TSTP Solution File: SWW183+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW183+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:05 EDT 2022
% Result : Timeout 300.07s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SWW183+1 : TPTP v8.1.0. Released v5.2.0.
% 0.13/0.15 % Command : bliksem %s
% 0.14/0.36 % Computer : n023.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sat Jun 4 16:04:55 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.45/1.79 *** allocated 10000 integers for termspace/termends
% 1.45/1.79 *** allocated 10000 integers for clauses
% 1.45/1.79 *** allocated 10000 integers for justifications
% 1.45/1.79 *** allocated 15000 integers for termspace/termends
% 1.45/1.79 *** allocated 22500 integers for termspace/termends
% 1.45/1.79 *** allocated 33750 integers for termspace/termends
% 1.45/1.79 Bliksem 1.12
% 1.45/1.79
% 1.45/1.79
% 1.45/1.79 Automatic Strategy Selection
% 1.45/1.79
% 1.45/1.79 *** allocated 50625 integers for termspace/termends
% 1.45/1.79 *** allocated 75937 integers for termspace/termends
% 1.45/1.79 *** allocated 113905 integers for termspace/termends
% 1.45/1.79
% 1.45/1.79 Clauses:
% 1.45/1.79
% 1.45/1.79 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.45/1.79 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.45/1.79 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.45/1.79 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.45/1.79 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.45/1.79 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.45/1.79 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.45/1.79 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.45/1.79 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 T, Y ), Z = Y }.
% 1.45/1.79 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 T, Y ) }.
% 1.45/1.79 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Y, Z ), T = Y }.
% 1.45/1.79 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Y, Z ) }.
% 1.45/1.79 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Y, T ), Z = Y }.
% 1.45/1.79 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 T, Y ), Z = Y }.
% 1.45/1.79 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 T, Y ), Z = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.45/1.79 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.45/1.79 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.45/1.79 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.45/1.79 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.45/1.79 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.45/1.79 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.45/1.79 c_Polynomial_OpCons( X, T,
% 1.45/1.79 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.45/1.79 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.45/1.79 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.45/1.79 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.45/1.79 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.45/1.79 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.45/1.79 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.45/1.79 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.45/1.79 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.45/1.79 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.45/1.79 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.45/1.79 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.45/1.79 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.45/1.79 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.45/1.79 , Y ) ) }.
% 1.45/1.79 { ! c_Groups_Osemigroup( Y, X ), hAPP( hAPP( X, hAPP( hAPP( X, U ), T ) ),
% 1.45/1.79 Z ) = hAPP( hAPP( X, U ), hAPP( hAPP( X, T ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.45/1.79 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol2( X
% 1.45/1.79 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol2( X, Y, Z ) ), Z = Y
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.45/1.79 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.45/1.79 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.45/1.79 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.45/1.79 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.45/1.79 c_Polynomial_Ocoeff( X, Y ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.45/1.79 ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.45/1.79 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.45/1.79 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.45/1.79 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.45/1.79 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.45/1.79 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.45/1.79 Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.45/1.79 , Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.45/1.79 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.45/1.79 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.45/1.79 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.45/1.79 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.45/1.79 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.45/1.79 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.45/1.79 ), ! U = T }.
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.45/1.79 ), ! Z = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.45/1.79 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.45/1.79 ) ), Z ) }.
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.45/1.79 ), U = Z, T = Y }.
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.45/1.79 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.45/1.79 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.45/1.79 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.45/1.79 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.45/1.79 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.45/1.79 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.45/1.79 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.45/1.79 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.45/1.79 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.45/1.79 ) ), T ), Y ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ) ) = Z }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.45/1.79 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), X ) = X }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ) ) = X }.
% 1.45/1.79 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.45/1.79 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.45/1.79 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.45/1.79 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.45/1.79 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.45/1.79 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha1
% 1.45/1.79 ( X, Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.45/1.79 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! alpha1( X, Y, Z ),
% 1.45/1.79 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.45/1.79 { ! alpha1( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.45/1.79 ( X ) ) }.
% 1.45/1.79 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.45/1.79 alpha1( X, Y, Z ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.45/1.79 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 1.45/1.79 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, Y, Z ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.45/1.79 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.45/1.79 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.79 Y ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Z ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.45/1.79 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.45/1.79 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.45/1.79 , X ) }.
% 1.45/1.79 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, T, Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , Y, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, Z, Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , T, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , Y, T ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , T, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.45/1.79 , T ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, Z, Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, Z, Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.79 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.45/1.79 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.79 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.79 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.45/1.79 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha2( X, Y, Z, T ),
% 1.45/1.79 alpha19( X, Y, Z, T ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.79 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha19( X, Y, Z, T ) }.
% 1.45/1.79 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.45/1.79 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.45/1.79 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha2( X, Y, Z, T ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha3( X, Y, Z, T ),
% 1.45/1.79 alpha20( X, Y, Z, T ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.79 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha20( X, Y, Z, T ) }.
% 1.45/1.79 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.45/1.79 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.45/1.79 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha3( X, Y, Z, T ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.79 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.45/1.79 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.45/1.79 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.45/1.79 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.45/1.79 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.45/1.79 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.45/1.79 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.45/1.79 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.45/1.79 .
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.79 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.45/1.79 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.45/1.79 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.45/1.79 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 1.45/1.79 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 1.45/1.79 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.45/1.79 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.45/1.79 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.45/1.79 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.45/1.79 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.45/1.79 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.45/1.79 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.45/1.79 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.45/1.79 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.45/1.79 X ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.45/1.79 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.45/1.79 ), X ) ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.45/1.79 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.79 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.45/1.79 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.79 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.45/1.79 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Nat_Onat ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Nat_Onat ) }.
% 1.45/1.79 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.45/1.79 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.45/1.79 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.45/1.79 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.45/1.79 , Y ), X ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.45/1.79 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { alpha41( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.45/1.79 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.45/1.79 { alpha41( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.45/1.79 ( X, Y ), Z ) ) }.
% 1.45/1.79 { ! alpha41( X, Y, Z ), alpha43( X, Y, Z ), Z = Y }.
% 1.45/1.79 { ! alpha41( X, Y, Z ), alpha43( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! alpha43( X, Y, Z ), alpha41( X, Y, Z ) }.
% 1.45/1.79 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha41( X, Y, Z ) }.
% 1.45/1.79 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.45/1.79 }.
% 1.45/1.79 { ! alpha43( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.45/1.79 X, Y ), Z ) ), alpha43( X, Y, Z ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.45/1.79 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.45/1.79 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.45/1.79 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.45/1.79 .
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.45/1.79 .
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.45/1.79 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.45/1.79 X ) ) }.
% 1.45/1.79 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.45/1.79 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.45/1.79 }.
% 1.45/1.79 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Nat_OSuc( X ) = X }.
% 1.45/1.79 { ! X = c_Nat_OSuc( X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.45/1.79 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.45/1.79 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.45/1.79 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.45/1.79 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.45/1.79 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.45/1.79 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.45/1.79 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.45/1.79 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Nat_Onat ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.45/1.79 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.45/1.79 c_Polynomial_Odegree( X, Y ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.45/1.79 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.45/1.79 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.45/1.79 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.45/1.79 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.45/1.79 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.45/1.79 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.45/1.79 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.45/1.79 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.45/1.79 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.45/1.79 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.45/1.79 = Y }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Y ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 = Y }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.45/1.79 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.45/1.79 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ), Z ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.45/1.79 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Z ), Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.79 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.79 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.45/1.79 ) ), Y ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.45/1.79 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.45/1.79 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.45/1.79 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.45/1.79 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.45/1.79 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.45/1.79 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Z, Y ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.45/1.79 Y ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.45/1.79 = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.45/1.79 = Y }.
% 1.45/1.79 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.45/1.79 = Y }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.45/1.79 = Y }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.45/1.79 = Y }.
% 1.45/1.79 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.45/1.79 = Y }.
% 1.45/1.79 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.45/1.79 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.45/1.79 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.45/1.79 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.45/1.79 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol3( X ) ) }.
% 1.45/1.79 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! alpha4( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.45/1.79 c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! alpha4( X, Y ), Y = c_Nat_OSuc( skol4( Z, Y ) ) }.
% 1.45/1.79 { ! alpha4( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol4( X, Y
% 1.45/1.79 ), X ) }.
% 1.45/1.79 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.45/1.79 ), alpha4( X, Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.45/1.79 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.45/1.79 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.45/1.79 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.45/1.79 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) ) }.
% 1.45/1.79 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.45/1.79 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.79 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.45/1.79 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.45/1.79 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.79 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.45/1.79 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.79 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.45/1.79 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.45/1.79 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.45/1.79 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.45/1.79 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.45/1.79 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.45/1.79 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.45/1.79 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.45/1.79 ( X ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.45/1.79 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , Y ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.45/1.79 , Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 1.45/1.79 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.79 Z ) = Y }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Z, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.45/1.79 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.45/1.79 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.45/1.79 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha5( X, Y ), alpha21
% 1.45/1.79 ( X, Y ) }.
% 1.45/1.79 { ! alpha5( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.45/1.79 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.45/1.79 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 1.45/1.79 { ! alpha5( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 1.45/1.79 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha6( X, Y ), alpha22( X
% 1.45/1.79 , Y ) }.
% 1.45/1.79 { ! alpha6( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.45/1.79 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! alpha22( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.45/1.79 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! alpha22( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 1.45/1.79 { ! alpha6( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! alpha6( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.45/1.79 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.45/1.79 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.45/1.79 c_Polynomial_Odegree( X, Y ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.45/1.79 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.45/1.79 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.45/1.79 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.45/1.79 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.45/1.79 c_Polynomial_Odegree( X, Z ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.45/1.79 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.45/1.79 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.45/1.79 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.45/1.79 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.45/1.79 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.45/1.79 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.45/1.79 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.45/1.79 tc_Nat_Onat ), X ), Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.45/1.79 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.79 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.45/1.79 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.45/1.79 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.45/1.79 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.45/1.79 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.45/1.79 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.45/1.79 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.45/1.79 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.45/1.79 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.45/1.79 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.45/1.79 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.45/1.79 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.45/1.79 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.45/1.79 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Nat_Onat ) ) = Y }.
% 1.45/1.79 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) }.
% 1.45/1.79 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.45/1.79 = c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.79 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.45/1.79 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.45/1.79 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.45/1.79 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.45/1.79 ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.45/1.79 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.45/1.79 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.79 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Z ) }.
% 1.45/1.79 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.45/1.79 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.45/1.79 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.45/1.79 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.45/1.79 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ) }.
% 1.45/1.79 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.45/1.79 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.45/1.79 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.45/1.79 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.45/1.79 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.45/1.79 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.45/1.79 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.45/1.79 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.45/1.79 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.45/1.79 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.45/1.79 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.79 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.45/1.79 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.45/1.79 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.45/1.79 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.45/1.79 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.45/1.79 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.45/1.79 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.45/1.79 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.45/1.79 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.45/1.79 Y ) ) ), Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.45/1.79 Y ) ) ), Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.45/1.79 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.45/1.79 , alpha33( X, Y, Z, T ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha33( X, Y, Z, T ),
% 1.45/1.79 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.45/1.79 { ! alpha33( X, Y, Z, T ), alpha7( X, Z, T ) }.
% 1.45/1.79 { ! alpha33( X, Y, Z, T ), alpha23( X, Y, T ) }.
% 1.45/1.79 { ! alpha7( X, Z, T ), ! alpha23( X, Y, T ), alpha33( X, Y, Z, T ) }.
% 1.45/1.79 { ! alpha23( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), alpha34( X, Y, Z ) }.
% 1.45/1.79 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha23( X
% 1.45/1.79 , Y, Z ) }.
% 1.45/1.79 { ! alpha34( X, Y, Z ), alpha23( X, Y, Z ) }.
% 1.45/1.79 { ! alpha34( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha34( X
% 1.45/1.79 , Y, Z ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.45/1.79 ), c_Polynomial_Odegree( X, Z ) ), alpha34( X, Y, Z ) }.
% 1.45/1.79 { ! alpha7( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha7( X, Y
% 1.45/1.79 , Z ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha7( X
% 1.45/1.79 , Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.45/1.79 = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Int_Oint ) ) ) }.
% 1.45/1.79 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Int_Oint ) ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.45/1.79 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.45/1.79 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.45/1.79 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.45/1.79 ( tc_Int_Oint ) }.
% 1.45/1.79 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.45/1.79 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.79 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.45/1.79 , Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.45/1.79 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.45/1.79 , Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.45/1.79 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.45/1.79 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.45/1.79 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.45/1.79 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.45/1.79 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.45/1.79 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 Z, T ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.45/1.79 ) }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Int_Oint ) ) = X }.
% 1.45/1.79 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Int_Oint ), X ) = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.45/1.79 .
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.45/1.79 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.45/1.79 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.45/1.79 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.45/1.79 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.45/1.79 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.45/1.79 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.45/1.79 X, T, Z ), Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.45/1.79 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.45/1.79 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.45/1.79 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.45/1.79 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha8( X
% 1.45/1.79 , Y, T ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha24( X
% 1.45/1.79 , Y, Z, T ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! alpha8( X, Y, T ), ! alpha24( X, Y, Z, T )
% 1.45/1.79 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.45/1.79 ( X, T, Z ), Y ) }.
% 1.45/1.79 { ! alpha24( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.45/1.79 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z, T ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha24( X
% 1.45/1.79 , Y, Z, T ) }.
% 1.45/1.79 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { Z = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 1.45/1.79 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X
% 1.45/1.79 , Y, Z ) }.
% 1.45/1.79 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.45/1.79 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.45/1.79 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.45/1.79 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.45/1.79 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.79 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.45/1.79 ( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.45/1.79 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.45/1.79 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.45/1.79 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.45/1.79 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.45/1.79 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.45/1.79 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.45/1.79 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.45/1.79 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.45/1.79 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.45/1.79 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.45/1.79 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Y ) }.
% 1.45/1.79 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.45/1.79 ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.45/1.79 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.45/1.79 hAPP( Z, skol6( U, W, Z ) ) ) }.
% 1.45/1.79 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.45/1.79 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol6( X
% 1.45/1.79 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.45/1.79 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.45/1.79 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol17( X,
% 1.45/1.79 Y, Z ) ) ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.45/1.79 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.45/1.79 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.45/1.79 , Y ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 tc_Nat_Onat, Z, skol7( T, U, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.79 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.45/1.79 skol7( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.79 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.45/1.79 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.45/1.79 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.45/1.79 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.45/1.79 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.79 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.79 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.45/1.79 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.45/1.79 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.45/1.79 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.45/1.79 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.45/1.79 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.45/1.79 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.45/1.79 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.45/1.79 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.45/1.79 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.45/1.79 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.79 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.79 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.45/1.79 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.45/1.79 }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.45/1.79 c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.45/1.79 , c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.45/1.79 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.45/1.79 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol8( X, Y ) ) }.
% 1.45/1.79 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.45/1.79 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.45/1.79 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.45/1.79 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.45/1.79 ) ) }.
% 1.45/1.79 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.45/1.79 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.45/1.79 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.45/1.79 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.45/1.79 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.45/1.79 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Int_Oint, Y, X ) }.
% 1.45/1.79 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) ), alpha9( X, Y, Z ), alpha25( X, Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha25( X, Y, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ) ) }.
% 1.45/1.79 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( X ), Y ), alpha25( X, Y, Z ) }.
% 1.45/1.79 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.45/1.79 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), alpha9( X, Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha10( X, Y
% 1.45/1.79 , Z ), alpha26( X, Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.79 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ) }.
% 1.45/1.79 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.45/1.79 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ), alpha10( X, Y, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.45/1.79 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Z, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 Y, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.45/1.79 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.45/1.79 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.45/1.79 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.45/1.79 , Y, T ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.45/1.79 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.45/1.79 , Z ), X ) ), T ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, U, T ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.45/1.79 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.45/1.79 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Oone__class_Oone( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.45/1.79 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ), Y ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.79 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.45/1.79 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.79 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ) }.
% 1.45/1.79 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.45/1.79 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.45/1.79 tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.79 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.79 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.45/1.79 X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.45/1.79 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.79 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.45/1.79 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.45/1.79 ), T ), U ), Y ) }.
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.79 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.45/1.79 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.45/1.79 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.45/1.79 .
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.45/1.79 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.45/1.79 ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.45/1.79 .
% 1.45/1.79 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.45/1.79 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 1.45/1.79 , c_Polynomial_Odegree( X, Y ) ) }.
% 1.45/1.79 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.45/1.79 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.79 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.45/1.79 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.45/1.79 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.45/1.79 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.45/1.79 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.45/1.79 ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.79 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.45/1.79 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.45/1.79 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.45/1.79 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.45/1.79 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 }.
% 1.45/1.79 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.79 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.45/1.79 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.45/1.79 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.45/1.79 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.45/1.79 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.45/1.79 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.45/1.79 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.45/1.79 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.79 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 X ), Y ), Z = Y }.
% 1.45/1.79 { ! class_Rings_Olinordered__semidom( X ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.45/1.79 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.79 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.79 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.45/1.79 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.79 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.45/1.79 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.79 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.45/1.79 ) }.
% 1.45/1.79 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.45/1.79 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.45/1.79 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.45/1.79 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.45/1.79 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.79 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.45/1.79 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.79 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.45/1.80 ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.45/1.80 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.45/1.80 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.45/1.80 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Int_Oint ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.45/1.80 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.45/1.80 }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.45/1.80 tc_Int_Oint ) ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.45/1.80 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.45/1.80 }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.45/1.80 tc_Int_Oint ) ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.45/1.80 tc_Int_Oint ) ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.45/1.80 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.45/1.80 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.45/1.80 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.45/1.80 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.45/1.80 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 1.45/1.80 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.45/1.80 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.45/1.80 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 1.45/1.80 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 1.45/1.80 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.45/1.80 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.45/1.80 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.45/1.80 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.45/1.80 ), Y ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__semidom( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.45/1.80 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.45/1.80 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.45/1.80 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.45/1.80 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.45/1.80 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.45/1.80 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.45/1.80 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.45/1.80 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.45/1.80 ( tc_Int_Oint ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.45/1.80 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.45/1.80 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.45/1.80 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.45/1.80 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.45/1.80 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Nat_Onat, Y, Z ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.45/1.80 , Z ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.45/1.80 Z, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Nat_Onat, Y, Z ) }.
% 1.45/1.80 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Nat_Onat, Y, Z ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.45/1.80 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.45/1.80 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.45/1.80 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! alpha11( X, Y ), ! Y = X }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha11( X, Y ) }
% 1.45/1.80 .
% 1.45/1.80 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! alpha11( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), alpha11( X, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha12( X, Y ), Y = X }
% 1.45/1.80 .
% 1.45/1.80 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! alpha12( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), alpha12( X, Y ) }.
% 1.45/1.80 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.45/1.80 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.45/1.80 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.45/1.80 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.45/1.80 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.45/1.80 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.45/1.80 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Int_Oint, Z, X ) }.
% 1.45/1.80 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.45/1.80 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.45/1.80 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.45/1.80 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Nat_Onat ) ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Int_Oint ) ) }.
% 1.45/1.80 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.45/1.80 tc_Nat_Onat ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Nat_Onat ), Y ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.45/1.80 tc_Int_Oint ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Int_Oint, X, Y ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Nat_Onat, Z, X ) }.
% 1.45/1.80 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.45/1.80 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Polynomial_Opoly( X ), Z, Y ), alpha44( X, Y, Z, T ), ! Y =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.45/1.80 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Polynomial_Opoly( X ), Z, Y ), alpha44( X, Y, Z, T ), ! hAPP(
% 1.45/1.80 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.45/1.80 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.45/1.80 .
% 1.45/1.80 { ! alpha44( X, Y, Z, T ), alpha45( X, Y, Z, T ), alpha42( X, Y, T ) }.
% 1.45/1.80 { ! alpha44( X, Y, Z, T ), alpha45( X, Y, Z, T ), ! hAPP(
% 1.45/1.80 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.80 { ! alpha45( X, Y, Z, T ), alpha44( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha42( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.45/1.80 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 alpha44( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha45( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.45/1.80 ( X ), Z, T ), alpha46( X, Y, Z, T ) }.
% 1.45/1.80 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha45( X, Y
% 1.45/1.80 , Z, T ) }.
% 1.45/1.80 { ! alpha46( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha46( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.45/1.80 ), skol9( X, Y, U, W ), Y ) }.
% 1.45/1.80 { ! alpha46( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.45/1.80 ), skol9( X, Y, U, T ), T ) }.
% 1.45/1.80 { ! alpha46( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.45/1.80 ( X ), skol9( X, Y, Z, T ), Z ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha46( X, Y
% 1.45/1.80 , Z, T ) }.
% 1.45/1.80 { ! alpha42( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! alpha42( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha42( X, Y, Z
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.45/1.80 , Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) }.
% 1.45/1.80 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.45/1.80 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.45/1.80 hAPP( Y, U ) ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.45/1.80 ( Z, skol11( X, Y, Z ) ), hAPP( Y, skol11( X, Y, Z ) ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.45/1.80 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.45/1.80 hAPP( Y, U ) ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.45/1.80 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.45/1.80 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.45/1.80 hAPP( Y, U ) ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.45/1.80 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), ! Z = Y }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 Z ), ! Z = Y }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.45/1.80 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , ! Z = Y }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , ! Z = Y }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , ! Y = Z }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.45/1.80 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.45/1.80 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.45/1.80 , ! Z = Y }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.45/1.80 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.80 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.45/1.80 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.80 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.80 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.80 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.45/1.80 , skol12( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Polynomial_Odegree( X, Y ), Z ) }.
% 1.45/1.80 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol12( X
% 1.45/1.80 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.45/1.80 Y ), Z ) }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.45/1.80 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.45/1.80 .
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.45/1.80 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.45/1.80 }.
% 1.45/1.80 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.45/1.80 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.45/1.80 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.45/1.80 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.45/1.80 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.45/1.80 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.45/1.80 ( X, Y ), Z = Y }.
% 1.45/1.80 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.45/1.80 ( X, Y ) }.
% 1.45/1.80 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.45/1.80 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.45/1.80 ) ) }.
% 1.45/1.80 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.45/1.80 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol13( Z, Y ) ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.45/1.80 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.45/1.80 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Int_Oint, skol13( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.45/1.80 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.45/1.80 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.45/1.80 ) ) }.
% 1.45/1.80 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.45/1.80 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol14( Z, Y
% 1.45/1.80 ), Y ) }.
% 1.45/1.80 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.45/1.80 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.45/1.80 skol14( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.45/1.80 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.45/1.80 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.45/1.80 , skol14( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.45/1.80 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.45/1.80 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.45/1.80 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.45/1.80 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.45/1.80 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Z, X ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.45/1.80 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.45/1.80 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.45/1.80 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.45/1.80 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.80 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.45/1.80 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.80 , Y ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.45/1.80 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.45/1.80 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.45/1.80 X, Y ) ) }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.45/1.80 X, Z, Y ) }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.45/1.80 X, Y ) }.
% 1.45/1.80 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( X ) ) }.
% 1.45/1.80 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.45/1.80 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.45/1.80 , Z, Y ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.45/1.80 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.45/1.80 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.45/1.80 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.45/1.80 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.45/1.80 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.45/1.80 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.45/1.80 ) ), Z ) }.
% 1.45/1.80 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.45/1.80 Z ) ), U ), T ) = Y }.
% 1.45/1.80 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.45/1.80 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), Z ), U ), Y ) }.
% 1.45/1.80 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.45/1.80 W ) ), U ), Y ) }.
% 1.45/1.80 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.45/1.80 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), Z ), U ), Y ) }.
% 1.45/1.80 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.45/1.80 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.45/1.80 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.45/1.80 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.45/1.80 Z ) ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.45/1.80 ) ), Y ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.45/1.80 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.45/1.80 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.45/1.80 = Y }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( X ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.45/1.80 X, Y ) ) = Y }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.45/1.80 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.45/1.80 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.45/1.80 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.45/1.80 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.45/1.80 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.45/1.80 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.45/1.80 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.45/1.80 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.45/1.80 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.45/1.80 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.45/1.80 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.45/1.80 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ) ) = Y }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.45/1.80 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.45/1.80 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.45/1.80 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.45/1.80 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.45/1.80 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.45/1.80 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.45/1.80 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.80 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.45/1.80 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.80 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.45/1.80 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.80 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.45/1.80 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.45/1.80 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.80 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.45/1.80 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Z, X ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Z, Y ), X ) }.
% 1.45/1.80 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.45/1.80 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.45/1.80 hAPP( Z, Y ) ) }.
% 1.45/1.80 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.45/1.80 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.45/1.80 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.45/1.80 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.45/1.80 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.45/1.80 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.45/1.80 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.45/1.80 c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.45/1.80 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.45/1.80 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.45/1.80 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.45/1.80 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.45/1.80 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( X, Z, W ) ), U ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.45/1.80 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.45/1.80 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.45/1.80 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 X, W, Z ) ), U ), T ), Y ) }.
% 1.45/1.80 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.45/1.80 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), Z ), U ), Y ) ) }.
% 1.45/1.80 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.45/1.80 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.45/1.80 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.45/1.80 .
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.45/1.80 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.45/1.80 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.45/1.80 }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.45/1.80 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.45/1.80 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.45/1.80 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.45/1.80 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.45/1.80 }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.45/1.80 ) ) = X }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.45/1.80 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.45/1.80 , alpha13( X, Y, Z ) }.
% 1.45/1.80 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.45/1.80 , alpha27( X, Y, Z ) }.
% 1.45/1.80 { ! alpha13( X, Y, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.45/1.80 { ! alpha27( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.45/1.80 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.45/1.80 { ! hBOOL( hAPP( Z, skol15( T, U, Z ) ) ), alpha27( X, Y, Z ) }.
% 1.45/1.80 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol15( X, Y, Z ) ),
% 1.45/1.80 alpha27( X, Y, Z ) }.
% 1.45/1.80 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.45/1.80 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 1.45/1.80 .
% 1.45/1.80 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 1.45/1.80 ( X, Y, Z ) }.
% 1.45/1.80 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.45/1.80 , ! alpha14( X, Y, Z ) }.
% 1.45/1.80 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.45/1.80 , ! alpha28( X, Y, Z ) }.
% 1.45/1.80 { alpha14( X, Y, Z ), alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.45/1.80 { ! alpha28( X, Y, Z ), ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ) }.
% 1.45/1.80 { ! alpha28( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.45/1.80 skol16( X, Y, Z ) ) }.
% 1.45/1.80 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.45/1.80 ) ), alpha28( X, Y, Z ) }.
% 1.45/1.80 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.45/1.80 }.
% 1.45/1.80 { ! alpha14( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Nat_Onat ) ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14( X, Y, Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.45/1.80 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.45/1.80 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.45/1.80 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.45/1.80 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.45/1.80 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.45/1.80 tc_Nat_Onat ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.45/1.80 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.45/1.80 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.45/1.80 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.45/1.80 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.45/1.80 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.45/1.80 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.45/1.80 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.45/1.80 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.45/1.80 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.45/1.80 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.45/1.80 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.45/1.80 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.45/1.80 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.45/1.80 ( tc_Nat_Onat ) ) ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.45/1.80 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.45/1.80 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.45/1.80 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.45/1.80 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.45/1.80 c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.80 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.45/1.80 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.45/1.80 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.45/1.80 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.45/1.80 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.80 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.45/1.80 tc_Polynomial_Opoly( X ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.45/1.80 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.45/1.80 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.45/1.80 }.
% 1.45/1.80 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.45/1.80 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.45/1.80 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.45/1.80 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.45/1.80 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.45/1.80 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.45/1.80 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.45/1.80 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.45/1.80 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.45/1.80 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.45/1.80 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.45/1.80 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.45/1.80 .
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.45/1.80 ( tc_Int_Oint ) ) ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.45/1.80 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.45/1.80 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.45/1.80 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.45/1.80 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.45/1.80 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) }.
% 1.45/1.80 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.45/1.80 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.45/1.80 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.80 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.45/1.80 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.45/1.80 = c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.45/1.80 ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.45/1.80 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.45/1.80 .
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.45/1.80 .
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.45/1.80 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.45/1.80 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.45/1.80 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.45/1.80 , Y ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.45/1.80 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 1.45/1.80 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.45/1.80 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.45/1.80 ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.80 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.45/1.80 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.45/1.80 c_Groups_Oone__class_Oone( X ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.45/1.80 }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.80 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.45/1.80 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.45/1.80 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.45/1.80 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.45/1.80 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 1.45/1.80 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.45/1.80 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.45/1.80 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.45/1.80 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 1.45/1.80 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 1.45/1.80 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 1.45/1.80 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 1.45/1.80 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.45/1.80 tc_Int_Oint, X, Y ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.45/1.80 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.80 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.45/1.80 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.45/1.80 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.45/1.80 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.45/1.80 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.45/1.80 { ! class_RealVector_Oreal__normed__field( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.45/1.80 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.45/1.80 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.45/1.80 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.45/1.80 X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.45/1.80 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.45/1.80 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.45/1.80 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.45/1.80 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.45/1.80 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.45/1.80 X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.45/1.80 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.45/1.80 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.45/1.80 , Y, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.45/1.80 , Y, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.45/1.80 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha15( X, Y, Z ), alpha29( X,
% 1.45/1.80 Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha15( X, Y, Z
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.45/1.80 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.45/1.80 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ), alpha29( X, Y, Z ) }.
% 1.45/1.80 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.45/1.80 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ), alpha15( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha16( X, Y, Z ), alpha30
% 1.45/1.80 ( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha16( X, Y, Z
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 1.45/1.80 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.45/1.80 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.45/1.80 ), alpha30( X, Y, Z ) }.
% 1.45/1.80 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.45/1.80 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.45/1.80 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.45/1.80 ), alpha16( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.45/1.80 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.45/1.80 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.45/1.80 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.45/1.80 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.45/1.80 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.80 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.45/1.80 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.45/1.80 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.45/1.80 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Y ), Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 Z, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 Z, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Y ), Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Y ), Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.45/1.80 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.45/1.80 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 Z, Y ) ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Z ), Y ), alpha31( X, Y, Z, T ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.45/1.80 Z ), Y ), alpha35( X, Y, Z, T ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 1.45/1.80 , T ), ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.45/1.80 { ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Z ), alpha37( X, Y, Z, T ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.45/1.80 , alpha35( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha37( X, Y, Z, T ), alpha35( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha37( X, Y, Z, T ), alpha39( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha37( X, Y, Z, T ), alpha17( X, Y, Z ) }.
% 1.45/1.80 { ! alpha39( X, Y, Z, T ), ! alpha17( X, Y, Z ), alpha37( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha39( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.80 alpha39( X, Y, Z, T ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha39( X, Y, Z, T )
% 1.45/1.80 }.
% 1.45/1.80 { ! alpha31( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.45/1.80 alpha31( X, Y, Z, T ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha31( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.80 , alpha17( X, Y, Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.45/1.80 , alpha17( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 Z, Y ) ), alpha32( X, Y, Z, T ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.45/1.80 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.45/1.80 Z, Y ) ), alpha36( X, Y, Z, T ) }.
% 1.45/1.80 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 1.45/1.80 , T ), ! alpha36( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.45/1.80 { ! alpha36( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Y ), alpha38( X, Y, Z, T ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.45/1.80 , alpha36( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha38( X, Y, Z, T ), alpha36( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha38( X, Y, Z, T ), alpha40( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha38( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 1.45/1.80 { ! alpha40( X, Y, Z, T ), ! alpha18( X, Y, T ), alpha38( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha40( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.45/1.80 alpha40( X, Y, Z, T ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha40( X, Y, Z, T ) }.
% 1.45/1.80 { ! alpha32( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.45/1.80 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.45/1.80 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.45/1.80 alpha32( X, Y, Z, T ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha32( X, Y, Z, T )
% 1.45/1.80 }.
% 1.45/1.80 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.80 , alpha18( X, Y, Z ) }.
% 1.45/1.80 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.45/1.80 , alpha18( X, Y, Z ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.45/1.80 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.45/1.80 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.45/1.80 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.45/1.80 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.45/1.80 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.45/1.80 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.45/1.80 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.45/1.80 .
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.45/1.80 ( X ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__add(
% 1.45/1.80 X ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ocomm__monoid__add( X
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring( X ) }
% 1.45/1.80 .
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Omonoid__add( X ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0( X ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero( X ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring( X ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ozero( X ) }.
% 1.45/1.80 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.45/1.80 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.45/1.80 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.45/1.80 ( tc_fun( Y, X ) ) }.
% 1.45/1.80 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.45/1.80 ) ) }.
% 1.45/1.80 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.45/1.80 .
% 1.45/1.80 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.45/1.80 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.45/1.80 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.45/1.80 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.45/1.80 tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.45/1.80 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.45/1.80 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.45/1.80 { class_Power_Opower( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.45/1.80 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.45/1.80 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.45/1.80 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.45/1.80 tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.45/1.80 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.45/1.80 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.45/1.80 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.45/1.80 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.45/1.80 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.45/1.80 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.45/1.80 { ! class_Rings_Oidom( X ),
% 1.45/1.80 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.45/1.80 ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.45/1.80 X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.45/1.80 ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.45/1.80 }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.45/1.80 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ),
% 1.45/1.80 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.45/1.80 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.45/1.80 ( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.45/1.80 ( tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.45/1.80 }.
% 1.45/1.80 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.45/1.80 ) ) }.
% 1.45/1.80 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.45/1.80 .
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.45/1.80 tc_Polynomial_Opoly( X ) ) }.
% 1.45/1.80 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.45/1.80 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.45/1.80 { hAPP( c_Polynomial_Opoly( t_a,
% 1.45/1.80 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h )
% 1.45/1.80 ), v_x ) = hAPP( c_Polynomial_Opoly( t_a, v_p ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( t_a, v_h, v_x ) ) }.
% 1.45/1.80 { ! hAPP( c_Polynomial_Opoly( t_a,
% 1.45/1.80 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a,
% 1.45/1.80 c_Polynomial_OpCons( t_a, v_a, v_p ), v_h ) ), v_x ) = hAPP(
% 1.45/1.80 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, v_a, v_p ) ),
% 1.45/1.80 c_Groups_Oplus__class_Oplus( t_a, v_h, v_x ) ) }.
% 1.45/1.80 { class_Rings_Ocomm__semiring__0( t_a ) }.
% 1.45/1.80
% 1.45/1.80 *** allocated 15000 integers for clauses
% 1.45/1.80 *** allocated 22500 integers for clauses
% 1.45/1.80 *** allocated 33750 integers for clauses
% 1.45/1.80 *** allocated 50625 integers for clauses
% 1.45/1.80 *** allocated 75937 integers for clauses
% 1.45/1.80 percentage equality = 0.251572, percentage horn = 0.894808
% 1.45/1.80 This is a problem with some equality
% 1.45/1.80
% 1.45/1.80
% 1.45/1.80
% 1.45/1.80 Options Used:
% 1.45/1.80
% 1.45/1.80 useres = 1
% 1.45/1.80 useparamod = 1
% 1.45/1.80 useeqrefl = 1
% 1.45/1.81 useeqfact = 1
% 1.45/1.81 usefactor = 1
% 1.45/1.81 usesimpsplitting = 0
% 1.45/1.81 usesimpdemod = 5
% 1.45/1.81 usesimpres = 3
% 1.45/1.81
% 1.45/1.81 resimpinuse = 1000
% 1.45/1.81 resimpclauses = 20000
% 1.45/1.81 substype = eqrewr
% 1.45/1.81 backwardsubs = 1
% 1.45/1.81 selectoldest = 5
% 1.45/1.81
% 1.45/1.81 litorderings [0] = split
% 1.45/1.81 litorderings [1] = extend the termordering, first sorting on arguments
% 1.45/1.81
% 1.45/1.81 termordering = kbo
% 1.45/1.81
% 1.45/1.81 litapriori = 0
% 1.45/1.81 termapriori = 1
% 1.45/1.81 litaposteriori = 0
% 1.45/1.81 termaposteriori = 0
% 1.45/1.81 demodaposteriori = 0
% 1.45/1.81 ordereqreflfact = 0
% 1.45/1.81
% 1.45/1.81 litselect = negord
% 1.45/1.81
% 1.45/1.81 maxweight = 15
% 1.45/1.81 maxdepth = 30000
% 1.45/1.81 maxlength = 115
% 1.45/1.81 maxnrvars = 195
% 1.45/1.81 excuselevel = 1
% 1.45/1.81 increasemaxweight = 1
% 1.45/1.81
% 1.45/1.81 maxselected = 10000000
% 1.45/1.81 maxnrclauses = 10000000
% 1.45/1.81
% 1.45/1.81 showgenerated = 0
% 1.45/1.81 showkept = 0
% 1.45/1.81 showselected = 0
% 1.45/1.81 showdeleted = 0
% 1.45/1.81 showresimp = 1
% 1.45/1.81 showstatus = 2000
% 1.45/1.81
% 1.45/1.81 prologoutput = 0
% 1.45/1.81 nrgoals = 5000000
% 1.45/1.81 totalproof = 1
% 1.45/1.81
% 1.45/1.81 Symbols occurring in the translation:
% 1.45/1.81
% 1.45/1.81 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.45/1.81 . [1, 2] (w:1, o:186, a:1, s:1, b:0),
% 1.45/1.81 ! [4, 1] (w:0, o:105, a:1, s:1, b:0),
% 1.45/1.81 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.45/1.81 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.45/1.81 hAPP [38, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Ocomm__semiring__0 [43, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.45/1.81 tc_Polynomial_Opoly [44, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.45/1.81 c_Groups_Oplus__class_Oplus [45, 3] (w:1, o:237, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Opoly [46, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Ocomm__monoid__add [49, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.45/1.81
% 1.45/1.81 c_Polynomial_OpCons [50, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.45/1.81 class_Int_Oring__char__0 [54, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Oidom [55, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Ozero [58, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Ocomm__semiring__1 [60, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Oab__semigroup__add [62, 1] (w:1, o:124, a:1, s:1, b:0)
% 1.45/1.81 ,
% 1.45/1.81 class_Groups_Ocancel__semigroup__add [64, 1] (w:1, o:125, a:1, s:1
% 1.45/1.81 , b:0),
% 1.45/1.81 class_Groups_Ocancel__ab__semigroup__add [65, 1] (w:1, o:126, a:1, s:
% 1.45/1.81 1, b:0),
% 1.45/1.81 c_Polynomial_Osynthetic__div [66, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.45/1.81 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [68, 3] (w:1
% 1.45/1.81 , o:236, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Osmult [69, 3] (w:1, o:244, a:1, s:1, b:0),
% 1.45/1.81 c_Groups_Otimes__class_Otimes [70, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Opcompose [71, 3] (w:1, o:245, a:1, s:1, b:0),
% 1.45/1.81 c_Groups_Ozero__class_Ozero [72, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Omonom [74, 3] (w:1, o:246, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Olinordered__idom [75, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Opos__poly [76, 2] (w:1, o:212, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Ocoeff [77, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.45/1.81 c_Groups_Osemigroup [79, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Oab__semigroup__mult [87, 1] (w:1, o:130, a:1, s:1, b:0)
% 1.45/1.81 ,
% 1.45/1.81 tc_Nat_Onat [90, 0] (w:1, o:61, a:1, s:1, b:0),
% 1.45/1.81 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [91
% 1.45/1.81 , 1] (w:1, o:159, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Omonoid__add [97, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Olinordered__ab__group__add [98, 1] (w:1, o:160, a:1, s:
% 1.45/1.81 1, b:0),
% 1.45/1.81 class_Rings_Olinordered__ring__strict [99, 1] (w:1, o:131, a:1, s:1
% 1.45/1.81 , b:0),
% 1.45/1.81 c_Polynomial_Oorder [100, 3] (w:1, o:241, a:1, s:1, b:0),
% 1.45/1.81 class_RealVector_Oreal__normed__algebra [102, 1] (w:1, o:132, a:1, s:
% 1.45/1.81 1, b:0),
% 1.45/1.81 class_Rings_Ocomm__semiring [104, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Osemiring [108, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Ono__zero__divisors [109, 1] (w:1, o:147, a:1, s:1, b:0)
% 1.45/1.81 ,
% 1.45/1.81 class_Rings_Omult__zero [110, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Oring__no__zero__divisors [111, 1] (w:1, o:134, a:1, s:1
% 1.45/1.81 , b:0),
% 1.45/1.81 c_Polynomial_Opoly__rec [114, 5] (w:1, o:301, a:1, s:1, b:0),
% 1.45/1.81 c_fequal [115, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.45/1.81 c_If [116, 4] (w:1, o:282, a:1, s:1, b:0),
% 1.45/1.81 c_Orderings_Oord__class_Oless [117, 3] (w:1, o:239, a:1, s:1, b:0),
% 1.45/1.81 c_Nat_Onat_Onat__case [118, 3] (w:1, o:238, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Oordered__ab__semigroup__add__imp__le [126, 1] (w:1, o:
% 1.45/1.81 162, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Oordered__cancel__ab__semigroup__add [127, 1] (w:1, o:
% 1.45/1.81 163, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Olinordered__comm__semiring__strict [128, 1] (w:1, o:139
% 1.45/1.81 , a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Olinordered__semiring__strict [129, 1] (w:1, o:141, a:1
% 1.45/1.81 , s:1, b:0),
% 1.45/1.81 class_Rings_Olinordered__ring [130, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Oordered__comm__monoid__add [131, 1] (w:1, o:164, a:1
% 1.45/1.81 , s:1, b:0),
% 1.45/1.81 class_Rings_Olinordered__semidom [132, 1] (w:1, o:142, a:1, s:1, b:0)
% 1.45/1.81 ,
% 1.45/1.81 c_Polynomial_OAbs__poly [133, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Odegree [134, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Ocomm__ring__1 [135, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.45/1.81 c_Groups_Ouminus__class_Ouminus [136, 2] (w:1, o:218, a:1, s:1, b:0)
% 1.45/1.81 ,
% 1.45/1.81 c_Groups_Oone__class_Oone [137, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.45/1.81 c_Nat_OSuc [139, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.45/1.81 c_Power_Opower__class_Opower [140, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.45/1.81 hBOOL [142, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Ocomm__ring [147, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Oab__group__add [148, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Ogroup__add [149, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Oone [150, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Oring__1__no__zero__divisors [151, 1] (w:1, o:135, a:1
% 1.45/1.81 , s:1, b:0),
% 1.45/1.81 tc_Int_Oint [152, 0] (w:1, o:83, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Oordered__ab__group__add [153, 1] (w:1, o:172, a:1, s:1
% 1.45/1.81 , b:0),
% 1.45/1.81 class_Rings_Oring [154, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Ozero__neq__one [155, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.45/1.81 class_Groups_Ocomm__monoid__mult [156, 1] (w:1, o:173, a:1, s:1, b:0)
% 1.45/1.81 ,
% 1.45/1.81 class_Groups_Omonoid__mult [157, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.45/1.81 class_Power_Opower [168, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Osemiring__0 [169, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Oring__1 [170, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.45/1.81 c_Power_Opower_Opower [171, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.45/1.81 c_Rings_Odvd__class_Odvd [172, 3] (w:1, o:248, a:1, s:1, b:0),
% 1.45/1.81 class_Fields_Ofield [174, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Opdivmod__rel [175, 5] (w:1, o:302, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Odvd [176, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.45/1.81 c_Polynomial_Opoly__gcd [186, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.45/1.81 c_Orderings_Oord__class_Oless__eq [187, 3] (w:1, o:240, a:1, s:1, b:0
% 1.45/1.81 ),
% 1.45/1.81 class_Groups_Oordered__ab__semigroup__add [190, 1] (w:1, o:180, a:1
% 1.45/1.81 , s:1, b:0),
% 1.45/1.81 class_Rings_Oordered__cancel__semiring [191, 1] (w:1, o:151, a:1, s:1
% 1.45/1.81 , b:0),
% 1.45/1.81 class_Rings_Oordered__ring [192, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.45/1.81 class_Rings_Oordered__semiring [193, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.45/1.81
% 1.45/1.81 class_Rings_Oordered__comm__semiring [194, 1] (w:1, o:154, a:1, s:1
% 1.45/1.81 , b:0),
% 1.45/1.81 class_Rings_Olinordered__semiring [197, 1] (w:1, o:143, a:1, s:1, b:0
% 1.45/1.81 ),
% 1.45/1.81 class_Rings_Olinordered__semiring__1 [199, 1] (w:1, o:144, a:1, s:1
% 1.45/1.81 , b:0),
% 1.45/1.81 class_Rings_Olinordered__semiring__1__strict [200, 1] (w:1, o:145, a:
% 1.45/1.81 1, s:1, b:0),
% 1.45/1.81 class_Orderings_Opreorder [201, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.45/1.81 class_Orderings_Oord [202, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.45/1.81 tc_fun [203, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.45/1.81 class_Orderings_Olinorder [204, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.45/1.81 class_Orderings_Oorder [205, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.45/1.81 class_Lattices_Oboolean__algebra [206, 1] (w:1, o:182, a:1, s:1, b:0)
% 1.45/1.81 ,
% 1.45/1.81 class_Lattices_Oab__semigroup__idem__mult [207, 1] (w:1, o:181, a:1
% 1.45/1.81 , s:1, b:0),
% 1.45/1.81 class_Groups_Ouminus [209, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.45/1.81 c_Rings_Oinverse__class_Oinverse [210, 2] (w:1, o:227, a:1, s:1, b:0)
% 6.11/6.49 ,
% 6.11/6.49 c_Groups_Ominus__class_Ominus [211, 3] (w:1, o:250, a:1, s:1, b:0),
% 6.11/6.49 class_Rings_Odivision__ring__inverse__zero [214, 1] (w:1, o:155, a:1
% 6.11/6.49 , s:1, b:0),
% 6.11/6.49 class_Rings_Odivision__ring [215, 1] (w:1, o:156, a:1, s:1, b:0),
% 6.11/6.49 class_Groups_Ominus [218, 1] (w:1, o:184, a:1, s:1, b:0),
% 6.11/6.49 class_Fields_Olinordered__field [222, 1] (w:1, o:116, a:1, s:1, b:0)
% 6.11/6.49 ,
% 6.11/6.49 class_Fields_Ofield__inverse__zero [223, 1] (w:1, o:117, a:1, s:1, b:
% 6.11/6.49 0),
% 6.11/6.49 class_Fields_Olinordered__field__inverse__zero [224, 1] (w:1, o:118
% 6.11/6.49 , a:1, s:1, b:0),
% 6.11/6.49 c_Rings_Oinverse__class_Odivide [225, 3] (w:1, o:251, a:1, s:1, b:0)
% 6.11/6.49 ,
% 6.11/6.49 c_Nat__Transfer_Otsub [226, 2] (w:1, o:228, a:1, s:1, b:0),
% 6.11/6.49 class_RealVector_Oreal__field [227, 1] (w:1, o:157, a:1, s:1, b:0),
% 6.11/6.49 class_RealVector_Oreal__normed__field [228, 1] (w:1, o:158, a:1, s:1
% 6.11/6.49 , b:0),
% 6.11/6.49 class_Groups_Ocancel__comm__monoid__add [231, 1] (w:1, o:185, a:1, s:
% 6.11/6.49 1, b:0),
% 6.11/6.49 tc_HOL_Obool [233, 0] (w:1, o:82, a:1, s:1, b:0),
% 6.11/6.49 t_a [235, 0] (w:1, o:100, a:1, s:1, b:0),
% 6.11/6.49 v_p [236, 0] (w:1, o:101, a:1, s:1, b:0),
% 6.11/6.49 v_h [237, 0] (w:1, o:102, a:1, s:1, b:0),
% 6.11/6.49 v_x [238, 0] (w:1, o:103, a:1, s:1, b:0),
% 6.11/6.49 v_a [239, 0] (w:1, o:104, a:1, s:1, b:0),
% 6.11/6.49 alpha1 [240, 3] (w:1, o:252, a:1, s:1, b:1),
% 6.11/6.49 alpha2 [241, 4] (w:1, o:284, a:1, s:1, b:1),
% 6.11/6.49 alpha3 [242, 4] (w:1, o:287, a:1, s:1, b:1),
% 6.11/6.49 alpha4 [243, 2] (w:1, o:229, a:1, s:1, b:1),
% 6.11/6.49 alpha5 [244, 2] (w:1, o:230, a:1, s:1, b:1),
% 6.11/6.49 alpha6 [245, 2] (w:1, o:231, a:1, s:1, b:1),
% 6.11/6.49 alpha7 [246, 3] (w:1, o:253, a:1, s:1, b:1),
% 6.11/6.49 alpha8 [247, 3] (w:1, o:254, a:1, s:1, b:1),
% 6.11/6.49 alpha9 [248, 3] (w:1, o:255, a:1, s:1, b:1),
% 6.11/6.49 alpha10 [249, 3] (w:1, o:256, a:1, s:1, b:1),
% 6.11/6.49 alpha11 [250, 2] (w:1, o:232, a:1, s:1, b:1),
% 6.11/6.49 alpha12 [251, 2] (w:1, o:233, a:1, s:1, b:1),
% 6.11/6.49 alpha13 [252, 3] (w:1, o:257, a:1, s:1, b:1),
% 6.11/6.49 alpha14 [253, 3] (w:1, o:258, a:1, s:1, b:1),
% 6.11/6.49 alpha15 [254, 3] (w:1, o:259, a:1, s:1, b:1),
% 6.11/6.49 alpha16 [255, 3] (w:1, o:260, a:1, s:1, b:1),
% 6.11/6.49 alpha17 [256, 3] (w:1, o:261, a:1, s:1, b:1),
% 6.11/6.49 alpha18 [257, 3] (w:1, o:262, a:1, s:1, b:1),
% 6.11/6.49 alpha19 [258, 4] (w:1, o:283, a:1, s:1, b:1),
% 6.11/6.49 alpha20 [259, 4] (w:1, o:285, a:1, s:1, b:1),
% 6.11/6.49 alpha21 [260, 2] (w:1, o:234, a:1, s:1, b:1),
% 6.11/6.49 alpha22 [261, 2] (w:1, o:235, a:1, s:1, b:1),
% 6.11/6.49 alpha23 [262, 3] (w:1, o:263, a:1, s:1, b:1),
% 6.11/6.49 alpha24 [263, 4] (w:1, o:286, a:1, s:1, b:1),
% 6.11/6.49 alpha25 [264, 3] (w:1, o:264, a:1, s:1, b:1),
% 6.11/6.49 alpha26 [265, 3] (w:1, o:265, a:1, s:1, b:1),
% 6.11/6.49 alpha27 [266, 3] (w:1, o:266, a:1, s:1, b:1),
% 6.11/6.49 alpha28 [267, 3] (w:1, o:267, a:1, s:1, b:1),
% 6.11/6.49 alpha29 [268, 3] (w:1, o:268, a:1, s:1, b:1),
% 6.11/6.49 alpha30 [269, 3] (w:1, o:269, a:1, s:1, b:1),
% 6.11/6.49 alpha31 [270, 4] (w:1, o:288, a:1, s:1, b:1),
% 6.11/6.49 alpha32 [271, 4] (w:1, o:289, a:1, s:1, b:1),
% 6.11/6.49 alpha33 [272, 4] (w:1, o:290, a:1, s:1, b:1),
% 6.11/6.49 alpha34 [273, 3] (w:1, o:270, a:1, s:1, b:1),
% 6.11/6.49 alpha35 [274, 4] (w:1, o:291, a:1, s:1, b:1),
% 6.11/6.49 alpha36 [275, 4] (w:1, o:292, a:1, s:1, b:1),
% 6.11/6.49 alpha37 [276, 4] (w:1, o:293, a:1, s:1, b:1),
% 6.11/6.49 alpha38 [277, 4] (w:1, o:294, a:1, s:1, b:1),
% 6.11/6.49 alpha39 [278, 4] (w:1, o:295, a:1, s:1, b:1),
% 6.11/6.49 alpha40 [279, 4] (w:1, o:296, a:1, s:1, b:1),
% 6.11/6.49 alpha41 [280, 3] (w:1, o:271, a:1, s:1, b:1),
% 6.11/6.49 alpha42 [281, 3] (w:1, o:272, a:1, s:1, b:1),
% 6.11/6.49 alpha43 [282, 3] (w:1, o:273, a:1, s:1, b:1),
% 6.11/6.49 alpha44 [283, 4] (w:1, o:297, a:1, s:1, b:1),
% 6.11/6.49 alpha45 [284, 4] (w:1, o:298, a:1, s:1, b:1),
% 6.11/6.49 alpha46 [285, 4] (w:1, o:299, a:1, s:1, b:1),
% 6.11/6.49 skol1 [286, 2] (w:1, o:219, a:1, s:1, b:1),
% 6.11/6.49 skol2 [287, 3] (w:1, o:279, a:1, s:1, b:1),
% 6.11/6.49 skol3 [288, 1] (w:1, o:113, a:1, s:1, b:1),
% 6.11/6.49 skol4 [289, 2] (w:1, o:220, a:1, s:1, b:1),
% 6.11/6.49 skol5 [290, 2] (w:1, o:221, a:1, s:1, b:1),
% 6.11/6.49 skol6 [291, 3] (w:1, o:280, a:1, s:1, b:1),
% 6.11/6.49 skol7 [292, 3] (w:1, o:281, a:1, s:1, b:1),
% 34.82/35.20 skol8 [293, 2] (w:1, o:222, a:1, s:1, b:1),
% 34.82/35.20 skol9 [294, 4] (w:1, o:300, a:1, s:1, b:1),
% 34.82/35.20 skol10 [295, 2] (w:1, o:223, a:1, s:1, b:1),
% 34.82/35.20 skol11 [296, 3] (w:1, o:274, a:1, s:1, b:1),
% 34.82/35.20 skol12 [297, 3] (w:1, o:275, a:1, s:1, b:1),
% 34.82/35.20 skol13 [298, 2] (w:1, o:224, a:1, s:1, b:1),
% 34.82/35.20 skol14 [299, 2] (w:1, o:225, a:1, s:1, b:1),
% 34.82/35.20 skol15 [300, 3] (w:1, o:276, a:1, s:1, b:1),
% 34.82/35.20 skol16 [301, 3] (w:1, o:277, a:1, s:1, b:1),
% 34.82/35.20 skol17 [302, 3] (w:1, o:278, a:1, s:1, b:1).
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Starting Search:
% 34.82/35.20
% 34.82/35.20 *** allocated 113905 integers for clauses
% 34.82/35.20 *** allocated 170857 integers for clauses
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 3499
% 34.82/35.20 Kept: 2024
% 34.82/35.20 Inuse: 41
% 34.82/35.20 Deleted: 0
% 34.82/35.20 Deletedinuse: 0
% 34.82/35.20
% 34.82/35.20 *** allocated 256285 integers for clauses
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 170857 integers for termspace/termends
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 384427 integers for clauses
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 9430
% 34.82/35.20 Kept: 4040
% 34.82/35.20 Inuse: 163
% 34.82/35.20 Deleted: 3
% 34.82/35.20 Deletedinuse: 0
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 256285 integers for termspace/termends
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 14937
% 34.82/35.20 Kept: 6050
% 34.82/35.20 Inuse: 230
% 34.82/35.20 Deleted: 4
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 *** allocated 576640 integers for clauses
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 23321
% 34.82/35.20 Kept: 8576
% 34.82/35.20 Inuse: 281
% 34.82/35.20 Deleted: 6
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 384427 integers for termspace/termends
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 864960 integers for clauses
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 32243
% 34.82/35.20 Kept: 11135
% 34.82/35.20 Inuse: 326
% 34.82/35.20 Deleted: 6
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 46599
% 34.82/35.20 Kept: 13138
% 34.82/35.20 Inuse: 365
% 34.82/35.20 Deleted: 6
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 *** allocated 576640 integers for termspace/termends
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 52700
% 34.82/35.20 Kept: 15448
% 34.82/35.20 Inuse: 386
% 34.82/35.20 Deleted: 6
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 1297440 integers for clauses
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 73080
% 34.82/35.20 Kept: 18638
% 34.82/35.20 Inuse: 425
% 34.82/35.20 Deleted: 7
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 864960 integers for termspace/termends
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying clauses:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 82046
% 34.82/35.20 Kept: 21128
% 34.82/35.20 Inuse: 460
% 34.82/35.20 Deleted: 142
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 92212
% 34.82/35.20 Kept: 23147
% 34.82/35.20 Inuse: 504
% 34.82/35.20 Deleted: 142
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 103477
% 34.82/35.20 Kept: 25329
% 34.82/35.20 Inuse: 530
% 34.82/35.20 Deleted: 142
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 1946160 integers for clauses
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 1297440 integers for termspace/termends
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 125348
% 34.82/35.20 Kept: 28510
% 34.82/35.20 Inuse: 570
% 34.82/35.20 Deleted: 142
% 34.82/35.20 Deletedinuse: 1
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 141345
% 34.82/35.20 Kept: 31219
% 34.82/35.20 Inuse: 605
% 34.82/35.20 Deleted: 144
% 34.82/35.20 Deletedinuse: 3
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 152921
% 34.82/35.20 Kept: 34725
% 34.82/35.20 Inuse: 630
% 34.82/35.20 Deleted: 144
% 34.82/35.20 Deletedinuse: 3
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 159133
% 34.82/35.20 Kept: 37892
% 34.82/35.20 Inuse: 640
% 34.82/35.20 Deleted: 144
% 34.82/35.20 Deletedinuse: 3
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 167226
% 34.82/35.20 Kept: 40805
% 34.82/35.20 Inuse: 670
% 34.82/35.20 Deleted: 144
% 34.82/35.20 Deletedinuse: 3
% 34.82/35.20
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 Resimplifying clauses:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20 *** allocated 2919240 integers for clauses
% 34.82/35.20 Resimplifying inuse:
% 34.82/35.20 Done
% 34.82/35.20
% 34.82/35.20
% 34.82/35.20 Intermediate Status:
% 34.82/35.20 Generated: 176568
% 34.82/35.20 Kept: 42808
% 34.82/35.20 Inuse: 699
% 34.82/35.20 Deleted: 770
% 34.82/35.20 Deletedinuse: 3
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 181800
% 109.33/109.69 Kept: 44813
% 109.33/109.69 Inuse: 715
% 109.33/109.69 Deleted: 772
% 109.33/109.69 Deletedinuse: 3
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 *** allocated 1946160 integers for termspace/termends
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 191264
% 109.33/109.69 Kept: 46953
% 109.33/109.69 Inuse: 766
% 109.33/109.69 Deleted: 775
% 109.33/109.69 Deletedinuse: 4
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 200416
% 109.33/109.69 Kept: 49004
% 109.33/109.69 Inuse: 811
% 109.33/109.69 Deleted: 777
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 210433
% 109.33/109.69 Kept: 51186
% 109.33/109.69 Inuse: 855
% 109.33/109.69 Deleted: 778
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 219697
% 109.33/109.69 Kept: 53187
% 109.33/109.69 Inuse: 888
% 109.33/109.69 Deleted: 778
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 228495
% 109.33/109.69 Kept: 55300
% 109.33/109.69 Inuse: 920
% 109.33/109.69 Deleted: 778
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 235551
% 109.33/109.69 Kept: 57306
% 109.33/109.69 Inuse: 974
% 109.33/109.69 Deleted: 778
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 243858
% 109.33/109.69 Kept: 59342
% 109.33/109.69 Inuse: 1025
% 109.33/109.69 Deleted: 778
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying clauses:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 256010
% 109.33/109.69 Kept: 62535
% 109.33/109.69 Inuse: 1060
% 109.33/109.69 Deleted: 1054
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 *** allocated 4378860 integers for clauses
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 278997
% 109.33/109.69 Kept: 66319
% 109.33/109.69 Inuse: 1080
% 109.33/109.69 Deleted: 1054
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 *** allocated 2919240 integers for termspace/termends
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 304110
% 109.33/109.69 Kept: 68899
% 109.33/109.69 Inuse: 1095
% 109.33/109.69 Deleted: 1054
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 329091
% 109.33/109.69 Kept: 71298
% 109.33/109.69 Inuse: 1105
% 109.33/109.69 Deleted: 1054
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 344946
% 109.33/109.69 Kept: 74646
% 109.33/109.69 Inuse: 1125
% 109.33/109.69 Deleted: 1054
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 357507
% 109.33/109.69 Kept: 77515
% 109.33/109.69 Inuse: 1135
% 109.33/109.69 Deleted: 1054
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 368669
% 109.33/109.69 Kept: 79516
% 109.33/109.69 Inuse: 1159
% 109.33/109.69 Deleted: 1054
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying clauses:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 380666
% 109.33/109.69 Kept: 81832
% 109.33/109.69 Inuse: 1180
% 109.33/109.69 Deleted: 1181
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 396635
% 109.33/109.69 Kept: 84191
% 109.33/109.69 Inuse: 1195
% 109.33/109.69 Deleted: 1181
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 405851
% 109.33/109.69 Kept: 86982
% 109.33/109.69 Inuse: 1205
% 109.33/109.69 Deleted: 1181
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 412379
% 109.33/109.69 Kept: 89292
% 109.33/109.69 Inuse: 1210
% 109.33/109.69 Deleted: 1181
% 109.33/109.69 Deletedinuse: 6
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 425619
% 109.33/109.69 Kept: 91338
% 109.33/109.69 Inuse: 1234
% 109.33/109.69 Deleted: 1182
% 109.33/109.69 Deletedinuse: 7
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 436748
% 109.33/109.69 Kept: 96682
% 109.33/109.69 Inuse: 1240
% 109.33/109.69 Deleted: 1182
% 109.33/109.69 Deletedinuse: 7
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 *** allocated 6568290 integers for clauses
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 455153
% 109.33/109.69 Kept: 101430
% 109.33/109.69 Inuse: 1275
% 109.33/109.69 Deleted: 1182
% 109.33/109.69 Deletedinuse: 7
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 Resimplifying clauses:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 466076
% 109.33/109.69 Kept: 105859
% 109.33/109.69 Inuse: 1285
% 109.33/109.69 Deleted: 1389
% 109.33/109.69 Deletedinuse: 7
% 109.33/109.69
% 109.33/109.69 Resimplifying inuse:
% 109.33/109.69 Done
% 109.33/109.69
% 109.33/109.69 *** allocated 4378860 integers for termspace/termends
% 109.33/109.69
% 109.33/109.69 Intermediate Status:
% 109.33/109.69 Generated: 473457
% 109.33/109.69 Kept: 107876
% 244.65/245.03 Inuse: 1295
% 244.65/245.03 Deleted: 1389
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 486397
% 244.65/245.03 Kept: 110943
% 244.65/245.03 Inuse: 1310
% 244.65/245.03 Deleted: 1389
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 493799
% 244.65/245.03 Kept: 112981
% 244.65/245.03 Inuse: 1347
% 244.65/245.03 Deleted: 1389
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 506358
% 244.65/245.03 Kept: 116359
% 244.65/245.03 Inuse: 1350
% 244.65/245.03 Deleted: 1389
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 517681
% 244.65/245.03 Kept: 119936
% 244.65/245.03 Inuse: 1360
% 244.65/245.03 Deleted: 1389
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying clauses:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 528454
% 244.65/245.03 Kept: 121951
% 244.65/245.03 Inuse: 1399
% 244.65/245.03 Deleted: 1508
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 538846
% 244.65/245.03 Kept: 128243
% 244.65/245.03 Inuse: 1401
% 244.65/245.03 Deleted: 1508
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 557074
% 244.65/245.03 Kept: 131315
% 244.65/245.03 Inuse: 1415
% 244.65/245.03 Deleted: 1508
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 567487
% 244.65/245.03 Kept: 133903
% 244.65/245.03 Inuse: 1435
% 244.65/245.03 Deleted: 1508
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 579374
% 244.65/245.03 Kept: 136579
% 244.65/245.03 Inuse: 1455
% 244.65/245.03 Deleted: 1508
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 586096
% 244.65/245.03 Kept: 139705
% 244.65/245.03 Inuse: 1460
% 244.65/245.03 Deleted: 1508
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 594413
% 244.65/245.03 Kept: 143702
% 244.65/245.03 Inuse: 1470
% 244.65/245.03 Deleted: 1508
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying clauses:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 602302
% 244.65/245.03 Kept: 145735
% 244.65/245.03 Inuse: 1499
% 244.65/245.03 Deleted: 1529
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 *** allocated 9852435 integers for clauses
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 636864
% 244.65/245.03 Kept: 150609
% 244.65/245.03 Inuse: 1520
% 244.65/245.03 Deleted: 1529
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 647154
% 244.65/245.03 Kept: 152660
% 244.65/245.03 Inuse: 1540
% 244.65/245.03 Deleted: 1529
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 654676
% 244.65/245.03 Kept: 154698
% 244.65/245.03 Inuse: 1562
% 244.65/245.03 Deleted: 1530
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 662906
% 244.65/245.03 Kept: 156707
% 244.65/245.03 Inuse: 1584
% 244.65/245.03 Deleted: 1530
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 670663
% 244.65/245.03 Kept: 159857
% 244.65/245.03 Inuse: 1594
% 244.65/245.03 Deleted: 1530
% 244.65/245.03 Deletedinuse: 7
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 679305
% 244.65/245.03 Kept: 162802
% 244.65/245.03 Inuse: 1604
% 244.65/245.03 Deleted: 1531
% 244.65/245.03 Deletedinuse: 8
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying clauses:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 689658
% 244.65/245.03 Kept: 164838
% 244.65/245.03 Inuse: 1641
% 244.65/245.03 Deleted: 1663
% 244.65/245.03 Deletedinuse: 8
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 699656
% 244.65/245.03 Kept: 166997
% 244.65/245.03 Inuse: 1667
% 244.65/245.03 Deleted: 1663
% 244.65/245.03 Deletedinuse: 8
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 *** allocated 6568290 integers for termspace/termends
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 728047
% 244.65/245.03 Kept: 171150
% 244.65/245.03 Inuse: 1687
% 244.65/245.03 Deleted: 1663
% 244.65/245.03 Deletedinuse: 8
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 735236
% 244.65/245.03 Kept: 173150
% 244.65/245.03 Inuse: 1703
% 244.65/245.03 Deleted: 1663
% 244.65/245.03 Deletedinuse: 8
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 745724
% 244.65/245.03 Kept: 175248
% 244.65/245.03 Inuse: 1727
% 244.65/245.03 Deleted: 1664
% 244.65/245.03 Deletedinuse: 9
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 Done
% 244.65/245.03
% 244.65/245.03
% 244.65/245.03 Intermediate Status:
% 244.65/245.03 Generated: 756822
% 244.65/245.03 Kept: 177291
% 244.65/245.03 Inuse: 1736
% 244.65/245.03 Deleted: 1664
% 244.65/245.03 Deletedinuse: 9
% 244.65/245.03
% 244.65/245.03 Resimplifying inuse:
% 244.65/245.03 DCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------