% 83.75/84.17 Deleted: 430
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 107923
% 83.75/84.17 Kept: 35984
% 83.75/84.17 Inuse: 688
% 83.75/84.17 Deleted: 430
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 128944
% 83.75/84.17 Kept: 39144
% 83.75/84.17 Inuse: 698
% 83.75/84.17 Deleted: 430
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying clauses:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 *** allocated 2919240 integers for clauses
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 139228
% 83.75/84.17 Kept: 41171
% 83.75/84.17 Inuse: 720
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 *** allocated 1946160 integers for termspace/termends
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 151090
% 83.75/84.17 Kept: 43399
% 83.75/84.17 Inuse: 748
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 157954
% 83.75/84.17 Kept: 45427
% 83.75/84.17 Inuse: 779
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 163149
% 83.75/84.17 Kept: 47559
% 83.75/84.17 Inuse: 828
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 168203
% 83.75/84.17 Kept: 49559
% 83.75/84.17 Inuse: 875
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 174099
% 83.75/84.17 Kept: 51612
% 83.75/84.17 Inuse: 923
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 180882
% 83.75/84.17 Kept: 53623
% 83.75/84.17 Inuse: 968
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 188821
% 83.75/84.17 Kept: 55738
% 83.75/84.17 Inuse: 998
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 197817
% 83.75/84.17 Kept: 58037
% 83.75/84.17 Inuse: 1028
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 205931
% 83.75/84.17 Kept: 60057
% 83.75/84.17 Inuse: 1064
% 83.75/84.17 Deleted: 662
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying clauses:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 83.75/84.17 Generated: 213179
% 83.75/84.17 Kept: 62084
% 83.75/84.17 Inuse: 1088
% 83.75/84.17 Deleted: 978
% 83.75/84.17 Deletedinuse: 5
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 Resimplifying inuse:
% 83.75/84.17 Done
% 83.75/84.17
% 83.75/84.17 *** allocated 4378860 integers for clauses
% 83.75/84.17
% 83.75/84.17 Intermediate Status:
% 226.51/226.93 Generated: 222331
% 226.51/226.93 Kept: 64136
% 226.51/226.93 Inuse: 1108
% 226.51/226.93 Deleted: 978
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 *** allocated 2919240 integers for termspace/termends
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 229667
% 226.51/226.93 Kept: 66149
% 226.51/226.93 Inuse: 1132
% 226.51/226.93 Deleted: 978
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 243098
% 226.51/226.93 Kept: 69664
% 226.51/226.93 Inuse: 1147
% 226.51/226.93 Deleted: 978
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 253955
% 226.51/226.93 Kept: 72828
% 226.51/226.93 Inuse: 1173
% 226.51/226.93 Deleted: 978
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 266648
% 226.51/226.93 Kept: 76400
% 226.51/226.93 Inuse: 1183
% 226.51/226.93 Deleted: 978
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 284510
% 226.51/226.93 Kept: 81363
% 226.51/226.93 Inuse: 1193
% 226.51/226.93 Deleted: 978
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying clauses:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 294823
% 226.51/226.93 Kept: 83838
% 226.51/226.93 Inuse: 1218
% 226.51/226.93 Deleted: 1337
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 302993
% 226.51/226.93 Kept: 85843
% 226.51/226.93 Inuse: 1230
% 226.51/226.93 Deleted: 1337
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 308921
% 226.51/226.93 Kept: 89409
% 226.51/226.93 Inuse: 1238
% 226.51/226.93 Deleted: 1337
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 315197
% 226.51/226.93 Kept: 92978
% 226.51/226.93 Inuse: 1248
% 226.51/226.93 Deleted: 1337
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 321413
% 226.51/226.93 Kept: 95612
% 226.51/226.93 Inuse: 1253
% 226.51/226.93 Deleted: 1337
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 *** allocated 4378860 integers for termspace/termends
% 226.51/226.93 *** allocated 6568290 integers for clauses
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 372143
% 226.51/226.93 Kept: 98600
% 226.51/226.93 Inuse: 1258
% 226.51/226.93 Deleted: 1337
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 403261
% 226.51/226.93 Kept: 103930
% 226.51/226.93 Inuse: 1303
% 226.51/226.93 Deleted: 1337
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying clauses:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 416728
% 226.51/226.93 Kept: 107365
% 226.51/226.93 Inuse: 1313
% 226.51/226.93 Deleted: 1405
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 431505
% 226.51/226.93 Kept: 111109
% 226.51/226.93 Inuse: 1323
% 226.51/226.93 Deleted: 1405
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 459468
% 226.51/226.93 Kept: 114916
% 226.51/226.93 Inuse: 1328
% 226.51/226.93 Deleted: 1405
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 467284
% 226.51/226.93 Kept: 116959
% 226.51/226.93 Inuse: 1333
% 226.51/226.93 Deleted: 1405
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 475263
% 226.51/226.93 Kept: 118990
% 226.51/226.93 Inuse: 1338
% 226.51/226.93 Deleted: 1405
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 483223
% 226.51/226.93 Kept: 121000
% 226.51/226.93 Inuse: 1346
% 226.51/226.93 Deleted: 1405
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 496191
% 226.51/226.93 Kept: 124280
% 226.51/226.93 Inuse: 1348
% 226.51/226.93 Deleted: 1405
% 226.51/226.93 Deletedinuse: 5
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying clauses:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 508613
% 226.51/226.93 Kept: 131224
% 226.51/226.93 Inuse: 1363
% 226.51/226.93 Deleted: 1553
% 226.51/226.93 Deletedinuse: 6
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 528317
% 226.51/226.93 Kept: 136424
% 226.51/226.93 Inuse: 1403
% 226.51/226.93 Deleted: 1553
% 226.51/226.93 Deletedinuse: 6
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 543718
% 226.51/226.93 Kept: 140333
% 226.51/226.93 Inuse: 1413
% 226.51/226.93 Deleted: 1553
% 226.51/226.93 Deletedinuse: 6
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 *** allocated 6568290 integers for termspace/termends
% 226.51/226.93
% 226.51/226.93 Intermediate Status:
% 226.51/226.93 Generated: 559194
% 226.51/226.93 Kept: 144043
% 226.51/226.93 Inuse: 1423
% 226.51/226.93 Deleted: 1553
% 226.51/226.93 Deletedinuse: 6
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying clauses:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 Resimplifying inuse:
% 226.51/226.93 Done
% 226.51/226.93
% 226.51/226.93 *** allocated 9852435 integers for clauses
% 226.51/226.93
% 226.51/226.93 Intermediate StatusCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------