TSTP Solution File: SWW284+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW284+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 23:21:49 EDT 2022
% Result : Timeout 300.05s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW284+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sat Jun 4 12:18:22 EDT 2022
% 0.21/0.35 % CPUTime :
% 1.28/1.63 *** allocated 10000 integers for termspace/termends
% 1.28/1.63 *** allocated 10000 integers for clauses
% 1.28/1.63 *** allocated 10000 integers for justifications
% 1.28/1.63 *** allocated 15000 integers for termspace/termends
% 1.28/1.63 *** allocated 22500 integers for termspace/termends
% 1.28/1.63 *** allocated 33750 integers for termspace/termends
% 1.28/1.63 Bliksem 1.12
% 1.28/1.63
% 1.28/1.63
% 1.28/1.63 Automatic Strategy Selection
% 1.28/1.63
% 1.28/1.63 *** allocated 50625 integers for termspace/termends
% 1.28/1.63 *** allocated 75937 integers for termspace/termends
% 1.28/1.63 *** allocated 113905 integers for termspace/termends
% 1.28/1.63
% 1.28/1.63 Clauses:
% 1.28/1.63
% 1.28/1.63 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.28/1.63 { v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.28/1.63 tc_Complex_Ocomplex ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.28/1.63 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.28/1.63 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.28/1.63 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.28/1.63 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.28/1.63 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.28/1.63 { c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 1.28/1.63 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 1.28/1.63 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol2( X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.28/1.63 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.28/1.63 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.28/1.63 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.28/1.63 X, T ) = hAPP( X, U ) }.
% 1.28/1.63 { ! hAPP( X, skol3( X ) ) = hAPP( X, skol20( X ) ),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), !
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.28/1.63 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.28/1.63 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.28/1.63 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.28/1.63 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.63 , Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.28/1.63 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.28/1.63 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.28/1.63 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.28/1.63 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol4( X
% 1.28/1.63 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol4( X, Y, Z ) ), Z = Y
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.28/1.63 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.28/1.63 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.28/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.28/1.63 , Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.28/1.63 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.28/1.63 c_Polynomial_Ocoeff( X, Y ) }.
% 1.28/1.63 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.28/1.63 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.28/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.28/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.28/1.63 c_Polynomial_OpCons( X, T,
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 T, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 T, Y ) }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Y, Z ), T = Y }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Y, Z ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.28/1.63 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 T, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 T, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Y, T ), Z = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.28/1.63 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.28/1.63 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) = Z }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.28/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.28/1.63 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.28/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.28/1.63 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.28/1.63 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 1.28/1.63 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.28/1.63 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.28/1.63 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.28/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( tc_Nat_Onat ) ) = X }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ), X ) = X }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.28/1.63 ) ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.28/1.63 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.28/1.63 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.28/1.63 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.28/1.63 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.28/1.63 { ! X = c_Nat_OSuc( X ) }.
% 1.28/1.63 { ! c_Nat_OSuc( X ) = X }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.28/1.63 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.28/1.63 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 1.28/1.63 }.
% 1.28/1.63 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.28/1.63 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.28/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.28/1.63 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.63 ), ! U = T }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.63 ), ! Z = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.28/1.63 ) ), Z ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.63 ), U = Z, T = Y }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.28/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.28/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.28/1.63 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha1( X, Y ), alpha25( X
% 1.28/1.63 , Y ) }.
% 1.28/1.63 { ! alpha1( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! alpha25( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! alpha25( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! alpha25( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha25( X, Y ) }.
% 1.28/1.63 { ! alpha1( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 1.28/1.63 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha2( X, Y ), alpha26
% 1.28/1.63 ( X, Y ) }.
% 1.28/1.63 { ! alpha2( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.28/1.63 { ! alpha26( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.63 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.28/1.63 { ! alpha26( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! alpha26( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha26( X, Y ) }.
% 1.28/1.63 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.28/1.63 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.28/1.63 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.28/1.63 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.63 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.28/1.63 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.63 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.28/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.28/1.63 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.28/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.28/1.63 Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.28/1.63 ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.28/1.63 , Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.63 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.63 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.63 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.28/1.63 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.28/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.28/1.63 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.28/1.63 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.28/1.63 ) ), T ), Y ) }.
% 1.28/1.63 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.28/1.63 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.28/1.63 .
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.28/1.63 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.28/1.63 .
% 1.28/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.28/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.28/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.63 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.28/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.28/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.28/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.28/1.63 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.28/1.63 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 1.28/1.63 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 1.28/1.63 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.28/1.63 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 1.28/1.63 c_Polynomial_Odegree( X, Y ) ) }.
% 1.28/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 1.28/1.63 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.63 ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.28/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.28/1.63 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.28/1.63 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.63 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.28/1.63 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.28/1.63 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.28/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.28/1.63 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.28/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.28/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.28/1.63 ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.28/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.28/1.63 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.63 , Y ), X ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.28/1.63 tc_Nat_Onat ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.28/1.63 tc_Nat_Onat ) }.
% 1.28/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.28/1.63 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.63 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.28/1.63 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.28/1.63 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.28/1.63 ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.28/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.28/1.63 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.28/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.63 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.63 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.63 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.63 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.63 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.63 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.63 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.28/1.63 c_Polynomial_Odegree( X, Y ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.63 = Y }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ) }.
% 1.28/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.63 , Y ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 = Y }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.28/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.63 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.63 ( X, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.63 ) ), Y ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.63 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.28/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.63 ( X, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.28/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.63 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.28/1.63 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 Z, Y ) ) = Y }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.63 Y ) ) = Y }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.28/1.63 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.28/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.63 = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.63 = Y }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.63 = Y }.
% 1.28/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.63 = Y }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.63 = Y }.
% 1.28/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.63 = Y }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.28/1.63 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.28/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.28/1.63 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.28/1.63 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 1.28/1.63 c_Polynomial_Odegree( X, Z ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.28/1.63 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 1.28/1.63 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.63 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( X, Y ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 Z ) = Y }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.64 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.64 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.64 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.28/1.64 c_Polynomial_Odegree( X, Y ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.64 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.64 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.64 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.28/1.64 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.28/1.64 c_Polynomial_Odegree( X, Z ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.28/1.64 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.28/1.64 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( X, Z ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.64 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.28/1.64 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.64 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.28/1.64 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.28/1.64 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.28/1.64 X, Z ), Y ) ) }.
% 1.28/1.64 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) ) = Y }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.28/1.64 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.28/1.64 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.64 Z, T ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.64 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.64 , Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.64 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.28/1.64 , Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.64 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.28/1.64 X, T, Z ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.28/1.64 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.28/1.64 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.64 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.64 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.28/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.28/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.28/1.64 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.64 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.28/1.64 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.28/1.64 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.64 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.28/1.64 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha3( X
% 1.28/1.64 , Y, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha27( X
% 1.28/1.64 , Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! alpha3( X, Y, T ), ! alpha27( X, Y, Z, T )
% 1.28/1.64 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.28/1.64 ( X, T, Z ), Y ) }.
% 1.28/1.64 { ! alpha27( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.64 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha27( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha27( X
% 1.28/1.64 , Y, Z, T ) }.
% 1.28/1.64 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha3( X
% 1.28/1.64 , Y, Z ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.28/1.64 Y ) ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.28/1.64 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.64 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.28/1.64 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.28/1.64 Y ) ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.28/1.64 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.28/1.64 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.64 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.64 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.28/1.64 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.28/1.64 hAPP( Z, skol5( U, W, Z ) ) ) }.
% 1.28/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.28/1.64 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol5( X
% 1.28/1.64 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.28/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.28/1.64 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol21( X,
% 1.28/1.64 Y, Z ) ) ) ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.64 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.64 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.28/1.64 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.28/1.64 , Z ), X ) ), T ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, U, T ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.28/1.64 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Int_Oint, Y, X ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.28/1.64 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.28/1.64 ) ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.64 X ) ) }.
% 1.28/1.64 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.64 = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.28/1.64 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.28/1.64 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) ) = Y }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.64 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.64 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.64 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ), alpha58( X, Y, Z, T ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ), alpha58( X, Y, Z, T ), ! hAPP(
% 1.28/1.64 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.28/1.64 .
% 1.28/1.64 { ! alpha58( X, Y, Z, T ), alpha60( X, Y, Z, T ), alpha55( X, Y, T ) }.
% 1.28/1.64 { ! alpha58( X, Y, Z, T ), alpha60( X, Y, Z, T ), ! hAPP(
% 1.28/1.64 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! alpha60( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha55( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.28/1.64 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 alpha58( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha60( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), Z, T ), alpha61( X, Y, Z, T ) }.
% 1.28/1.64 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha60( X, Y
% 1.28/1.64 , Z, T ) }.
% 1.28/1.64 { ! alpha61( X, Y, Z, T ), alpha60( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha61( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.28/1.64 ), skol6( X, Y, U, W ), Y ) }.
% 1.28/1.64 { ! alpha61( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.28/1.64 ), skol6( X, Y, U, T ), T ) }.
% 1.28/1.64 { ! alpha61( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), skol6( X, Y, Z, T ), Z ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha61( X, Y
% 1.28/1.64 , Z, T ) }.
% 1.28/1.64 { ! alpha55( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! alpha55( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha55( X, Y, Z
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.28/1.64 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.28/1.64 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Int_Oint, Z, X ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.64 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.28/1.64 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ),
% 1.28/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( X, X,
% 1.28/1.64 c_Polynomial_Opoly( X, Y ) ), ! skol7( X, Z ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Oidom( X ),
% 1.28/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( X, X,
% 1.28/1.64 c_Polynomial_Opoly( X, Y ) ), alpha56( X, Y, skol7( X, Y ) ) }.
% 1.28/1.64 { ! alpha56( X, Y, Z ), ! skol8( T, U, W ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) }.
% 1.28/1.64 { ! alpha56( X, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, skol22( X, Y, Z ) )
% 1.28/1.64 , skol8( X, Y, Z ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.28/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) }.
% 1.28/1.64 { ! alpha56( X, Y, Z ), hAPP( c_Polynomial_Opoly( X, Y ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, Y ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), skol8( X, Y, Z ) ) ), hAPP(
% 1.28/1.64 c_Polynomial_Opoly( X, c_Polynomial_OpCons( X, Z, skol22( X, Y, Z ) ) ),
% 1.28/1.64 T ) ) ) }.
% 1.28/1.64 { T = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, U ), T
% 1.28/1.64 ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.28/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ), ! hAPP(
% 1.28/1.64 c_Polynomial_Opoly( X, Y ), skol24( X, Y, Z, T, U ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, Y ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), skol24( X, Y, Z, T, U ) ), T ) ), hAPP
% 1.28/1.64 ( c_Polynomial_Opoly( X, c_Polynomial_OpCons( X, Z, U ) ), skol24( X, Y,
% 1.28/1.64 Z, T, U ) ) ) ), alpha56( X, Y, Z ) }.
% 1.28/1.64 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.28/1.64 .
% 1.28/1.64 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha4( X, Y ), Y = X }
% 1.28/1.64 .
% 1.28/1.64 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! alpha4( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), alpha4( X, Y ) }.
% 1.28/1.64 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! alpha5( X, Y ), ! Y = X }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha5( X, Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! alpha5( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), alpha5( X, Y ) }.
% 1.28/1.64 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.64 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.64 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.28/1.64 , Z ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.28/1.64 Z, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), X ) = X }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ) ) = X }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.28/1.64 , Y ) ) = Y }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.28/1.64 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.64 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.28/1.64 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.28/1.64 ( tc_Int_Oint ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.28/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.28/1.64 X, Y ) ) = Y }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.28/1.64 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.28/1.64 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.64 = Y }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.28/1.64 ) ), Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.64 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.28/1.64 ) ), Z ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.28/1.64 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.28/1.64 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.28/1.64 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, Z, X ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.28/1.64 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.28/1.64 ) }.
% 1.28/1.64 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.64 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.28/1.64 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.28/1.64 = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.28/1.64 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.28/1.64 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.28/1.64 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.64 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.64 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, Y ), skol9( Z, Y ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.28/1.64 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = T, T =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.28/1.64 ), X ), T ) ) }.
% 1.28/1.64 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol9( X, Y ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), !
% 1.28/1.64 c_Polynomial_Odegree( tc_Complex_Ocomplex, Y ) = Z, Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Polynomial_Opoly( tc_Complex_Ocomplex ), Y, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( tc_Complex_Ocomplex )
% 1.28/1.64 ), X ), Z ) ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.28/1.64 ( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.28/1.64 X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.64 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.64 , T ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , T, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , Y, T ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , T, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.64 , Y, Z ) ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.28/1.64 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.28/1.64 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( X, Y ), Z ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( X, Z ), Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.28/1.64 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.28/1.64 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.28/1.64 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.28/1.64 X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.28/1.64 .
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.28/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.28/1.64 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.28/1.64 , X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.28/1.64 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.28/1.64 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.28/1.64 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.28/1.64 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.28/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.28/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.28/1.64 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.28/1.64 { alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.28/1.64 ( X, Y ), Z ) ) }.
% 1.28/1.64 { ! alpha57( X, Y, Z ), alpha59( X, Y, Z ), Z = Y }.
% 1.28/1.64 { ! alpha57( X, Y, Z ), alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! alpha59( X, Y, Z ), alpha57( X, Y, Z ) }.
% 1.28/1.64 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha57( X, Y, Z ) }.
% 1.28/1.64 { ! alpha59( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.28/1.64 X, Y ), Z ) ), alpha59( X, Y, Z ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.28/1.64 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.28/1.64 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.28/1.64 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.28/1.64 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.28/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, Z ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.64 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.64 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.64 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.64 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.28/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.28/1.64 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Z, X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.28/1.64 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.28/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.64 , alpha6( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.64 , alpha28( X, Y, Z ) }.
% 1.28/1.64 { ! alpha6( X, Y, Z ), ! alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.64 { ! alpha28( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.64 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, skol10( T, U, Z ) ) ), alpha28( X, Y, Z ) }.
% 1.28/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol10( X, Y, Z ) ),
% 1.28/1.64 alpha28( X, Y, Z ) }.
% 1.28/1.64 { ! alpha6( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.28/1.64 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha6( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha6
% 1.28/1.64 ( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.64 , ! alpha7( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.64 , ! alpha29( X, Y, Z ) }.
% 1.28/1.64 { alpha7( X, Y, Z ), alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.64 { ! alpha29( X, Y, Z ), ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ) }.
% 1.28/1.64 { ! alpha29( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.64 skol11( X, Y, Z ) ) }.
% 1.28/1.64 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.28/1.64 ) ), alpha29( X, Y, Z ) }.
% 1.28/1.64 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.28/1.64 .
% 1.28/1.64 { ! alpha7( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha7( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.28/1.64 ) ) = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( X, Z, W ) ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.64 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 X, W, Z ) ), U ), T ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.28/1.64 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.28/1.64 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.28/1.64 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.64 Z ) ), Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.64 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.64 W ) ), U ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ) }.
% 1.28/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.64 Z ) ), U ), T ) = Y }.
% 1.28/1.64 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.64 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), U ), Y ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.64 X, Y ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.28/1.64 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.28/1.64 X, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.64 X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.28/1.64 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.28/1.64 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.64 , Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 1.28/1.64 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha8( X, Y, Z, T ),
% 1.28/1.64 alpha30( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha30( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha30( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha8( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 1.28/1.64 alpha31( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z, T ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha31( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.28/1.64 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Y ) }.
% 1.28/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.64 , Y ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.28/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.28/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.28/1.64 , Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.28/1.64 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol12( X ) ) }.
% 1.28/1.64 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.64 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.64 c_Nat_OSuc( X ) ) }.
% 1.28/1.64 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol13( Z, Y ) ) }.
% 1.28/1.64 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol13( X
% 1.28/1.64 , Y ), X ) }.
% 1.28/1.64 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.28/1.64 ), alpha10( X, Y ) }.
% 1.28/1.64 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.28/1.64 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.28/1.64 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol14( X, Y ) ) ) }.
% 1.28/1.64 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.28/1.64 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.64 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.64 ), X ) ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.28/1.64 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.28/1.64 ), X ) ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.28/1.64 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.28/1.64 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.28/1.64 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.28/1.64 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.28/1.64 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.28/1.64 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.64 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.28/1.64 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.64 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.64 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.28/1.64 ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.64 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.28/1.64 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.28/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.28/1.64 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.64 ( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.28/1.64 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.28/1.64 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.64 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.28/1.64 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.28/1.64 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), Y ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.28/1.64 ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.64 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.28/1.64 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Int_Oint, Z, X ), Y ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Int_Oint, Z, Y ), X ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 1.28/1.64 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 1.28/1.64 ( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( tc_Int_Oint, Y ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.28/1.64 ( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.64 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 1.28/1.64 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 1.28/1.64 .
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 1.28/1.64 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 1.28/1.64 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.28/1.64 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.28/1.64 }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.64 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 1.28/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 1.28/1.64 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.64 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol15( X, Y ) ) }.
% 1.28/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.28/1.64 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, Y, X ), X ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 tc_Nat_Onat, Y, X ), X ) }.
% 1.28/1.64 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol16( X, Y ) ) }.
% 1.28/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.28/1.64 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.28/1.64 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.64 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 1.28/1.64 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Int_Oint, Y, X ), X ) }.
% 1.28/1.64 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.28/1.64 ( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.64 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.28/1.64 = X }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) ) }.
% 1.28/1.64 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Int_Oint ) ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.28/1.64 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.28/1.64 alpha11( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.28/1.64 alpha32( X, Y, Z ) }.
% 1.28/1.64 { ! alpha11( X, Y, Z ), ! alpha32( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.64 { ! alpha32( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 alpha45( X, Y, Z ) }.
% 1.28/1.64 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha32( X, Y, Z ) }.
% 1.28/1.64 { ! alpha45( X, Y, Z ), alpha32( X, Y, Z ) }.
% 1.28/1.64 { ! alpha45( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.28/1.64 ), alpha50( X, Y, Z, T ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( X, T, U ), X ),
% 1.28/1.64 alpha45( X, Y, Z ) }.
% 1.28/1.64 { ! alpha50( X, Y, Z, skol17( X, Y, Z ) ), alpha45( X, Y, Z ) }.
% 1.28/1.64 { ! alpha50( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.28/1.64 hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.64 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol18( X, Y, T ) ), T
% 1.28/1.64 ), alpha50( X, Y, Z, T ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, T ) ), alpha50( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha11( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.64 hBOOL( hAPP( Z, Y ) ) }.
% 1.28/1.64 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y, Z ) }.
% 1.28/1.64 { ! hBOOL( hAPP( Z, Y ) ), alpha11( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.64 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 1.28/1.64 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.64 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.28/1.64 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.28/1.64 X, Z, Y ) }.
% 1.28/1.64 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.64 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.28/1.64 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.28/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.28/1.64 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.28/1.64 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.28/1.64 ), Z ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.28/1.64 , Y ) ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.64 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, Z, Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, Y, Z ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 1.28/1.64 , Y ) ), Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.28/1.64 ), Z ), Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.28/1.64 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.28/1.64 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 T, Z ), Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 1.28/1.64 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.64 T, Y ), Z ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.28/1.64 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 1.28/1.64 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 1.28/1.64 ), Z ) }.
% 1.28/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.28/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 1.28/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 1.28/1.64 Y ) ), Y ) }.
% 1.28/1.64 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.28/1.64 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.28/1.64 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 1.28/1.64 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 1.28/1.64 , U ), Z ) }.
% 1.28/1.64 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.28/1.64 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.28/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.64 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 1.28/1.64 , Y ) ), Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 1.28/1.64 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.64 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.64 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 1.28/1.64 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 1.28/1.64 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.64 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.64 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.28/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.28/1.64 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.64 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 X ) }.
% 1.28/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 1.28/1.64 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.28/1.64 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.64 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.28/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 1.28/1.64 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 1.28/1.64 ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , alpha46( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.28/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha46( X, Y, Z, T ),
% 1.28/1.64 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.28/1.64 { ! alpha46( X, Y, Z, T ), alpha12( X, Z, T ) }.
% 1.28/1.64 { ! alpha46( X, Y, Z, T ), alpha33( X, Y, T ) }.
% 1.28/1.64 { ! alpha12( X, Z, T ), ! alpha33( X, Y, T ), alpha46( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha33( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), alpha47( X, Y, Z ) }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha33( X
% 1.28/1.64 , Y, Z ) }.
% 1.28/1.64 { ! alpha47( X, Y, Z ), alpha33( X, Y, Z ) }.
% 1.28/1.64 { ! alpha47( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.64 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha47( X
% 1.28/1.64 , Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.28/1.64 ), c_Polynomial_Odegree( X, Z ) ), alpha47( X, Y, Z ) }.
% 1.28/1.64 { ! alpha12( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X,
% 1.28/1.64 Y, Z ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X
% 1.28/1.64 , Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.28/1.64 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.64 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.64 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.28/1.64 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.28/1.64 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Y, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.28/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Y, Z ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.64 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ), alpha34( X,
% 1.28/1.64 Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), alpha34( X, Y, Z ) }.
% 1.28/1.64 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), alpha13( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha14( X, Y, Z ), alpha35
% 1.28/1.64 ( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 1.28/1.64 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 ), alpha35( X, Y, Z ) }.
% 1.28/1.64 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.64 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.64 ), alpha14( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.28/1.64 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha36( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha15( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha36( X, Y, Z, T ), !
% 1.28/1.64 alpha15( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.28/1.64 { ! alpha36( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.28/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha36( X, Y, Z, T ) }.
% 1.28/1.64 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha36(
% 1.28/1.64 X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha15( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha37( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha16( X, Y, T ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha37( X, Y, Z, T ), !
% 1.28/1.64 alpha16( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.64 { ! alpha37( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.28/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.28/1.64 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha37( X, Y, Z, T ) }.
% 1.28/1.64 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha37(
% 1.28/1.64 X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha16( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { Y = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 1.28/1.64 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.64 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.64 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.28/1.64 ( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.64 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.64 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.28/1.64 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.28/1.64 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.64 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.64 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.64 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.28/1.64 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.28/1.64 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.64 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.64 ), Y ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.64 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.64 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.64 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.28/1.64 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.64 }.
% 1.28/1.64 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.28/1.64 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.64 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.64 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 1.28/1.64 .
% 1.28/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.28/1.64 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 1.28/1.64 , Y ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 Z, Y ) ), alpha38( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.64 Z, Y ) ), alpha48( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 1.28/1.64 , T ), ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.64 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha51( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.64 , alpha48( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha51( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha51( X, Y, Z, T ), alpha53( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha51( X, Y, Z, T ), alpha17( X, Y, T ) }.
% 1.28/1.64 { ! alpha53( X, Y, Z, T ), ! alpha17( X, Y, T ), alpha51( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 alpha53( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha53( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha38( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.64 alpha38( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha38( X, Y, Z, T )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , alpha17( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , alpha17( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Z ), Y ), alpha39( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.64 Z ), Y ), alpha49( X, Y, Z, T ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 1.28/1.64 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.28/1.64 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), alpha52( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.64 , alpha49( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha52( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha52( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha52( X, Y, Z, T ), alpha18( X, Y, Z ) }.
% 1.28/1.64 { ! alpha54( X, Y, Z, T ), ! alpha18( X, Y, Z ), alpha52( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.64 alpha54( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha54( X, Y, Z, T )
% 1.28/1.64 }.
% 1.28/1.64 { ! alpha39( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.64 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.64 alpha39( X, Y, Z, T ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha39( X, Y, Z, T ) }.
% 1.28/1.64 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.64 , alpha18( X, Y, Z ) }.
% 1.28/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.64 , alpha18( X, Y, Z ) }.
% 1.28/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 Z, Y ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.65 Y ), Z ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.65 Y ), Z ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 Z, Y ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 Z, Y ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.65 Y ), Z ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.65 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.65 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.65 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.28/1.65 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.65 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.65 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.65 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.65 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.65 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.28/1.65 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.65 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.65 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 1.28/1.65 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 1.28/1.65 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 1.28/1.65 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 1.28/1.65 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.28/1.65 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.28/1.65 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 1.28/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.28/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.28/1.65 Y ) ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Y, Z ), T ) ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.65 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.65 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.65 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.65 alpha19( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.65 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! alpha19( X, Y, Z ),
% 1.28/1.65 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.28/1.65 { ! alpha19( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.65 alpha19( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.65 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.65 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.65 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 1.28/1.65 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.28/1.65 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 1.28/1.65 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( tc_Int_Oint, Y ), X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.65 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.28/1.65 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 1.28/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 1.28/1.65 , Z ) ) }.
% 1.28/1.65 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.28/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 1.28/1.65 , Z ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.28/1.65 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.28/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ) ) = X }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, X, Y ), X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Z, Y ), X ) }.
% 1.28/1.65 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.65 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.28/1.65 ( tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.28/1.65 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.28/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.28/1.65 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.28/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 1.28/1.65 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, Z, Y ) = T }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.28/1.65 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 1.28/1.65 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.28/1.65 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 1.28/1.65 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 1.28/1.65 , Z ) ) = Y }.
% 1.28/1.65 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.28/1.65 ), Y ) ) = Z }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 1.28/1.65 ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.28/1.65 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 1.28/1.65 ( X ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha20( X, Y, T,
% 1.28/1.65 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha20( X, Y, skol19( X, Y
% 1.28/1.65 , Z ), skol23( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.28/1.65 skol19( X, Y, Z ) ), skol23( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.28/1.65 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 1.28/1.65 ) }.
% 1.28/1.65 { ! alpha20( X, Y, Z, T ), alpha40( X, Y, Z, T ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha40( X, Y, Z
% 1.28/1.65 , T ), alpha20( X, Y, Z, T ) }.
% 1.28/1.65 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.65 { ! alpha40( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha40( X,
% 1.28/1.65 Y, Z, T ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Nat_Onat, Z, Y ), X ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.28/1.65 ( X ), T, Z ), Y ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.28/1.65 ( X ), Z, Y ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.28/1.65 ( X ), Z, Y ) ) }.
% 1.28/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.28/1.65 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.28/1.65 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.65 , Y, T ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.28/1.65 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.28/1.65 .
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.28/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha21( X, Y, Z ), alpha41
% 1.28/1.65 ( X, Y, Z ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha21( X, Y, Z
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.65 { ! alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), alpha41( X, Y, Z ) }.
% 1.28/1.65 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.65 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), alpha21( X, Y, Z ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.65 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ), alpha42
% 1.28/1.65 ( X, Y, Z ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha22( X, Y, Z
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.65 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha42( X, Y, Z
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.65 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! alpha42( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! alpha42( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ), Y ), alpha42( X, Y, Z ) }.
% 1.28/1.65 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.65 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.65 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.65 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.65 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha23( X, Y
% 1.28/1.65 , Z ), alpha43( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha43( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), alpha43( X, Y, Z ) }.
% 1.28/1.65 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.65 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), alpha23( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ), alpha24( X, Y, Z ), alpha44( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha24( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha44( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ), Y ), alpha44( X, Y, Z ) }.
% 1.28/1.65 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.65 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), alpha24( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Z, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Y, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.65 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.28/1.65 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ), Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.28/1.65 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.28/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.65 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.28/1.65 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 1.28/1.65 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 1.28/1.65 .
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.65 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.65 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.65 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.28/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.28/1.65 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.28/1.65 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.28/1.65 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 1.28/1.65 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.28/1.65 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.65 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.28/1.65 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.28/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.28/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.28/1.65 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.65 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.65 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.65 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.65 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.65 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.65 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.65 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.65 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.65 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.65 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.65 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.65 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.65 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.65 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.28/1.65 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.28/1.65 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.28/1.65 { class_Power_Opower( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.28/1.65 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.28/1.65 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.28/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.28/1.65 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ),
% 1.28/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.28/1.65 X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.65 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.65 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.65 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.28/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.28/1.65 ( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.28/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.65 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.28/1.65 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.28/1.65 { ! hBOOL( c_fFalse ) }.
% 1.28/1.65 { hBOOL( c_fTrue ) }.
% 1.28/1.65 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q ), X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.28/1.65 { ! v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.28/1.65 tc_Complex_Ocomplex ) ) }.
% 1.28/1.65
% 1.28/1.65 *** allocated 15000 integers for clauses
% 1.28/1.65 *** allocated 22500 integers for clauses
% 1.28/1.65 *** allocated 33750 integers for clauses
% 1.28/1.65 *** allocated 50625 integers for clauses
% 1.28/1.65 *** allocated 75937 integers for clauses
% 1.28/1.65 *** allocated 113905 integers for clauses
% 1.28/1.65 percentage equality = 0.321854, percentage horn = 0.879534
% 1.28/1.65 This is a problem with some equality
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Options Used:
% 1.28/1.65
% 1.28/1.65 useres = 1
% 1.28/1.65 useparamod = 1
% 1.28/1.65 useeqrefl = 1
% 1.28/1.65 useeqfact = 1
% 1.28/1.65 usefactor = 1
% 1.28/1.65 usesimpsplitting = 0
% 1.28/1.65 usesimpdemod = 5
% 1.28/1.65 usesimpres = 3
% 1.28/1.65
% 1.28/1.65 resimpinuse = 1000
% 1.28/1.65 resimpclauses = 20000
% 1.28/1.65 substype = eqrewr
% 1.28/1.65 backwardsubs = 1
% 1.28/1.65 selectoldest = 5
% 1.28/1.65
% 1.28/1.65 litorderings [0] = split
% 1.28/1.65 litorderings [1] = extend the termordering, first sorting on arguments
% 1.28/1.65
% 1.28/1.65 termordering = kbo
% 1.28/1.65
% 1.28/1.65 litapriori = 0
% 1.28/1.65 termapriori = 1
% 1.28/1.65 litaposteriori = 0
% 1.28/1.65 termaposteriori = 0
% 1.28/1.65 demodaposteriori = 0
% 1.28/1.65 ordereqreflfact = 0
% 1.28/1.65
% 1.28/1.65 litselect = negord
% 1.28/1.65
% 1.28/1.65 maxweight = 15
% 1.28/1.65 maxdepth = 30000
% 1.28/1.65 maxlength = 115
% 1.28/1.65 maxnrvars = 195
% 1.28/1.65 excuselevel = 1
% 1.28/1.65 increasemaxweight = 1
% 1.28/1.65
% 1.28/1.65 maxselected = 10000000
% 1.28/1.65 maxnrclauses = 10000000
% 1.28/1.65
% 1.28/1.65 showgenerated = 0
% 1.28/1.65 showkept = 0
% 1.28/1.65 showselected = 0
% 1.28/1.65 showdeleted = 0
% 1.28/1.65 showresimp = 1
% 1.28/1.65 showstatus = 2000
% 1.28/1.65
% 1.28/1.65 prologoutput = 0
% 1.28/1.65 nrgoals = 5000000
% 1.28/1.65 totalproof = 1
% 1.28/1.65
% 1.28/1.65 Symbols occurring in the translation:
% 1.28/1.65
% 1.28/1.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.28/1.65 . [1, 2] (w:1, o:185, a:1, s:1, b:0),
% 1.28/1.65 ! [4, 1] (w:0, o:103, a:1, s:1, b:0),
% 1.28/1.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.65 hAPP [38, 2] (w:1, o:209, a:1, s:1, b:0),
% 1.28/1.65 v_p [39, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.28/1.65 tc_Complex_Ocomplex [40, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.28/1.65 tc_Polynomial_Opoly [41, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Ocomm__semiring__0 [45, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Opoly [46, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.28/1.65 class_Int_Oring__char__0 [48, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oidom [49, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Oorder [52, 3] (w:1, o:237, a:1, s:1, b:0),
% 1.28/1.65 tc_Nat_Onat [53, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Ozero [55, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.28/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [57, 3] (w:1
% 1.28/1.65 , o:238, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Opoly__rec [61, 5] (w:1, o:321, a:1, s:1, b:0),
% 1.28/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [62, 3] (w:1, o:
% 1.28/1.65 239, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Omonom [65, 3] (w:1, o:240, a:1, s:1, b:0),
% 1.28/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [69, 2] (w:1, o:211
% 1.28/1.65 , a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_OpCons [70, 3] (w:1, o:241, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Opcompose [74, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Oplus__class_Oplus [75, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.28/1.65 c_fequal [76, 2] (w:1, o:212, a:1, s:1, b:0),
% 1.28/1.65 c_If [77, 4] (w:1, o:297, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Osynthetic__div [79, 3] (w:1, o:244, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Ocoeff [81, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Osmult [82, 3] (w:1, o:245, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oab__semigroup__add [86, 1] (w:1, o:124, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Groups_Ocomm__monoid__add [87, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.28/1.65
% 1.28/1.65 class_Groups_Ocancel__semigroup__add [89, 1] (w:1, o:126, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_Groups_Ocancel__ab__semigroup__add [90, 1] (w:1, o:127, a:1, s:
% 1.28/1.65 1, b:0),
% 1.28/1.65 class_Groups_Omonoid__add [92, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Olinordered__ab__group__add [93, 1] (w:1, o:128, a:1, s:
% 1.28/1.65 1, b:0),
% 1.28/1.65 class_Rings_Ocomm__semiring__1 [94, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.28/1.65 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [95
% 1.28/1.65 , 1] (w:1, o:161, a:1, s:1, b:0),
% 1.28/1.65 c_Nat_Onat_Onat__case [96, 3] (w:1, o:246, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Otimes__class_Otimes [97, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.28/1.65 c_Nat_OSuc [98, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oab__semigroup__mult [112, 1] (w:1, o:164, a:1, s:1, b:0
% 1.28/1.65 ),
% 1.28/1.65 class_Rings_Olinordered__ring__strict [118, 1] (w:1, o:131, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 class_RealVector_Oreal__normed__algebra [120, 1] (w:1, o:132, a:1, s:
% 1.28/1.65 1, b:0),
% 1.28/1.65 class_Rings_Ocomm__semiring [122, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Osemiring [126, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Ono__zero__divisors [127, 1] (w:1, o:146, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Rings_Omult__zero [128, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oring__no__zero__divisors [129, 1] (w:1, o:134, a:1, s:1
% 1.28/1.65 , b:0),
% 1.28/1.65 c_Polynomial_OAbs__poly [130, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.28/1.65 c_Nat_Onat_Onat__size [132, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Odegree [133, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.28/1.65 c_Nat_Osize__class_Osize [134, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Ocomm__ring__1 [138, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus [139, 2] (w:1, o:217, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 c_Groups_Oone__class_Oone [140, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oring__1__no__zero__divisors [141, 1] (w:1, o:135, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Groups_Oab__group__add [142, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Ocomm__ring [143, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Ogroup__add [144, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oone [145, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oring [146, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Ozero__neq__one [147, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Ocomm__monoid__mult [148, 1] (w:1, o:170, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Groups_Omonoid__mult [149, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.28/1.65 class_Fields_Ofield [150, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.28/1.65 c_Polynomial_Opoly__gcd [151, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.28/1.65 c_Rings_Odvd__class_Odvd [152, 3] (w:1, o:248, a:1, s:1, b:0),
% 1.28/1.65 c_Power_Opower__class_Opower [153, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.28/1.65 c_fTrue [154, 0] (w:1, o:85, a:1, s:1, b:0),
% 1.28/1.65 c_HOL_Obool_Obool__size [155, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.28/1.65 c_fFalse [156, 0] (w:1, o:86, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Odvd [157, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.28/1.65 tc_Int_Oint [158, 0] (w:1, o:87, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Oring__1 [159, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.28/1.65 class_Power_Opower [160, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.28/1.65 class_Rings_Osemiring__0 [161, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.28/1.65 hBOOL [164, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.28/1.65 c_Power_Opower_Opower [171, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.28/1.65 c_Rings_Oinverse__class_Oinverse [172, 2] (w:1, o:218, a:1, s:1, b:0)
% 1.28/1.65 ,
% 1.28/1.65 class_Rings_Odivision__ring__inverse__zero [175, 1] (w:1, o:150, a:1
% 1.28/1.65 , s:1, b:0),
% 1.28/1.65 class_Rings_Odivision__ring [176, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.28/1.65 class_Fields_Ofield__inverse__zero [179, 1] (w:1, o:120, a:1, s:1, b:
% 1.28/1.65 0),
% 1.28/1.65 c_Divides_Odiv__class_Omod [180, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.28/1.65 c_Groups_Ominus__class_Ominus [181, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.28/1.65 c_Orderings_Oord__class_Oless [182, 3] (w:1, o:235, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__ab__semigroup__add__imp__le [183, 1] (w:1, o:
% 1.28/1.65 176, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__cancel__ab__semigroup__add [184, 1] (w:1, o:
% 1.28/1.65 177, a:1, s:1, b:0),
% 1.28/1.65 class_Groups_Oordered__ab__group__add [185, 1] (w:1, o:178, a:1, s:1
% 1.80/2.16 , b:0),
% 1.80/2.16 class_Rings_Olinordered__idom [189, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.80/2.16 class_Rings_Oordered__ring [194, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.80/2.16 class_Rings_Olinordered__semidom [196, 1] (w:1, o:141, a:1, s:1, b:0)
% 1.80/2.16 ,
% 1.80/2.16 class_Rings_Olinordered__ring [197, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.80/2.16 class_Rings_Olinordered__semiring__strict [198, 1] (w:1, o:142, a:1
% 1.80/2.16 , s:1, b:0),
% 1.80/2.16 class_Rings_Olinordered__comm__semiring__strict [199, 1] (w:1, o:143
% 1.80/2.16 , a:1, s:1, b:0),
% 1.80/2.16 class_Groups_Oordered__comm__monoid__add [200, 1] (w:1, o:179, a:1
% 1.80/2.16 , s:1, b:0),
% 1.80/2.16 class_Fields_Olinordered__field__inverse__zero [201, 1] (w:1, o:121
% 1.80/2.16 , a:1, s:1, b:0),
% 1.80/2.16 class_Fields_Olinordered__field [202, 1] (w:1, o:122, a:1, s:1, b:0)
% 1.80/2.16 ,
% 1.80/2.16 class_Divides_Osemiring__div [206, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.80/2.16 class_Divides_Oring__div [209, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.80/2.16 c_Rings_Oinverse__class_Odivide [210, 3] (w:1, o:252, a:1, s:1, b:0)
% 1.80/2.16 ,
% 1.80/2.16 c_Polynomial_Opdivmod__rel [212, 5] (w:1, o:322, a:1, s:1, b:0),
% 1.80/2.16 class_RealVector_Oreal__normed__field [213, 1] (w:1, o:153, a:1, s:1
% 1.80/2.16 , b:0),
% 1.80/2.16 class_RealVector_Oreal__field [218, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.80/2.16 c_Polynomial_Opos__poly [221, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.80/2.16 c_Divides_Odiv__class_Odiv [222, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.80/2.16 c_Groups_Osgn__class_Osgn [223, 2] (w:1, o:220, a:1, s:1, b:0),
% 1.80/2.16 c_Orderings_Oord__class_Oless__eq [224, 3] (w:1, o:236, a:1, s:1, b:0
% 1.80/2.16 ),
% 1.80/2.16 class_Rings_Oordered__cancel__semiring [227, 1] (w:1, o:155, a:1, s:1
% 1.80/2.16 , b:0),
% 1.80/2.16 class_Rings_Oordered__semiring [228, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.80/2.16
% 1.80/2.16 class_Rings_Oordered__comm__semiring [229, 1] (w:1, o:157, a:1, s:1
% 1.80/2.16 , b:0),
% 1.80/2.16 class_Groups_Oordered__ab__semigroup__add [230, 1] (w:1, o:182, a:1
% 1.80/2.16 , s:1, b:0),
% 1.80/2.16 class_RealVector_Oreal__normed__vector [231, 1] (w:1, o:158, a:1, s:1
% 1.80/2.16 , b:0),
% 1.80/2.16 class_RealVector_Oreal__normed__algebra__1 [232, 1] (w:1, o:159, a:1
% 1.80/2.16 , s:1, b:0),
% 1.80/2.16 class_RealVector_Oreal__normed__div__algebra [233, 1] (w:1, o:160, a:
% 1.80/2.16 1, s:1, b:0),
% 1.80/2.16 class_Groups_Osgn__if [234, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.80/2.16 class_Rings_Olinordered__semiring [235, 1] (w:1, o:144, a:1, s:1, b:0
% 1.80/2.16 ),
% 1.80/2.16 class_Groups_Ocancel__comm__monoid__add [237, 1] (w:1, o:184, a:1, s:
% 1.80/2.16 1, b:0),
% 1.80/2.16 v_q [238, 0] (w:1, o:102, a:1, s:1, b:0),
% 1.80/2.16 alpha1 [239, 2] (w:1, o:221, a:1, s:1, b:1),
% 1.80/2.16 alpha2 [240, 2] (w:1, o:223, a:1, s:1, b:1),
% 1.80/2.16 alpha3 [241, 3] (w:1, o:260, a:1, s:1, b:1),
% 1.80/2.16 alpha4 [242, 2] (w:1, o:224, a:1, s:1, b:1),
% 1.80/2.16 alpha5 [243, 2] (w:1, o:225, a:1, s:1, b:1),
% 1.80/2.16 alpha6 [244, 3] (w:1, o:265, a:1, s:1, b:1),
% 1.80/2.16 alpha7 [245, 3] (w:1, o:266, a:1, s:1, b:1),
% 1.80/2.16 alpha8 [246, 4] (w:1, o:298, a:1, s:1, b:1),
% 1.80/2.16 alpha9 [247, 4] (w:1, o:299, a:1, s:1, b:1),
% 1.80/2.16 alpha10 [248, 2] (w:1, o:222, a:1, s:1, b:1),
% 1.80/2.16 alpha11 [249, 3] (w:1, o:267, a:1, s:1, b:1),
% 1.80/2.16 alpha12 [250, 3] (w:1, o:268, a:1, s:1, b:1),
% 1.80/2.16 alpha13 [251, 3] (w:1, o:269, a:1, s:1, b:1),
% 1.80/2.16 alpha14 [252, 3] (w:1, o:270, a:1, s:1, b:1),
% 1.80/2.16 alpha15 [253, 3] (w:1, o:271, a:1, s:1, b:1),
% 1.80/2.16 alpha16 [254, 3] (w:1, o:272, a:1, s:1, b:1),
% 1.80/2.16 alpha17 [255, 3] (w:1, o:273, a:1, s:1, b:1),
% 1.80/2.16 alpha18 [256, 3] (w:1, o:274, a:1, s:1, b:1),
% 1.80/2.16 alpha19 [257, 3] (w:1, o:275, a:1, s:1, b:1),
% 1.80/2.16 alpha20 [258, 4] (w:1, o:300, a:1, s:1, b:1),
% 1.80/2.16 alpha21 [259, 3] (w:1, o:254, a:1, s:1, b:1),
% 1.80/2.16 alpha22 [260, 3] (w:1, o:255, a:1, s:1, b:1),
% 1.80/2.16 alpha23 [261, 3] (w:1, o:256, a:1, s:1, b:1),
% 1.80/2.16 alpha24 [262, 3] (w:1, o:257, a:1, s:1, b:1),
% 1.80/2.16 alpha25 [263, 2] (w:1, o:226, a:1, s:1, b:1),
% 1.80/2.16 alpha26 [264, 2] (w:1, o:227, a:1, s:1, b:1),
% 1.80/2.16 alpha27 [265, 4] (w:1, o:301, a:1, s:1, b:1),
% 1.80/2.16 alpha28 [266, 3] (w:1, o:258, a:1, s:1, b:1),
% 1.80/2.16 alpha29 [267, 3] (w:1, o:259, a:1, s:1, b:1),
% 1.80/2.16 alpha30 [268, 4] (w:1, o:302, a:1, s:1, b:1),
% 1.80/2.16 alpha31 [269, 4] (w:1, o:303, a:1, s:1, b:1),
% 1.80/2.16 alpha32 [270, 3] (w:1, o:276, a:1, s:1, b:1),
% 15.16/15.55 alpha33 [271, 3] (w:1, o:277, a:1, s:1, b:1),
% 15.16/15.55 alpha34 [272, 3] (w:1, o:278, a:1, s:1, b:1),
% 15.16/15.55 alpha35 [273, 3] (w:1, o:279, a:1, s:1, b:1),
% 15.16/15.55 alpha36 [274, 4] (w:1, o:304, a:1, s:1, b:1),
% 15.16/15.55 alpha37 [275, 4] (w:1, o:305, a:1, s:1, b:1),
% 15.16/15.55 alpha38 [276, 4] (w:1, o:306, a:1, s:1, b:1),
% 15.16/15.55 alpha39 [277, 4] (w:1, o:307, a:1, s:1, b:1),
% 15.16/15.55 alpha40 [278, 4] (w:1, o:308, a:1, s:1, b:1),
% 15.16/15.55 alpha41 [279, 3] (w:1, o:280, a:1, s:1, b:1),
% 15.16/15.55 alpha42 [280, 3] (w:1, o:281, a:1, s:1, b:1),
% 15.16/15.55 alpha43 [281, 3] (w:1, o:282, a:1, s:1, b:1),
% 15.16/15.55 alpha44 [282, 3] (w:1, o:283, a:1, s:1, b:1),
% 15.16/15.55 alpha45 [283, 3] (w:1, o:284, a:1, s:1, b:1),
% 15.16/15.55 alpha46 [284, 4] (w:1, o:309, a:1, s:1, b:1),
% 15.16/15.55 alpha47 [285, 3] (w:1, o:285, a:1, s:1, b:1),
% 15.16/15.55 alpha48 [286, 4] (w:1, o:310, a:1, s:1, b:1),
% 15.16/15.55 alpha49 [287, 4] (w:1, o:311, a:1, s:1, b:1),
% 15.16/15.55 alpha50 [288, 4] (w:1, o:312, a:1, s:1, b:1),
% 15.16/15.55 alpha51 [289, 4] (w:1, o:313, a:1, s:1, b:1),
% 15.16/15.55 alpha52 [290, 4] (w:1, o:314, a:1, s:1, b:1),
% 15.16/15.55 alpha53 [291, 4] (w:1, o:315, a:1, s:1, b:1),
% 15.16/15.55 alpha54 [292, 4] (w:1, o:316, a:1, s:1, b:1),
% 15.16/15.55 alpha55 [293, 3] (w:1, o:261, a:1, s:1, b:1),
% 15.16/15.55 alpha56 [294, 3] (w:1, o:262, a:1, s:1, b:1),
% 15.16/15.55 alpha57 [295, 3] (w:1, o:263, a:1, s:1, b:1),
% 15.16/15.55 alpha58 [296, 4] (w:1, o:317, a:1, s:1, b:1),
% 15.16/15.55 alpha59 [297, 3] (w:1, o:264, a:1, s:1, b:1),
% 15.16/15.55 alpha60 [298, 4] (w:1, o:318, a:1, s:1, b:1),
% 15.16/15.55 alpha61 [299, 4] (w:1, o:319, a:1, s:1, b:1),
% 15.16/15.55 skol1 [300, 2] (w:1, o:228, a:1, s:1, b:1),
% 15.16/15.55 skol2 [301, 1] (w:1, o:109, a:1, s:1, b:1),
% 15.16/15.55 skol3 [302, 1] (w:1, o:111, a:1, s:1, b:1),
% 15.16/15.55 skol4 [303, 3] (w:1, o:286, a:1, s:1, b:1),
% 15.16/15.55 skol5 [304, 3] (w:1, o:287, a:1, s:1, b:1),
% 15.16/15.55 skol6 [305, 4] (w:1, o:320, a:1, s:1, b:1),
% 15.16/15.55 skol7 [306, 2] (w:1, o:229, a:1, s:1, b:1),
% 15.16/15.55 skol8 [307, 3] (w:1, o:288, a:1, s:1, b:1),
% 15.16/15.55 skol9 [308, 2] (w:1, o:230, a:1, s:1, b:1),
% 15.16/15.55 skol10 [309, 3] (w:1, o:289, a:1, s:1, b:1),
% 15.16/15.55 skol11 [310, 3] (w:1, o:290, a:1, s:1, b:1),
% 15.16/15.55 skol12 [311, 1] (w:1, o:108, a:1, s:1, b:1),
% 15.16/15.55 skol13 [312, 2] (w:1, o:231, a:1, s:1, b:1),
% 15.16/15.55 skol14 [313, 2] (w:1, o:232, a:1, s:1, b:1),
% 15.16/15.55 skol15 [314, 2] (w:1, o:233, a:1, s:1, b:1),
% 15.16/15.55 skol16 [315, 2] (w:1, o:234, a:1, s:1, b:1),
% 15.16/15.55 skol17 [316, 3] (w:1, o:291, a:1, s:1, b:1),
% 15.16/15.55 skol18 [317, 3] (w:1, o:292, a:1, s:1, b:1),
% 15.16/15.55 skol19 [318, 3] (w:1, o:293, a:1, s:1, b:1),
% 15.16/15.55 skol20 [319, 1] (w:1, o:110, a:1, s:1, b:1),
% 15.16/15.55 skol21 [320, 3] (w:1, o:294, a:1, s:1, b:1),
% 15.16/15.55 skol22 [321, 3] (w:1, o:295, a:1, s:1, b:1),
% 15.16/15.55 skol23 [322, 3] (w:1, o:296, a:1, s:1, b:1),
% 15.16/15.55 skol24 [323, 5] (w:1, o:323, a:1, s:1, b:1).
% 15.16/15.55
% 15.16/15.55
% 15.16/15.55 Starting Search:
% 15.16/15.55
% 15.16/15.55 *** allocated 170857 integers for clauses
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55
% 15.16/15.55 Intermediate Status:
% 15.16/15.55 Generated: 3031
% 15.16/15.55 Kept: 2006
% 15.16/15.55 Inuse: 34
% 15.16/15.55 Deleted: 2
% 15.16/15.55 Deletedinuse: 0
% 15.16/15.55
% 15.16/15.55 *** allocated 256285 integers for clauses
% 15.16/15.55 *** allocated 170857 integers for termspace/termends
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55 *** allocated 384427 integers for clauses
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55
% 15.16/15.55 Intermediate Status:
% 15.16/15.55 Generated: 7346
% 15.16/15.55 Kept: 4074
% 15.16/15.55 Inuse: 159
% 15.16/15.55 Deleted: 2
% 15.16/15.55 Deletedinuse: 0
% 15.16/15.55
% 15.16/15.55 *** allocated 256285 integers for termspace/termends
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55 *** allocated 576640 integers for clauses
% 15.16/15.55
% 15.16/15.55 Intermediate Status:
% 15.16/15.55 Generated: 14257
% 15.16/15.55 Kept: 6374
% 15.16/15.55 Inuse: 204
% 15.16/15.55 Deleted: 3
% 15.16/15.55 Deletedinuse: 1
% 15.16/15.55
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55 *** allocated 384427 integers for termspace/termends
% 15.16/15.55
% 15.16/15.55 Intermediate Status:
% 15.16/15.55 Generated: 21738
% 15.16/15.55 Kept: 8751
% 15.16/15.55 Inuse: 259
% 15.16/15.55 Deleted: 3
% 15.16/15.55 Deletedinuse: 1
% 15.16/15.55
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55 *** allocated 864960 integers for clauses
% 15.16/15.55
% 15.16/15.55 Intermediate Status:
% 15.16/15.55 Generated: 29217
% 15.16/15.55 Kept: 10918
% 15.16/15.55 Inuse: 289
% 15.16/15.55 Deleted: 3
% 15.16/15.55 Deletedinuse: 1
% 15.16/15.55
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55 Resimplifying inuse:
% 15.16/15.55 Done
% 15.16/15.55
% 15.16/15.55
% 15.16/15.55 Intermediate Status:
% 15.16/15.55 Generated: 34263
% 15.16/15.55 Kept: 12944
% 15.16/15.55 Inuse: 310
% 73.20/73.55 Deleted: 3
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 *** allocated 576640 integers for termspace/termends
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 40807
% 73.20/73.55 Kept: 15446
% 73.20/73.55 Inuse: 344
% 73.20/73.55 Deleted: 3
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 *** allocated 1297440 integers for clauses
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 46264
% 73.20/73.55 Kept: 17527
% 73.20/73.55 Inuse: 379
% 73.20/73.55 Deleted: 3
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 52587
% 73.20/73.55 Kept: 20226
% 73.20/73.55 Inuse: 409
% 73.20/73.55 Deleted: 3
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying clauses:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 *** allocated 864960 integers for termspace/termends
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 57120
% 73.20/73.55 Kept: 22290
% 73.20/73.55 Inuse: 434
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 60650
% 73.20/73.55 Kept: 24456
% 73.20/73.55 Inuse: 444
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 66762
% 73.20/73.55 Kept: 26466
% 73.20/73.55 Inuse: 465
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 *** allocated 1946160 integers for clauses
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 73249
% 73.20/73.55 Kept: 28492
% 73.20/73.55 Inuse: 486
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 81906
% 73.20/73.55 Kept: 31061
% 73.20/73.55 Inuse: 514
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 92725
% 73.20/73.55 Kept: 33074
% 73.20/73.55 Inuse: 556
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 *** allocated 1297440 integers for termspace/termends
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 112812
% 73.20/73.55 Kept: 35217
% 73.20/73.55 Inuse: 564
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 122264
% 73.20/73.55 Kept: 38056
% 73.20/73.55 Inuse: 584
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 *** allocated 2919240 integers for clauses
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 127458
% 73.20/73.55 Kept: 41074
% 73.20/73.55 Inuse: 594
% 73.20/73.55 Deleted: 154
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying clauses:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 131867
% 73.20/73.55 Kept: 43075
% 73.20/73.55 Inuse: 607
% 73.20/73.55 Deleted: 244
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 154917
% 73.20/73.55 Kept: 45783
% 73.20/73.55 Inuse: 624
% 73.20/73.55 Deleted: 244
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 164767
% 73.20/73.55 Kept: 48116
% 73.20/73.55 Inuse: 643
% 73.20/73.55 Deleted: 244
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 175287
% 73.20/73.55 Kept: 50421
% 73.20/73.55 Inuse: 689
% 73.20/73.55 Deleted: 244
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 *** allocated 1946160 integers for termspace/termends
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 183786
% 73.20/73.55 Kept: 52633
% 73.20/73.55 Inuse: 704
% 73.20/73.55 Deleted: 244
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 205042
% 73.20/73.55 Kept: 56046
% 73.20/73.55 Inuse: 734
% 73.20/73.55 Deleted: 244
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 225565
% 73.20/73.55 Kept: 58055
% 73.20/73.55 Inuse: 744
% 73.20/73.55 Deleted: 244
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 258543
% 73.20/73.55 Kept: 61296
% 73.20/73.55 Inuse: 754
% 73.20/73.55 Deleted: 244
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying clauses:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 *** allocated 4378860 integers for clauses
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 272145
% 73.20/73.55 Kept: 63538
% 73.20/73.55 Inuse: 779
% 73.20/73.55 Deleted: 521
% 73.20/73.55 Deletedinuse: 1
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55 Resimplifying inuse:
% 73.20/73.55 Done
% 73.20/73.55
% 73.20/73.55
% 73.20/73.55 Intermediate Status:
% 73.20/73.55 Generated: 281204
% 73.20/73.55 Kept: 65544
% 73.20/73.55 Inuse: 811
% 73.20/73.55 Deleted: 521
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 299245
% 154.77/155.10 Kept: 67925
% 154.77/155.10 Inuse: 824
% 154.77/155.10 Deleted: 521
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 309597
% 154.77/155.10 Kept: 70093
% 154.77/155.10 Inuse: 844
% 154.77/155.10 Deleted: 521
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 323831
% 154.77/155.10 Kept: 72307
% 154.77/155.10 Inuse: 874
% 154.77/155.10 Deleted: 521
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 *** allocated 2919240 integers for termspace/termends
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 328726
% 154.77/155.10 Kept: 74456
% 154.77/155.10 Inuse: 879
% 154.77/155.10 Deleted: 521
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 333609
% 154.77/155.10 Kept: 76607
% 154.77/155.10 Inuse: 884
% 154.77/155.10 Deleted: 521
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 350925
% 154.77/155.10 Kept: 79376
% 154.77/155.10 Inuse: 903
% 154.77/155.10 Deleted: 522
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying clauses:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 362064
% 154.77/155.10 Kept: 81447
% 154.77/155.10 Inuse: 933
% 154.77/155.10 Deleted: 585
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 376216
% 154.77/155.10 Kept: 84626
% 154.77/155.10 Inuse: 953
% 154.77/155.10 Deleted: 585
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 385680
% 154.77/155.10 Kept: 87347
% 154.77/155.10 Inuse: 963
% 154.77/155.10 Deleted: 585
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 395127
% 154.77/155.10 Kept: 90419
% 154.77/155.10 Inuse: 983
% 154.77/155.10 Deleted: 585
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 402161
% 154.77/155.10 Kept: 93284
% 154.77/155.10 Inuse: 993
% 154.77/155.10 Deleted: 585
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 *** allocated 6568290 integers for clauses
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 434597
% 154.77/155.10 Kept: 97542
% 154.77/155.10 Inuse: 1023
% 154.77/155.10 Deleted: 585
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 444597
% 154.77/155.10 Kept: 99580
% 154.77/155.10 Inuse: 1044
% 154.77/155.10 Deleted: 585
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying clauses:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 454461
% 154.77/155.10 Kept: 101809
% 154.77/155.10 Inuse: 1072
% 154.77/155.10 Deleted: 719
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 477075
% 154.77/155.10 Kept: 104701
% 154.77/155.10 Inuse: 1087
% 154.77/155.10 Deleted: 719
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 492966
% 154.77/155.10 Kept: 107553
% 154.77/155.10 Inuse: 1117
% 154.77/155.10 Deleted: 719
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 502719
% 154.77/155.10 Kept: 110183
% 154.77/155.10 Inuse: 1137
% 154.77/155.10 Deleted: 719
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 *** allocated 4378860 integers for termspace/termends
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 516347
% 154.77/155.10 Kept: 112337
% 154.77/155.10 Inuse: 1150
% 154.77/155.10 Deleted: 721
% 154.77/155.10 Deletedinuse: 1
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 524872
% 154.77/155.10 Kept: 114780
% 154.77/155.10 Inuse: 1152
% 154.77/155.10 Deleted: 730
% 154.77/155.10 Deletedinuse: 2
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 533267
% 154.77/155.10 Kept: 116816
% 154.77/155.10 Inuse: 1167
% 154.77/155.10 Deleted: 743
% 154.77/155.10 Deletedinuse: 2
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 545960
% 154.77/155.10 Kept: 119621
% 154.77/155.10 Inuse: 1174
% 154.77/155.10 Deleted: 743
% 154.77/155.10 Deletedinuse: 2
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 573076
% 154.77/155.10 Kept: 122276
% 154.77/155.10 Inuse: 1184
% 154.77/155.10 Deleted: 743
% 154.77/155.10 Deletedinuse: 2
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying clauses:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 585312
% 154.77/155.10 Kept: 124629
% 154.77/155.10 Inuse: 1204
% 154.77/155.10 Deleted: 1016
% 154.77/155.10 Deletedinuse: 2
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 595975
% 154.77/155.10 Kept: 126977
% 154.77/155.10 Inuse: 1214
% 154.77/155.10 Deleted: 1016
% 154.77/155.10 Deletedinuse: 2
% 154.77/155.10
% 154.77/155.10 Resimplifying inuse:
% 154.77/155.10 Done
% 154.77/155.10
% 154.77/155.10
% 154.77/155.10 Intermediate Status:
% 154.77/155.10 Generated: 603551
% 154.77/155.10 Kept: 129393
% 154.77/155.10 Inuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------