TSTP Solution File: SWW248+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW248+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 23:21:33 EDT 2022
% Result : Timeout 300.02s 300.46s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW248+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jun 4 08:19:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.35/1.68 *** allocated 10000 integers for termspace/termends
% 1.35/1.68 *** allocated 10000 integers for clauses
% 1.35/1.68 *** allocated 10000 integers for justifications
% 1.35/1.68 *** allocated 15000 integers for termspace/termends
% 1.35/1.68 *** allocated 22500 integers for termspace/termends
% 1.35/1.68 *** allocated 33750 integers for termspace/termends
% 1.35/1.68 Bliksem 1.12
% 1.35/1.68
% 1.35/1.68
% 1.35/1.68 Automatic Strategy Selection
% 1.35/1.68
% 1.35/1.68 *** allocated 50625 integers for termspace/termends
% 1.35/1.68 *** allocated 75937 integers for termspace/termends
% 1.35/1.68 *** allocated 113905 integers for termspace/termends
% 1.35/1.68 *** allocated 170857 integers for termspace/termends
% 1.35/1.68
% 1.35/1.68 Clauses:
% 1.35/1.68
% 1.35/1.68 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), !
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.35/1.68 c_Polynomial_Opoly( t_a, v_p ) ) }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), ! skol2 = c_Groups_Ozero__class_Ozero( t_a )
% 1.35/1.68 }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_cs____ ),
% 1.35/1.68 skol2 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), ! skol3 = c_Groups_Ozero__class_Ozero( t_a )
% 1.35/1.68 }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_cs____ ),
% 1.35/1.68 skol3 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.35/1.68 ( hAPP( c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.35/1.68 , Y ) ) ) }.
% 1.35/1.68 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.68 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.68 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.35/1.68 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.35/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.68 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.35/1.68 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.35/1.68 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.35/1.68 .
% 1.35/1.68 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.35/1.68 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.35/1.68 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Nat_Onat ) }.
% 1.35/1.68 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.35/1.68 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.35/1.68 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.35/1.68 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.35/1.68 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.68 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.35/1.68 , Z ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 1.35/1.68 , Y ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.35/1.68 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.35/1.68 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.68 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.68 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.68 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.35/1.68 X, T ) = hAPP( X, U ) }.
% 1.35/1.68 { ! hAPP( X, skol4( X ) ) = hAPP( X, skol23( X ) ),
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ),
% 1.35/1.68 c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), !
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ),
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.68 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 1.35/1.68 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.68 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.35/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.68 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.35/1.68 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.68 ( X ), T ), Z ) ), Y ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 1.35/1.68 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), U = Z }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 1.35/1.68 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), T = Y }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, hAPP( hAPP(
% 1.35/1.68 c_Polynomial_OpCons( X ), U ), T ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.35/1.68 , Z ), Y ) }.
% 1.35/1.68 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.35/1.68 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.35/1.68 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.35/1.68 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.35/1.68 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.35/1.68 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 1.35/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.35/1.68 ( X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.68 = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.35/1.68 tc_Nat_Onat ) ) = Y }.
% 1.35/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.35/1.68 tc_Nat_Onat ) ) = Y }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.35/1.68 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.35/1.68 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.68 c_Polynomial_OpCons( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.68 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.68 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.35/1.68 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.35/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.35/1.68 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.68 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.35/1.68 ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.35/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 1.35/1.68 ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.35/1.68 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.35/1.68 ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.35/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.35/1.68 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.35/1.68 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.35/1.68 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.35/1.68 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.35/1.68 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 1.35/1.68 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), !
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.35/1.68 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), v_c____
% 1.35/1.68 ), v_cs____ ) ) ) }.
% 1.35/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.35/1.68 .
% 1.35/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.35/1.68 .
% 1.35/1.68 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.68 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.35/1.68 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), ! skol5 = c_Groups_Ozero__class_Ozero( t_a )
% 1.35/1.68 }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, skol29 ) ),
% 1.35/1.68 skol24 ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a,
% 1.35/1.68 v_cs____ ) }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), X
% 1.35/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( t_a ), X ), skol24 ) ), hAPP(
% 1.35/1.68 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), skol5 )
% 1.35/1.68 , skol29 ) ), X ) ) }.
% 1.35/1.68 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.35/1.68 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 1.35/1.68 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 1.35/1.68 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.68 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = Y }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.68 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.35/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y )
% 1.35/1.68 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 1.35/1.68 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.35/1.68 ( X ) ), Z ), Y ) ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.68 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.68 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ), Y = X }.
% 1.35/1.68 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.68 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.68 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ) }.
% 1.35/1.68 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), hAPP( c_Nat_OSuc, X )
% 1.35/1.68 ) = hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y
% 1.35/1.68 ), X ) ) }.
% 1.35/1.68 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 1.35/1.68 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 1.35/1.68 { ! Y = X, hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.68 { ! hAPP( c_Nat_OSuc, X ) = X }.
% 1.35/1.68 { ! X = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.68 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.68 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.68 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.35/1.68 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = hAPP
% 1.35/1.68 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = hAPP
% 1.35/1.68 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.35/1.68 = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.35/1.68 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.35/1.68 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP(
% 1.35/1.68 c_Nat_OSuc, X ) ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.35/1.68 , Y ) ), X ) = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.68 ( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.35/1.68 , Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y
% 1.35/1.68 ), hAPP( c_Nat_OSuc, X ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.68 c_Nat_OSuc, Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.68 tc_Nat_Onat ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.68 tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), hAPP(
% 1.35/1.68 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.35/1.68 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 1.35/1.68 ) ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( c_Nat_OSuc,
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc
% 1.35/1.68 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.35/1.68 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.35/1.68 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.35/1.68 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = hAPP( c_Nat_OSuc
% 1.35/1.68 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP(
% 1.35/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha1( X, Y
% 1.35/1.68 ), alpha22( X, Y ) }.
% 1.35/1.68 { ! alpha1( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.68 , Y ), X ) }.
% 1.35/1.68 { ! alpha22( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.68 , Y ), X ) }.
% 1.35/1.68 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! alpha22( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 1.35/1.68 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 1.35/1.68 { ! alpha1( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.35/1.68 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.35/1.68 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y
% 1.35/1.68 ), alpha23( X, Y ) }.
% 1.35/1.68 { ! alpha2( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.68 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.68 ) }.
% 1.35/1.68 { ! alpha23( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.35/1.68 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.68 ) }.
% 1.35/1.68 { ! alpha23( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! alpha23( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 1.35/1.68 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha23( X, Y ) }.
% 1.35/1.68 { ! alpha2( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.35/1.68 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.35/1.68 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Nat_OSuc,
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.68 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.68 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.35/1.68 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.68 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.35/1.68 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.68 hAPP( c_Nat_OSuc, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.35/1.68 , Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.35/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.35/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.35/1.68 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.68 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.35/1.68 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.35/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.35/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 1.35/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.35/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.35/1.68 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.35/1.68 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 1.35/1.68 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.35/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.68 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.35/1.68 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.35/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.35/1.68 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.35/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.35/1.68 .
% 1.35/1.68 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.35/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.35/1.68 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.35/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.35/1.68 .
% 1.35/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.35/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.35/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 1.35/1.68 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.35/1.68 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.35/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 1.35/1.68 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.35/1.68 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.35/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.68 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.35/1.68 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.68 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.68 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.35/1.68 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.35/1.68 , Y ), X ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.35/1.68 tc_Nat_Onat ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.35/1.68 tc_Nat_Onat ) }.
% 1.35/1.68 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.68 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.68 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 1.35/1.68 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 1.35/1.68 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 1.35/1.68 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.68 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.35/1.68 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.35/1.68 = Y }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ),
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.35/1.68 c_Polynomial_Opoly( t_a, v_cs____ ) ), ! skol6 =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.35/1.68 { ! class_Rings_Oidom( t_a ),
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.35/1.68 c_Polynomial_Opoly( t_a, v_cs____ ) ), alpha49( skol6 ) }.
% 1.35/1.68 { ! alpha49( X ), ! skol7( Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.68 }.
% 1.35/1.68 { ! alpha49( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, skol25( X ) ) ),
% 1.35/1.68 skol7( X ) ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ) }.
% 1.35/1.68 { ! alpha49( X ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), Y ) = hAPP(
% 1.35/1.68 hAPP( c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 1.35/1.68 v_cs____ ), c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( t_a ), Y ), skol7( X ) ) ), hAPP(
% 1.35/1.68 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ),
% 1.35/1.68 skol25( X ) ) ), Y ) ) ) }.
% 1.35/1.68 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, Z ) ), Y ) ),
% 1.35/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.35/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, v_cs____ ), !
% 1.35/1.68 hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), skol30( X, Y, Z ) ) = hAPP(
% 1.35/1.68 hAPP( c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 1.35/1.68 v_cs____ ), c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.35/1.68 c_Power_Opower__class_Opower( t_a ), skol30( X, Y, Z ) ), Y ) ), hAPP(
% 1.35/1.68 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ), Z )
% 1.35/1.68 ), skol30( X, Y, Z ) ) ) ), alpha49( X ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, hAPP(
% 1.35/1.68 hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.68 c_Polynomial_OpCons( X ), T ), c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.68 ( tc_Polynomial_Opoly( X ) ), Y ), c_Polynomial_Opcompose( X, Z, Y ) ) )
% 1.35/1.68 }.
% 1.35/1.68 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.68 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.68 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.68 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 1.35/1.68 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 1.35/1.68 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.35/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.35/1.68 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.35/1.68 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.35/1.68 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.35/1.68 .
% 1.35/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.68 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.68 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.68 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.35/1.68 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.35/1.68 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.68 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.68 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.68 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.35/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.68 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.69 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.69 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, Z, Y )
% 1.35/1.69 = c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.35/1.69 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 1.35/1.69 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 1.35/1.69 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 1.35/1.69 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 1.35/1.69 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 1.35/1.69 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 1.35/1.69 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.35/1.69 c_Polynomial_OpCons( X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ) ) ) ), hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), Y ) ) ), Z ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.35/1.69 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.35/1.69 X, Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.35/1.69 Z, hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T ) ) = hAPP( hAPP( hAPP( Z
% 1.35/1.69 , U ), T ), c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.35/1.69 { c_Nat_Onat_Onat__size( hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Nat_Onat_Onat__size( X ) )
% 1.35/1.69 , hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.35/1.69 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.35/1.69 hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.35/1.69 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.35/1.69 ( X ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T, hAPP(
% 1.35/1.69 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y
% 1.35/1.69 ), hAPP( hAPP( hAPP( c_If( W ), hAPP( c_fequal( Y ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), U ),
% 1.35/1.69 c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.35/1.69 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.69 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.69 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), T ), c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP
% 1.35/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.35/1.69 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol8( X
% 1.35/1.69 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol8( X, Y, Z ) ), Z = Y
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.35/1.69 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.35/1.69 c_Polynomial_Ocoeff( X, Y ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.35/1.69 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.35/1.69 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.35/1.69 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.35/1.69 ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.35/1.69 , T ), Z ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), c_Groups_Oone__class_Oone( X ) ), Y ) = Y }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X
% 1.35/1.69 ) ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 1.35/1.69 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 1.35/1.69 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 1.35/1.69 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 1.35/1.69 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.69 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 1.35/1.69 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), T ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.35/1.69 , T ), Z ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Z ), Y ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) ) = Z }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), T ), Z ) ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.35/1.69 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.35/1.69 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.35/1.69 , Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP( c_Polynomial_Osmult
% 1.35/1.69 ( X ), T ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T )
% 1.35/1.69 , Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.35/1.69 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.35/1.69 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 1.35/1.69 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T )
% 1.35/1.69 , Y ), Z ) }.
% 1.35/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.35/1.69 ), Z ), Y ) ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.69 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.35/1.69 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.35/1.69 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 1.35/1.69 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 1.35/1.69 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 1.35/1.69 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 1.35/1.69 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 1.35/1.69 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 1.35/1.69 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.35/1.69 c_Polynomial_Osmult( X ) ), Y ) ) ) ), hAPP( c_Polynomial_OpCons( X ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) ), Z ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, hAPP( c_Nat_OSuc, Y
% 1.35/1.69 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ) ), c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.69 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.35/1.69 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.35/1.69 ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.35/1.69 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 1.35/1.69 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), Z ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.35/1.69 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.35/1.69 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.35/1.69 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP
% 1.35/1.69 ( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ), hAPP(
% 1.35/1.69 c_COMBS( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X )
% 1.35/1.69 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Groups_Oplus__class_Oplus(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), hAPP( c_Polynomial_Osmult( X ), Y ) ) ) ),
% 1.35/1.69 c_Polynomial_OpCons( X ) ) ), Z ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Polynomial_Osmult( X ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.35/1.69 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X
% 1.35/1.69 , Z ), Y ) ), c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 1.35/1.69 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 1.35/1.69 ( X ), Y ), Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 1.35/1.69 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 1.35/1.69 ( X ), Y ), Z ), Z = c_Polynomial_Osynthetic__div( X, U, T ) }.
% 1.35/1.69 { c_Nat_Osize__class_Osize( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ) ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.69 c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) ), hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), Y ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ),
% 1.35/1.69 hAPP( hAPP( c_Polynomial_OpCons( X ), T ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.35/1.69 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 1.35/1.69 hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat ),
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 1.35/1.69 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), Z ), Y ) = c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBB( X, X,
% 1.35/1.69 tc_Nat_Onat ), hAPP( c_Groups_Otimes__class_Otimes( X ), Z ) ),
% 1.35/1.69 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.35/1.69 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) }.
% 1.35/1.69 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.35/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 1.35/1.69 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OAbs__poly( X, hAPP( c_COMBK( X
% 1.35/1.69 , tc_Nat_Onat ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) =
% 1.35/1.69 c_Polynomial_OAbs__poly( X, hAPP( c_COMBC( tc_Nat_Onat, X, X, hAPP(
% 1.35/1.69 c_COMBC( tc_Nat_Onat, X, tc_fun( X, X ), hAPP( hAPP( c_COMBB(
% 1.35/1.69 tc_HOL_Obool, tc_fun( X, tc_fun( X, X ) ), tc_Nat_Onat ), c_If( X ) ),
% 1.35/1.69 c_fequal( Y ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.35/1.69 ) = hAPP( c_Polynomial_Opoly( X, T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.35/1.69 hAPP( hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ),
% 1.35/1.69 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Z ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.35/1.69 , Z ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.69 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z )
% 1.35/1.69 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.35/1.69 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.35/1.69 c_Polynomial_Osynthetic__div( X, Y, Z ) ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Y ), Z ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y )
% 1.35/1.69 = c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 1.35/1.69 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.69 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.35/1.69 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.35/1.69 hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.35/1.69 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Z ), Y ) ) = c_Nat_Onat_Onat__case( X, Z,
% 1.35/1.69 c_Polynomial_Ocoeff( X, Y ) ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Polynomial_Odegree( X, Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.35/1.69 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X
% 1.35/1.69 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X
% 1.35/1.69 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y
% 1.35/1.69 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.35/1.69 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ) ), Y ) =
% 1.35/1.69 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_Polynomial_Opoly( X
% 1.35/1.69 , Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) =
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.35/1.69 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ), Z = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Z ) = Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) = Z }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Y ) = Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Z ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! U = T, Z = Y }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! Z = Y, U = T }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.35/1.69 ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.35/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.35/1.69 ( tc_Int_Oint ) }.
% 1.35/1.69 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.35/1.69 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.35/1.69 }.
% 1.35/1.69 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ), X ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.35/1.69 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 1.35/1.69 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T
% 1.35/1.69 ), Y ), Z ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.35/1.69 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 1.35/1.69 ), Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.35/1.69 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.35/1.69 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ) ), Y ) =
% 1.35/1.69 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_Polynomial_Ocoeff( X
% 1.35/1.69 , Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 ) = Y }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Y ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), ! Z = Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.35/1.69 ), c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.35/1.69 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Y ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), Y = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) = Y, Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Y ) = Y }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), Y ) =
% 1.35/1.69 Z }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), Y ) = Z }.
% 1.35/1.69 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Z ) ), Y ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.35/1.69 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.35/1.69 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.35/1.69 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.35/1.69 Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.35/1.69 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP
% 1.35/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.35/1.69 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP
% 1.35/1.69 ( c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Y ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) = Y }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = Y }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.35/1.69 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.35/1.69 ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), X ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.35/1.69 ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 1.35/1.69 , Z ), Y ) ), X ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.35/1.69 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) = Y }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) = X }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z )
% 1.35/1.69 , hAPP( c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y )
% 1.35/1.69 ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.35/1.69 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 1.35/1.69 hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat ),
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 1.35/1.69 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.35/1.69 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBB( X, X, tc_Nat_Onat ),
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ) ), c_Polynomial_Ocoeff( X, Y ) ) ) }
% 1.35/1.69 .
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP(
% 1.35/1.69 c_Nat_OSuc, X ) ) = hAPP( c_Nat_Onat_Onat__case( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_COMBI( tc_Nat_Onat ) ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.35/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 1.35/1.69 c_Polynomial_Odegree( X, Z ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), Y ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ), Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Y ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.35/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.69 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.35/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y }.
% 1.35/1.69 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.35/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y, hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) )
% 1.35/1.69 , Y ) }.
% 1.35/1.69 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.35/1.69 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.69 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) ) = Y }.
% 1.35/1.69 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), hAPP( c_Nat_OSuc, X ) ) = hAPP( Y
% 1.35/1.69 , X ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP(
% 1.35/1.69 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.35/1.69 Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.35/1.69 c_Nat_OSuc, X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 c_Polynomial_Odegree( X, hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) )
% 1.35/1.69 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 c_Polynomial_Odegree( X, hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) )
% 1.35/1.69 = c_Polynomial_Odegree( X, Y ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.35/1.69 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.35/1.69 ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.35/1.69 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.35/1.69 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Y ), Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), Y ), Z ) ) = hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Polynomial_Odegree( X, Z ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.35/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.35/1.69 ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.69 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.35/1.69 ), c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = X }.
% 1.35/1.69 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc,
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 1.35/1.69 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.35/1.69 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.69 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.69 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ), hAPP(
% 1.35/1.69 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.35/1.69 , Z ), hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y )
% 1.35/1.69 , hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) ) ) ), Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.35/1.69 ), Y ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.35/1.69 ( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.35/1.69 ), Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), hAPP(
% 1.35/1.69 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.69 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP(
% 1.35/1.69 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.35/1.69 ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X
% 1.35/1.69 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.35/1.69 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Y ),
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X )
% 1.35/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ), Y = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 1.35/1.69 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.35/1.69 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 1.35/1.69 }.
% 1.35/1.69 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.69 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = X }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 1.35/1.69 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.35/1.69 ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.35/1.69 ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 1.35/1.69 ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Y ), T ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.35/1.69 , Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.35/1.69 , Z ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.69 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 1.35/1.69 ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) = hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 1.35/1.69 hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T )
% 1.35/1.69 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 Z ), Y ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 1.35/1.69 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.35/1.69 Z ), Y ) ) ), Z = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.35/1.69 X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.35/1.69 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.35/1.69 hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.35/1.69 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.35/1.69 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.35/1.69 X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.35/1.69 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 1.35/1.69 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 1.35/1.69 Z ) ), Z = Y }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.35/1.69 Z ) ), Y ) ), alpha3( X, Y, T ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.35/1.69 Z ) ), Y ) ), alpha24( X, Y, Z, T ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! alpha3( X, Y, T ), ! alpha24( X, Y, Z, T )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 1.35/1.69 { ! alpha24( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z, T ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , Z ), Y ) ), alpha24( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha3( X
% 1.35/1.69 , Y, Z ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ),
% 1.35/1.69 hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 1.35/1.69 hAPP( c_Polynomial_Opoly( X, Y ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) = c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.35/1.69 X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y )
% 1.35/1.69 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.35/1.69 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) )
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ),
% 1.35/1.69 hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.35/1.69 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ), hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ), hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 1.35/1.69 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.35/1.69 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.35/1.69 hAPP( Z, skol9( U, W, Z ) ) ) }.
% 1.35/1.69 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.35/1.69 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), skol9( X, Y, Z ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 1.35/1.69 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), skol26( X, Y, Z ) ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Z, Y ) =
% 1.35/1.69 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP( c_COMBB(
% 1.35/1.69 tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ), hAPP( c_COMBC(
% 1.35/1.69 tc_Nat_Onat, tc_Polynomial_Opoly( X ), tc_HOL_Obool, hAPP( hAPP( c_COMBB
% 1.35/1.69 ( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.35/1.69 tc_HOL_Obool ), tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Nat_Onat,
% 1.35/1.69 tc_Polynomial_Opoly( X ), tc_Nat_Onat ), hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z )
% 1.35/1.69 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.35/1.69 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ) ),
% 1.35/1.69 c_Nat_OSuc ) ) ), Y ) ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) }.
% 1.35/1.69 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) ), hBOOL( hAPP
% 1.35/1.69 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ), hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ) ), ! hBOOL
% 1.35/1.69 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL
% 1.35/1.69 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.69 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.35/1.69 tc_Nat_Onat ) ) ) }.
% 1.35/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.35/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 1.35/1.69 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ),
% 1.35/1.69 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X = hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.69 { ! X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.35/1.69 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) ) ), c_Orderings_Oord__class_OLeast( tc_Nat_Onat, X ) =
% 1.35/1.69 hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.69 ( c_COMBB( tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat ), X ), c_Nat_OSuc ) )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.35/1.69 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 1.35/1.69 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.35/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.35/1.69 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) }.
% 1.35/1.69 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.35/1.69 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.35/1.69 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.35/1.69 ), Z ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.35/1.69 Z ), Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! X = Y }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! Y = X }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , ! Y = X }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.35/1.69 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.35/1.69 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.35/1.69 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.35/1.69 ), Z ) ) }.
% 1.35/1.69 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.35/1.69 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.35/1.69 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.35/1.69 Z ), Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.35/1.69 ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), Y = X }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), Y = X }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.35/1.69 ), Z ) ) }.
% 1.35/1.69 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.35/1.69 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.35/1.69 ), Z ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.35/1.69 , X ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.35/1.69 ), Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , Y = X }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), Y = X }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), X = Y }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.35/1.69 ), Y ) ) }.
% 1.35/1.69 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.35/1.69 , X ) ) }.
% 1.35/1.69 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.35/1.69 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.35/1.69 , X ) ) }.
% 1.35/1.69 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.35/1.69 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.35/1.69 ), Y ) ) }.
% 1.35/1.69 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! alpha4( X, Y ), ! Y = X }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , Y = X, alpha4( X, Y ) }.
% 1.35/1.69 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! alpha4( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), X ), Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , alpha4( X, Y ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , alpha5( X, Y ), Y = X }.
% 1.35/1.69 { ! alpha5( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.35/1.69 , X ) ) }.
% 1.35/1.69 { ! alpha5( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! alpha5( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), X ), Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.35/1.69 , alpha5( X, Y ) }.
% 1.35/1.69 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.35/1.69 , X ) ) }.
% 1.35/1.69 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 1.35/1.69 , Y ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.35/1.69 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.35/1.69 ), Y = X }.
% 1.35/1.69 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.69 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 1.35/1.69 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 1.35/1.69 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.35/1.69 , hAPP( Z, Y ) ) }.
% 1.35/1.69 { ! class_Groups_Ominus( X ), hAPP( hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_fun( U, X ) ), T ), Z ), Y ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( T, Y ) ), hAPP( Z, Y ) )
% 1.35/1.69 }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP(
% 1.35/1.69 c_Nat_OSuc, X ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 1.35/1.69 .
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), hAPP( c_Nat_OSuc, X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.35/1.69 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.35/1.69 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, Y, Z ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.35/1.69 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.69 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.35/1.69 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.35/1.69 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.69 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.35/1.69 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.35/1.69 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.35/1.69 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.35/1.69 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.35/1.69 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.69 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.35/1.69 , ! Y = Z }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.35/1.69 , ! Z = Y }.
% 1.35/1.69 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.69 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.69 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.35/1.69 , ! Z = Y }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.35/1.69 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.35/1.69 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.35/1.69 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.35/1.69 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.69 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.69 Y ), ! Z = Y }.
% 1.35/1.69 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.69 Z ), ! Z = Y }.
% 1.35/1.69 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.69 Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.35/1.69 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.35/1.69 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.35/1.69 { alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.35/1.69 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.35/1.69 { alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.35/1.69 ( X, Y ), Z ) ) }.
% 1.35/1.69 { ! alpha50( X, Y, Z ), alpha52( X, Y, Z ), Z = Y }.
% 1.35/1.69 { ! alpha50( X, Y, Z ), alpha52( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! alpha52( X, Y, Z ), alpha50( X, Y, Z ) }.
% 1.35/1.69 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha50( X, Y, Z ) }.
% 1.35/1.69 { ! alpha52( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.35/1.69 }.
% 1.35/1.69 { ! alpha52( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.35/1.69 X, Y ), Z ) ), alpha52( X, Y, Z ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ), X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) )
% 1.35/1.69 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc
% 1.35/1.69 , X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP
% 1.35/1.69 ( c_Nat_OSuc, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.35/1.69 .
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP(
% 1.35/1.69 c_Nat_OSuc, X ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ), Y
% 1.35/1.69 = X }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ), X
% 1.35/1.69 = Y }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hAPP( c_Nat_OSuc, Y
% 1.35/1.69 ) = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y )
% 1.35/1.69 , X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), Z ) }
% 1.35/1.69 .
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP
% 1.35/1.69 ( c_Nat_OSuc, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.35/1.69 .
% 1.35/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.35/1.69 .
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Z ), Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Y ), Z ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, Z, Y ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, U, T ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), Z ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.35/1.69 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, U, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Orderings_Owellorder( X ), ! c_Orderings_Oord__class_Oless( X, Z
% 1.35/1.69 , c_Orderings_Oord__class_OLeast( X, Y ) ), ! hBOOL( hAPP( Y, Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.35/1.69 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , T ), Z ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 1.35/1.69 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , T ), Y ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 1.35/1.69 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) =
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha6( X, Y, Z, T ),
% 1.35/1.69 alpha25( X, Y, Z, T ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha25( X, Y, Z, T ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha25( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.35/1.69 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.35/1.69 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha6( X, Y, Z, T ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha7( X, Y, Z, T ),
% 1.35/1.69 alpha26( X, Y, Z, T ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z, T ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.69 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha26( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.35/1.69 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.35/1.69 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha7( X, Y, Z, T ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), c_Groups_Ozero__class_Ozero(
% 1.35/1.69 X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, T, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( X ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Y ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.35/1.69 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Y ), Y ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.69 ( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.69 ( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ),
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), X = hAPP( c_Nat_OSuc, skol10( X ) ) }.
% 1.35/1.69 { ! X = hAPP( c_Nat_OSuc, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 1.35/1.69 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP(
% 1.35/1.69 c_Nat_OSuc, X ) ) }.
% 1.35/1.69 { ! alpha8( X, Y ), Y = hAPP( c_Nat_OSuc, skol11( Z, Y ) ) }.
% 1.35/1.69 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol11( X,
% 1.35/1.69 Y ), X ) }.
% 1.35/1.69 { ! Y = hAPP( c_Nat_OSuc, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.69 , Z, X ), alpha8( X, Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.35/1.69 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.69 Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, hAPP(
% 1.35/1.69 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = hAPP(
% 1.35/1.69 c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.35/1.69 skol12( X, Y ) ) ) }.
% 1.35/1.69 { ! X = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.69 tc_Nat_Onat ), Y ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.35/1.69 , X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.35/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), Z ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.35/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.35/1.69 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.35/1.69 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.69 Y ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.35/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.35/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.69 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.69 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.69 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.69 tc_Nat_Onat ), X ), Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 1.35/1.69 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.35/1.69 Y ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.35/1.69 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.69 c_Nat_OSuc, Z ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.35/1.69 X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.35/1.69 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.35/1.69 c_Nat_OSuc, Z ) ), X ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), hAPP( c_Nat_OSuc
% 1.35/1.69 , Y ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = Y }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.35/1.69 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.35/1.69 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.35/1.69 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.35/1.69 ), X ) ) }.
% 1.35/1.69 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.35/1.69 , c_Polynomial_Odegree( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), Y ), Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.35/1.69 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.35/1.69 , c_Polynomial_Odegree( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.35/1.69 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.35/1.69 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.35/1.69 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z
% 1.35/1.69 ), T ) ), Y ) }.
% 1.35/1.69 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.35/1.69 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.35/1.69 X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , Z ), T ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ), ! Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.35/1.69 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.35/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ), Y ) }.
% 1.35/1.69 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc
% 1.35/1.69 , Y ) ), X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.69 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.35/1.69 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.35/1.69 ), Y ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.69 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.35/1.69 , Y ) ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.35/1.69 ), Y ), X ) ) ), ! alpha9( X, Y, Z ) }.
% 1.35/1.69 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.35/1.69 ), Y ), X ) ) ), ! alpha27( X, Y, Z ) }.
% 1.35/1.69 { alpha9( X, Y, Z ), alpha27( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.69 { ! alpha27( X, Y, Z ), ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ) }.
% 1.35/1.69 { ! alpha27( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.69 tc_Nat_Onat ), X ), skol13( X, Y, Z ) ) }.
% 1.35/1.69 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 1.35/1.69 hBOOL( hAPP( Z, T ) ), alpha27( X, Y, Z ) }.
% 1.35/1.69 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.35/1.69 .
% 1.35/1.69 { ! alpha9( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ) ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha9( X, Y, Z ) }.
% 1.35/1.69 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.35/1.69 ), Y ), X ) ) ), alpha10( X, Y, Z ) }.
% 1.35/1.69 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.35/1.69 ), Y ), X ) ) ), alpha28( X, Y, Z ) }.
% 1.35/1.69 { ! alpha10( X, Y, Z ), ! alpha28( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.35/1.69 { ! alpha28( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.69 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( Z, skol14( T, U, Z ) ) ), alpha28( X, Y, Z ) }.
% 1.35/1.69 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol14(
% 1.35/1.69 X, Y, Z ) ), alpha28( X, Y, Z ) }.
% 1.35/1.69 { ! alpha10( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.35/1.69 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha10( X, Y, Z ) }
% 1.35/1.69 .
% 1.35/1.69 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha10
% 1.35/1.69 ( X, Y, Z ) }.
% 1.35/1.69 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.35/1.69 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.35/1.69 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Groups_Ominus( X ), hAPP( hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_fun( U, X ) ), T ), Z ), Y ) = hAPP(
% 1.35/1.69 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( T, Y ) ), hAPP( Z, Y ) )
% 1.35/1.69 }.
% 1.35/1.69 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.35/1.69 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Lattices_Oboolean__algebra( X ), ! hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 1.35/1.69 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y, hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.35/1.69 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.35/1.69 , hAPP( Z, Y ) ) }.
% 1.35/1.69 { ! class_Lattices_Oboolean__algebra( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.35/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ),
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 1.35/1.69 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.69 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.35/1.69 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), X = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.69 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.35/1.69 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.69 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.35/1.69 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.35/1.69 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 1.35/1.69 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.35/1.69 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), Y ) }.
% 1.35/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.35/1.69 ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, hAPP(
% 1.35/1.69 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = hAPP( c_Nat_OSuc,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha53( X, Y, Z, T ), ! Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha53( X, Y, Z, T ), ! hAPP(
% 1.35/1.69 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.35/1.69 .
% 1.35/1.69 { ! alpha53( X, Y, Z, T ), alpha54( X, Y, Z, T ), alpha51( X, Y, T ) }.
% 1.35/1.69 { ! alpha53( X, Y, Z, T ), alpha54( X, Y, Z, T ), ! hAPP(
% 1.35/1.69 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! alpha54( X, Y, Z, T ), alpha53( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha51( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.35/1.69 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.69 alpha53( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha54( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha55( X, Y, Z, T ) }.
% 1.35/1.69 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 Z ), T ) ), alpha54( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha55( X, Y, Z, T ), alpha54( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha55( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), skol15( X, Y, U, W ) ), Y ) ) }.
% 1.35/1.69 { ! alpha55( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), skol15( X, Y, U, T ) ), T ) ) }.
% 1.35/1.69 { ! alpha55( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), skol15( X, Y, Z, T ) ), Z ) ) }.
% 1.35/1.69 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha55
% 1.35/1.69 ( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha51( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! alpha51( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha51( X, Y, Z
% 1.35/1.69 ) }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 1.35/1.69 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.35/1.69 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 1.35/1.69 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.35/1.69 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.35/1.69 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 1.35/1.69 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 1.35/1.69 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.35/1.69 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.35/1.69 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.35/1.69 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 1.35/1.69 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 1.35/1.69 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ) ) ) ), Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), T ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ), Z ), T ) ), c_Orderings_Oord__class_Oless( X, hAPP( Y, T )
% 1.35/1.69 , hAPP( Y, Z ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.35/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.35/1.69 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.35/1.69 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.35/1.69 tc_Int_Oint ) ), X ) ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) )
% 1.35/1.69 , c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.35/1.69 tc_Int_Oint ) ), X ) ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) )
% 1.35/1.69 }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.69 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.69 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.69 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.35/1.69 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.35/1.69 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 1.35/1.69 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.35/1.69 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 1.35/1.69 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.35/1.69 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.35/1.69 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 1.35/1.69 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 1.35/1.69 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.35/1.69 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.35/1.69 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.35/1.69 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 1.35/1.69 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 1.35/1.69 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 1.35/1.69 tc_Nat_Onat ) ) ) ), Y ), c_Orderings_Oorder_Omono( tc_Nat_Onat, X,
% 1.35/1.69 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.69 , U = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) )
% 1.35/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 Z ), T ) ), Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.69 , alpha39( X, Y, Z, T ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! U = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.69 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), Z ), T ) ), Y ), ! alpha39( X, Y, Z, T ),
% 1.35/1.69 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.35/1.69 { ! alpha39( X, Y, Z, T ), alpha11( X, Z, T ) }.
% 1.35/1.69 { ! alpha39( X, Y, Z, T ), alpha29( X, Y, T ) }.
% 1.35/1.69 { ! alpha11( X, Z, T ), ! alpha29( X, Y, T ), alpha39( X, Y, Z, T ) }.
% 1.35/1.69 { ! alpha29( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), alpha40( X, Y, Z ) }.
% 1.35/1.69 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha29( X
% 1.35/1.69 , Y, Z ) }.
% 1.35/1.69 { ! alpha40( X, Y, Z ), alpha29( X, Y, Z ) }.
% 1.35/1.69 { ! alpha40( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.69 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha40( X
% 1.35/1.69 , Y, Z ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.35/1.69 ), c_Polynomial_Odegree( X, Z ) ), alpha40( X, Y, Z ) }.
% 1.35/1.69 { ! alpha11( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X,
% 1.35/1.69 Y, Z ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X
% 1.35/1.69 , Y, Z ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.69 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.69 , c_Polynomial_Opdivmod__rel( X, hAPP( hAPP( c_Polynomial_Osmult( X ), W
% 1.35/1.69 ), U ), T, hAPP( hAPP( c_Polynomial_Osmult( X ), W ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_Osmult( X ), W ), Y ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.35/1.69 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.35/1.69 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.69 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.69 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.69 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.35/1.69 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.35/1.69 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 1.35/1.69 ), W ) ), Y ) ) }.
% 1.35/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.35/1.69 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.35/1.69 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.35/1.69 c_Polynomial_Ocoeff( X, hAPP( hAPP( c_Polynomial_OpCons( X ), W ), Y ) )
% 1.35/1.69 , c_Polynomial_Odegree( X, T ) ) ), hAPP( c_Polynomial_Ocoeff( X, T ),
% 1.35/1.69 c_Polynomial_Odegree( X, T ) ) ), c_Polynomial_Opdivmod__rel( X, hAPP(
% 1.35/1.69 hAPP( c_Polynomial_OpCons( X ), W ), U ), T, hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), V0 ), Z ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.35/1.69 c_Polynomial_OpCons( X ), W ), Y ) ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.35/1.69 ), V0 ), T ) ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.69 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.69 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.35/1.69 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 1.35/1.69 ( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ), c_Polynomial_Opos__poly( X
% 1.35/1.69 , Y ), alpha12( X, Y, Z ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.35/1.69 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! alpha12( X, Y, Z ),
% 1.35/1.69 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.35/1.69 ) ) }.
% 1.35/1.69 { ! alpha12( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.69 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.35/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.35/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.35/1.69 alpha12( X, Y, Z ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.69 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) =
% 1.35/1.69 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Y ), c_Groups_Oone__class_Oone( X )
% 1.35/1.69 ) = Y }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.69 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 1.35/1.69 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Z
% 1.35/1.69 ) ), Y ) }.
% 1.35/1.69 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.69 hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.35/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.35/1.69 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.35/1.69 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , ! hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , ! Z = Y, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) =
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , ! T = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), hAPP
% 1.35/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.35/1.69 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , ! hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z, T =
% 1.35/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), hAPP(
% 1.35/1.69 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), hAPP(
% 1.35/1.69 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z }.
% 1.35/1.69 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.69 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.35/1.69 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.35/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.35/1.69 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.35/1.69 ( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.35/1.69 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.35/1.69 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.35/1.69 ( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.35/1.69 .
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 1.35/1.69 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ), Z
% 1.35/1.69 ) ), c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.35/1.69 { ! class_RealVector_Oreal__field( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ), Y ) = hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), W ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Ominus__class_Ominus( X ), W ), T ) ), Y ) ), Z ) ) }.
% 1.35/1.69 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.35/1.69 c_Polynomial_Opos__poly( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.69 tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.35/1.69 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.69 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.69 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.69 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.35/1.69 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.69 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.70 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), Z ) ), Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), T ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), T ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Y ), T ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Z ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Z ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ), alpha30( X, Y, Z
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 1.35/1.70 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 1.35/1.70 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.70 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.70 ), alpha30( X, Y, Z ) }.
% 1.35/1.70 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.35/1.70 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.35/1.70 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 ), alpha13( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.70 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha14( X, Y,
% 1.35/1.70 Z ), alpha31( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 1.35/1.70 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 1.35/1.70 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.70 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 ), alpha31( X, Y, Z ) }.
% 1.35/1.70 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.35/1.70 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.35/1.70 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.70 ), alpha14( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) = Y, alpha32( X, Y, Z, T )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) = Y, alpha15( X, Y, Z ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha32( X, Y, Z, T ), !
% 1.35/1.70 alpha15( X, Y, Z ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T )
% 1.35/1.70 , Z ) = Y }.
% 1.35/1.70 { ! alpha32( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.35/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.35/1.70 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha32( X, Y, Z, T ) }.
% 1.35/1.70 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha32(
% 1.35/1.70 X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha15( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.35/1.70 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), ! T = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), alpha33( X, Y, Z, T ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), ! T = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), alpha16( X, Y, T ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha33( X, Y, Z, T ), !
% 1.35/1.70 alpha16( X, Y, T ), T = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X )
% 1.35/1.70 , Z ), Y ) }.
% 1.35/1.70 { ! alpha33( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.35/1.70 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.35/1.70 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha33( X, Y, Z, T ) }.
% 1.35/1.70 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha33(
% 1.35/1.70 X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha16( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { Y = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 1.35/1.70 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, T, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, T, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ), alpha34( X, Y, Z, T
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ), alpha41( X, Y, Z, T
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha34( X, Y, Z
% 1.35/1.70 , T ), ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.35/1.70 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ) }.
% 1.35/1.70 { ! alpha41( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Z ), alpha44( X, Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.35/1.70 , alpha41( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha44( X, Y, Z, T ), alpha41( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha44( X, Y, Z, T ), alpha47( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha44( X, Y, Z, T ), alpha17( X, Y, Z ) }.
% 1.35/1.70 { ! alpha47( X, Y, Z, T ), ! alpha17( X, Y, Z ), alpha44( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha47( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.35/1.70 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.70 alpha47( X, Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha47( X, Y, Z, T )
% 1.35/1.70 }.
% 1.35/1.70 { ! alpha34( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.70 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.35/1.70 alpha34( X, Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha34( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.70 , alpha17( X, Y, Z ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.35/1.70 , alpha17( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha35( X, Y, Z, T ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha42( X, Y, Z, T ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 1.35/1.70 , T ), ! alpha42( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, hAPP
% 1.35/1.70 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! alpha42( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ), alpha45( X, Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.35/1.70 , alpha42( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha45( X, Y, Z, T ), alpha42( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha45( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha45( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 1.35/1.70 { ! alpha48( X, Y, Z, T ), ! alpha18( X, Y, T ), alpha45( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha48( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.70 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.70 alpha48( X, Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha48( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha35( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.35/1.70 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.70 alpha35( X, Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha35( X, Y, Z, T )
% 1.35/1.70 }.
% 1.35/1.70 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.70 , alpha18( X, Y, Z ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.70 , alpha18( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), U ), Y ) ), hAPP
% 1.35/1.70 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.70 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z )
% 1.35/1.70 = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.70 hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), Z ) ), Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), T ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) )
% 1.35/1.70 = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.70 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), T ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), T ), Z )
% 1.35/1.70 , Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X
% 1.35/1.70 ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), T ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) ), hAPP(
% 1.35/1.70 hAPP( c_Polynomial_Osmult( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.35/1.70 ( hAPP( c_Polynomial_OpCons( X ), T ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ) ),
% 1.35/1.70 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) ), Y
% 1.35/1.70 ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), hAPP( W, Z ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X, hAPP( hAPP( c_COMBS
% 1.35/1.70 ( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( W, Z ) ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( T, Z ) ) ) ), hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), hAPP( W, Z ) ), hAPP( c_Nat_OSuc, hAPP
% 1.35/1.70 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 1.35/1.70 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Groups_Oone__class_Oone(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.35/1.70 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.35/1.70 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.35/1.70 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, hAPP( hAPP(
% 1.35/1.70 c_Polynomial_Osmult( X ), Y ), Z ) ) = c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Z, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), Y ) ) = c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), Z ), Y ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.70 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.35/1.70 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.35/1.70 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.70 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), c_Deriv_Oderiv( X, hAPP(
% 1.35/1.70 c_COMBK( X, X ), Z ), Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z )
% 1.35/1.70 , Y ) = hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), c_Deriv_Oderiv( X, hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y, Z ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, T, Z, U ), Y = U }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! Y = U, c_Deriv_Oderiv( X, T, Z, U ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! Y = U, c_Deriv_Oderiv( X, T, Z, U ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), c_Deriv_Oderiv( X, hAPP( hAPP( c_COMBB( X, X, X ),
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ) ), T ), Z, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), c_Deriv_Oderiv( X, c_COMBI
% 1.35/1.70 ( X ), Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.35/1.70 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), Y ), U ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.35/1.70 ( X, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.35/1.70 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), U ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, U,
% 1.35/1.70 hAPP( T, Z ), Y ), ! c_Deriv_Oderiv( X, T, Z, W ), c_Deriv_Oderiv( X,
% 1.35/1.70 hAPP( hAPP( c_COMBB( X, X, X ), U ), T ), Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), W ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, W, hAPP( T, Z ), U ), c_Deriv_Oderiv( X, hAPP(
% 1.35/1.70 hAPP( c_COMBB( X, X, X ), W ), T ), Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), c_Deriv_Oderiv( X, hAPP( hAPP( c_COMBB( X, X, X ), hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ) ), T ), Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), c_Deriv_Oderiv( X, hAPP( c_COMBC( X, X, X, hAPP( hAPP( c_COMBB( X,
% 1.35/1.70 tc_fun( X, X ), X ), c_Rings_Oinverse__class_Odivide( X ) ), T ) ), U ),
% 1.35/1.70 Z, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), U ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.35/1.70 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( T, Z ) ), U ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( W, Z ) ) ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.35/1.70 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( W, Z ) ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( T, Z ) ) ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.35/1.70 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ) ), T ) ), hAPP( hAPP( c_COMBB( X, X, X )
% 1.35/1.70 , c_Groups_Ouminus__class_Ouminus( X ) ), W ) ), Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), U ) ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.70 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.35/1.70 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.35/1.70 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.35/1.70 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.35/1.70 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), hAPP( W, Z ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X, hAPP( hAPP( c_COMBS
% 1.35/1.70 ( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( W, Z ) ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( T, Z ) ), U ) ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( W, Z ) ), hAPP( W, Z ) ) ) ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.70 c_Groups_Osgn__class_Osgn( X, Y ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.70 ( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.35/1.70 ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.35/1.70 = hAPP( c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone
% 1.35/1.70 ( X ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.35/1.70 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.35/1.70 ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 1.35/1.70 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 1.35/1.70 Z ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 1.35/1.70 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.35/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.35/1.70 ( tc_Int_Oint, Y, X ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.35/1.70 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, Y, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X )
% 1.35/1.70 ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, Y, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X )
% 1.35/1.70 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.35/1.70 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X
% 1.35/1.70 ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X
% 1.35/1.70 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ), Y ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), c_Divides_Odiv__class_Omod
% 1.35/1.70 ( tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z
% 1.35/1.70 ), X ), Y ) }.
% 1.35/1.70 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol16( X, Y ) ) }.
% 1.35/1.70 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.35/1.70 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 1.35/1.70 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 1.35/1.70 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.35/1.70 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.35/1.70 }.
% 1.35/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol17( X, Y ) ) }.
% 1.35/1.70 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.35/1.70 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.70 { ! hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X
% 1.35/1.70 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.70 { hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.35/1.70 hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.35/1.70 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.70 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP( hAPP
% 1.35/1.70 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.35/1.70 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.35/1.70 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), Z )
% 1.35/1.70 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) ) }.
% 1.35/1.70 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.35/1.70 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.35/1.70 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), X ) ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.35/1.70 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ) ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.35/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.35/1.70 alpha19( X, Y, Z ) }.
% 1.35/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.35/1.70 alpha36( X, Y, Z ) }.
% 1.35/1.70 { ! alpha19( X, Y, Z ), ! alpha36( X, Y, Z ), hBOOL( hAPP( Z,
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 1.35/1.70 { ! alpha36( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.70 alpha43( X, Y, Z ) }.
% 1.35/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha36( X, Y, Z ) }.
% 1.35/1.70 { ! alpha43( X, Y, Z ), alpha36( X, Y, Z ) }.
% 1.35/1.70 { ! alpha43( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.35/1.70 ), alpha46( X, Y, Z, T ) }.
% 1.35/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol18( X, T, U ), X ),
% 1.35/1.70 alpha43( X, Y, Z ) }.
% 1.35/1.70 { ! alpha46( X, Y, Z, skol18( X, Y, Z ) ), alpha43( X, Y, Z ) }.
% 1.35/1.70 { ! alpha46( X, Y, Z, T ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.70 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.35/1.70 X ), U ) ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.35/1.70 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol19( X, Y, T ) ) )
% 1.35/1.70 , T ), alpha46( X, Y, Z, T ) }.
% 1.35/1.70 { ! hBOOL( hAPP( Z, T ) ), alpha46( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha19( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.70 hBOOL( hAPP( Z, Y ) ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha19( X, Y, Z ) }.
% 1.35/1.70 { ! hBOOL( hAPP( Z, Y ) ), alpha19( X, Y, Z ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.35/1.70 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP(
% 1.35/1.70 c_Nat_OSuc, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.35/1.70 , Y ) ), X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.35/1.70 X, Z, Y ) }.
% 1.35/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.70 c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) =
% 1.35/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ), X ), c_Groups_Osgn__class_Osgn( tc_Int_Oint, X ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), c_Groups_Oone__class_Oone
% 1.35/1.70 ( tc_Int_Oint ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.35/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.70 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.70 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.70 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.35/1.70 , Y ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.35/1.70 ), Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.35/1.70 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.35/1.70 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.35/1.70 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.35/1.70 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, Z, Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Z ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, Y, Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.70 ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.70 ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.70 ), c_Divides_Odiv__class_Omod( X, T, Y ) ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 X, Z, Y ) ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), c_Divides_Odiv__class_Omod
% 1.35/1.70 ( X, Z, Y ) ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Omod( X,
% 1.35/1.70 T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.35/1.70 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.35/1.70 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.35/1.70 ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), U ), Z ) }.
% 1.35/1.70 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.35/1.70 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.35/1.70 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.70 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), Y ), U ), Z ) }.
% 1.35/1.70 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.35/1.70 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.70 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.70 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.35/1.70 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.70 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.35/1.70 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.35/1.70 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.35/1.70 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.70 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.35/1.70 , c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.35/1.70 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.35/1.70 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 1.35/1.70 hAPP( c_Groups_Ouminus__class_Ouminus( X ), T ), Z ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.35/1.70 , Y ), Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.35/1.70 ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.35/1.70 ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 1.35/1.70 , c_Divides_Odiv__class_Omod( X, T, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.35/1.70 ( X, T, Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, Y, T )
% 1.35/1.70 ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.35/1.70 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ),
% 1.35/1.70 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.35/1.70 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), hAPP( T, Z ) = c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X,
% 1.35/1.70 hAPP( hAPP( c_COMBB( X, X, X ), c_Rings_Oinverse__class_Oinverse( X ) ),
% 1.35/1.70 T ), Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), hAPP( T, Z ) ), hAPP( c_Nat_OSuc, hAPP
% 1.35/1.70 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) ) ) ) }
% 1.35/1.70 .
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.35/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.35/1.70 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.35/1.70 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) = hAPP( hAPP
% 1.35/1.70 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.35/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ) ), X ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) }.
% 1.35/1.70 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.35/1.70 ( tc_Int_Oint, Z, Y ) ), Y ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 1.35/1.70 Z, Y ) ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint )
% 1.35/1.70 , Z ), X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ), X ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) )
% 1.35/1.70 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.35/1.70 , X ) ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ) ) = X }.
% 1.35/1.70 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 1.35/1.70 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), c_Divides_Odiv__class_Odiv( X, Y, Z
% 1.35/1.70 ) ) }.
% 1.35/1.70 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 1.35/1.70 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), c_Divides_Odiv__class_Odiv( X, Y, Z
% 1.35/1.70 ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.35/1.70 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ), hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.35/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), c_Divides_Odiv__class_Odiv( X
% 1.35/1.70 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z ) = hAPP(
% 1.35/1.70 hAPP( c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Odiv( X, Y
% 1.35/1.70 , Z ) ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.35/1.70 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.35/1.70 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.35/1.70 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.35/1.70 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.35/1.70 ), Z ) = Y }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv( X, Y
% 1.35/1.70 , Z ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 1.35/1.70 , Z ) ) = Y }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.35/1.70 }.
% 1.35/1.70 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.35/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.35/1.70 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ), Y ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide(
% 1.35/1.70 X ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP
% 1.35/1.70 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.70 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Oone__class_Oone( X
% 1.35/1.70 ), Y = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.35/1.70 c_Groups_Oone__class_Oone( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.70 ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( c_Rings_Oinverse__class_Oinverse
% 1.35/1.70 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, hAPP( c_Rings_Oinverse__class_Oinverse
% 1.35/1.70 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.70 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.35/1.70 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z = Y }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z = Y }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y, hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = Y }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.35/1.70 ( X ), Z ) ), Y ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Oone__class_Oone( X ) ) =
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.35/1.70 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.35/1.70 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , ! hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = Y }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), ! hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), ! hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.35/1.70 = Y }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.35/1.70 ( X ), Y ) ), Z ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.35/1.70 ( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ) = Y }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ),
% 1.35/1.70 Y ) = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ),
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Y
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.35/1.70 ( X ), Y ) ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP(
% 1.35/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.35/1.70 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.35/1.70 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.35/1.70 X, c_Groups_Oone__class_Oone( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.35/1.70 ( X ), Y ) ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y ) =
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = c_Groups_Oone__class_Oone
% 1.35/1.70 ( X ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.35/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y ) =
% 1.35/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) = hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Y
% 1.35/1.70 ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.35/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.35/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, X, Y ), X ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.35/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, Z, Y ), X ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.35/1.70 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.35/1.70 X, W, hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), U ), hAPP( hAPP(
% 1.35/1.70 c_Polynomial_Osmult( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y
% 1.35/1.70 ) ), T ), Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y
% 1.35/1.70 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y
% 1.35/1.70 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), Y ), Z ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! c_Divides_Odiv__class_Odiv(
% 1.35/1.70 X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.35/1.70 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), !
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T, Z = hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), ! Z =
% 1.35/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( X, T, Z ) ) ), Y ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.35/1.70 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, Z, T ) ) ), c_Divides_Odiv__class_Omod( X
% 1.35/1.70 , Z, T ) ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.35/1.70 ), Y ) ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 1.35/1.70 , Z ) ) ), c_Divides_Odiv__class_Omod( X, Y, Z ) ) = Y }.
% 1.35/1.70 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Omod( X, Z, Y ) )
% 1.35/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), Y ) ) = Z }.
% 1.35/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 1.35/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) = hAPP(
% 1.35/1.70 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, Z, Y ), X ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z
% 1.35/1.70 , Y ) ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, Y, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X )
% 1.35/1.70 ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, Y, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X )
% 1.35/1.70 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X
% 1.35/1.70 ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X
% 1.35/1.70 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.35/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.35/1.70 Y ), hAPP( T, Z ) = c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X,
% 1.35/1.70 hAPP( hAPP( c_COMBB( X, X, X ), c_Rings_Oinverse__class_Oinverse( X ) ),
% 1.35/1.70 T ), Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP( T, Z ) ) ), Y ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), hAPP( T, Z ) ) ) ) ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.70 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) ), T ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) ), T ) ) ), hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = hAPP( hAPP(
% 1.35/1.70 c_Polynomial_Osmult( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ),
% 1.35/1.70 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) ), Y
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X,
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y, hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.35/1.70 ( X ), Y ) ), hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) = hAPP(
% 1.35/1.70 hAPP( c_Polynomial_Osmult( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X
% 1.35/1.70 ), hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) )
% 1.35/1.70 , Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.35/1.70 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha20( X, Y, T,
% 1.35/1.70 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha20( X, Y, skol20( X, Y
% 1.35/1.70 , Z ), skol27( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.35/1.70 skol20( X, Y, Z ) ), skol27( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.70 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 1.35/1.70 ) }.
% 1.35/1.70 { ! alpha20( X, Y, Z, T ), alpha37( X, Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha37( X, Y, Z
% 1.35/1.70 , T ), alpha20( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha37( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.35/1.70 { ! alpha37( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.70 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.70 X ), Z ) ), T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y = hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha37( X
% 1.35/1.70 , Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 1.35/1.70 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 1.35/1.70 ) ), ! alpha21( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), alpha21( X, Y, skol21( X, Y, Z ), skol28( X, Y, Z )
% 1.35/1.70 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 1.35/1.70 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol21( X, Y, Z ) ), skol28
% 1.35/1.70 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.35/1.70 ) }.
% 1.35/1.70 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 1.35/1.70 { ! alpha21( X, Y, Z, T ), alpha38( X, Y, Z, T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha38( X, Y, Z, T )
% 1.35/1.70 , alpha21( X, Y, Z, T ) }.
% 1.35/1.70 { ! alpha38( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.35/1.70 ) }.
% 1.35/1.70 { ! alpha38( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.35/1.70 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.35/1.70 X ), Z ) ), T ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y = hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha38( X
% 1.35/1.70 , Y, Z, T ) }.
% 1.35/1.70 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.35/1.70 , Y ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Nat_Onat, Z, X ) ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) )
% 1.35/1.70 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Nat_Onat, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) )
% 1.35/1.70 , X ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.35/1.70 tc_Int_Oint, X, Y ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Int_Oint, X, Y ) ) }.
% 1.35/1.70 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Nat_Onat, Z, Y ), X ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 1.35/1.70 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.35/1.70 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.70 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.35/1.70 ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.35/1.70 X ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.35/1.70 c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.35/1.70 X ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.35/1.70 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.35/1.70 ( X ), T, Z ), Y ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Polynomial_Opoly( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), Z ), Y ) = hAPP(
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Z, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ), Y ) ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 1.35/1.70 ( tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.35/1.70 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z )
% 1.35/1.70 , Y ) = hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.35/1.70 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.35/1.70 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.35/1.70 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 1.35/1.70 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.35/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.35/1.70 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.35/1.70 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 1.35/1.70 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.35/1.70 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 1.35/1.70 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.35/1.70 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.35/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.35/1.70 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.35/1.70 ( X ) ) }.
% 1.35/1.70 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.35/1.70 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.70 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.35/1.70 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.35/1.70 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.35/1.70 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.35/1.70 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.35/1.70 { ! class_Rings_Oordered__semiring( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.35/1.70 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.35/1.70 { ! class_Rings_Oordered__semiring( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.35/1.70 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.35/1.70 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.35/1.70 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.35/1.70 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.35/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.35/1.70 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.35/1.70 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.35/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.35/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.35/1.70 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.35/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.35/1.70 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ),
% 1.35/1.70 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ouminus( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ominus( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.35/1.70 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.35/1.70 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.35/1.70 ( tc_fun( Y, X ) ) }.
% 1.35/1.70 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.35/1.70 ) ) }.
% 1.35/1.70 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.35/1.70 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.35/1.70 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.35/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.35/1.70 tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.35/1.70 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.35/1.70 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.35/1.70 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.35/1.70 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.35/1.70 { class_Power_Opower( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.35/1.70 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.35/1.70 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.35/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.35/1.70 tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Orderings_Owellorder( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.35/1.70 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.35/1.70 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.35/1.70 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.35/1.70 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.35/1.70 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.35/1.70 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ),
% 1.35/1.70 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.35/1.70 ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.35/1.70 X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.35/1.70 ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.35/1.70 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.35/1.70 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.35/1.70 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.35/1.70 ( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.35/1.70 ( tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.35/1.70 ( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.35/1.70 }.
% 1.35/1.70 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.35/1.70 ) ) }.
% 1.35/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.35/1.70 .
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.35/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.35/1.70 { hAPP( c_COMBI( Y ), X ) = X }.
% 1.35/1.70 { hAPP( hAPP( c_COMBK( T, Z ), Y ), X ) = Y }.
% 1.35/1.70 { hAPP( hAPP( hAPP( c_COMBB( W, U, T ), Z ), Y ), X ) = hAPP( Z, hAPP( Y, X
% 1.35/1.70 ) ) }.
% 1.35/1.70 { hAPP( hAPP( c_COMBC( W, U, T, Z ), Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 1.35/1.70 { hAPP( hAPP( hAPP( c_COMBS( W, U, T ), Z ), Y ), X ) = hAPP( hAPP( Z, X )
% 1.35/1.70 , hAPP( Y, X ) ) }.
% 1.35/1.70 { ! hBOOL( hAPP( c_fequal( Y ), X ) ), Y = X }.
% 1.35/1.70 { ! Y = X, hBOOL( hAPP( c_fequal( Y ), X ) ) }.
% 1.35/1.70 { ! hBOOL( c_fFalse ) }.
% 1.35/1.70 { hBOOL( c_fTrue ) }.
% 1.35/1.70 { ! hBOOL( hAPP( c_fNot, X ) ), ! hBOOL( X ) }.
% 1.35/1.70 { hBOOL( X ), hBOOL( hAPP( c_fNot, X ) ) }.
% 1.35/1.70 { ! hBOOL( X ), ! hBOOL( Y ), hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ) }.
% 1.35/1.70 { ! hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ), hBOOL( X ) }.
% 1.35/1.70 { ! hBOOL( hAPP( hAPP( c_fconj, Y ), X ) ), hBOOL( X ) }.
% 1.35/1.70 { X = c_Groups_Ozero__class_Ozero( t_a ), Y = c_Groups_Ozero__class_Ozero(
% 1.35/1.70 tc_Nat_Onat ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.70 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.35/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, Z ) ), Y ) ),
% 1.35/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.35/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, hAPP( hAPP(
% 1.35/1.70 c_Polynomial_OpCons( t_a ), v_c____ ), v_cs____ ) ), ! hAPP(
% 1.35/1.70 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), v_c____
% 1.35/1.70 ), v_cs____ ) ), skol22( X, Y, Z ) ) = hAPP( hAPP(
% 1.35/1.70 c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a, hAPP(
% 1.35/1.70 hAPP( c_Polynomial_OpCons( t_a ), v_c____ ), v_cs____ ) ),
% 1.35/1.70 c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 1.35/1.70 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.35/1.70 c_Power_Opower__class_Opower( t_a ), skol22( X, Y, Z ) ), Y ) ), hAPP(
% 1.35/1.70 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ), Z )
% 1.35/1.70 ), skol22( X, Y, Z ) ) ) ) }.
% 1.35/1.70 { class_Rings_Oidom( t_a ) }.
% 1.35/1.70
% 1.35/1.70 *** allocated 15000 integers for clauses
% 1.35/1.70 *** allocated 22500 integers for clauses
% 1.35/1.70 *** allocated 33750 integers for clauses
% 1.35/1.70 *** allocated 50625 integers for clauses
% 1.35/1.70 *** allocated 75937 integers for clauses
% 1.35/1.70 *** allocated 113905 integers for clauses
% 1.35/1.70 percentage equality = 0.337590, percentage horn = 0.871281
% 1.35/1.70 This is a problem with some equality
% 1.35/1.70
% 1.35/1.70
% 1.35/1.70
% 1.35/1.70 Options Used:
% 1.35/1.70
% 1.35/1.70 useres = 1
% 1.35/1.70 useparamod = 1
% 1.35/1.70 useeqrefl = 1
% 1.35/1.70 useeqfact = 1
% 1.35/1.70 usefactor = 1
% 1.35/1.70 usesimpsplitting = 0
% 1.35/1.70 usesimpdemod = 5
% 1.35/1.70 usesimpres = 3
% 1.35/1.70
% 1.35/1.70 resimpinuse = 1000
% 1.35/1.70 resimpclauses = 20000
% 1.35/1.70 substype = eqrewr
% 1.35/1.70 backwardsubs = 1
% 1.35/1.70 selectoldest = 5
% 1.35/1.70
% 1.35/1.70 litorderings [0] = split
% 1.35/1.70 litorderings [1] = extend the termordering, first sorting on arguments
% 1.35/1.70
% 1.35/1.70 termordering = kbo
% 1.35/1.70
% 1.35/1.70 litapriori = 0
% 1.35/1.70 termapriori = 1
% 1.35/1.70 litaposteriori = 0
% 1.35/1.70 termaposteriori = 0
% 1.35/1.70 demodaposteriori = 0
% 1.35/1.70 ordereqreflfact = 0
% 1.35/1.70
% 1.35/1.70 litselect = negord
% 1.35/1.70
% 1.35/1.70 maxweight = 15
% 1.35/1.70 maxdepth = 30000
% 1.35/1.70 maxlength = 115
% 1.35/1.70 maxnrvars = 195
% 1.35/1.70 excuselevel = 1
% 1.35/1.70 increasemaxweight = 1
% 1.35/1.70
% 1.35/1.70 maxselected = 10000000
% 1.35/1.70 maxnrclauses = 10000000
% 1.35/1.70
% 1.35/1.70 showgenerated = 0
% 1.35/1.70 showkept = 0
% 1.35/1.70 showselected = 0
% 1.35/1.70 showdeleted = 0
% 1.35/1.70 showresimp = 1
% 1.35/1.70 showstatus = 2000
% 1.35/1.70
% 1.35/1.70 prologoutput = 0
% 1.35/1.70 nrgoals = 5000000
% 1.35/1.70 totalproof = 1
% 1.35/1.70
% 1.35/1.70 Symbols occurring in the translation:
% 1.35/1.70
% 1.35/1.70 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.35/1.70 . [1, 2] (w:1, o:229, a:1, s:1, b:0),
% 1.35/1.70 ! [4, 1] (w:0, o:128, a:1, s:1, b:0),
% 1.35/1.70 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.35/1.70 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.35/1.70 hAPP [38, 2] (w:1, o:253, a:1, s:1, b:0),
% 1.35/1.70 t_a [39, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Oidom [40, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.35/1.70 v_p [41, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_Opoly [42, 2] (w:1, o:255, a:1, s:1, b:0),
% 1.35/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [43, 3] (w:1, o:
% 1.35/1.70 277, a:1, s:1, b:0),
% 1.35/1.70 c_Groups_Ozero__class_Ozero [45, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.35/1.70 v_cs____ [46, 0] (w:1, o:25, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Ocomm__semiring__0 [51, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_OpCons [52, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.35/1.70 c_Groups_Oplus__class_Oplus [53, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.35/1.70 c_Groups_Otimes__class_Otimes [54, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.35/1.70 class_Power_Opower [56, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Osemiring__0 [57, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.35/1.70 tc_Nat_Onat [58, 0] (w:1, o:50, a:1, s:1, b:0),
% 1.35/1.70 c_Power_Opower__class_Opower [59, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.35/1.70 c_Groups_Oone__class_Oone [60, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Omonoid__mult [62, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Ocomm__semiring__1 [64, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Omult__zero [68, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Ono__zero__divisors [69, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.35/1.70
% 1.35/1.70 class_Rings_Ozero__neq__one [70, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.35/1.70 class_Int_Oring__char__0 [72, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.35/1.70 tc_Polynomial_Opoly [73, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Ozero [76, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.35/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [77, 2] (w:1, o:256
% 1.35/1.70 , a:1, s:1, b:0),
% 1.35/1.70 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [87
% 1.35/1.70 , 1] (w:1, o:193, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Oring__1__no__zero__divisors [96, 1] (w:1, o:148, a:1, s:
% 1.35/1.70 1, b:0),
% 1.35/1.70 class_Groups_Ocomm__monoid__mult [97, 1] (w:1, o:194, a:1, s:1, b:0)
% 1.35/1.70 ,
% 1.35/1.70 class_Groups_Ocomm__monoid__add [98, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.35/1.70
% 1.35/1.70 v_c____ [100, 0] (w:1, o:79, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Olinordered__ring__strict [101, 1] (w:1, o:161, a:1, s:1
% 1.35/1.70 , b:0),
% 1.35/1.70 c_Power_Opower_Opower [102, 3] (w:1, o:280, a:1, s:1, b:0),
% 1.35/1.70 c_Nat_OSuc [106, 0] (w:1, o:85, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Oab__semigroup__mult [116, 1] (w:1, o:196, a:1, s:1, b:0
% 1.35/1.70 ),
% 1.35/1.70 class_Groups_Oab__semigroup__add [117, 1] (w:1, o:197, a:1, s:1, b:0)
% 1.35/1.70 ,
% 1.35/1.70 class_Groups_Ocancel__semigroup__add [118, 1] (w:1, o:198, a:1, s:1
% 1.35/1.70 , b:0),
% 1.35/1.70 class_Groups_Ocancel__ab__semigroup__add [119, 1] (w:1, o:199, a:1
% 1.35/1.70 , s:1, b:0),
% 1.35/1.70 class_Groups_Oone [120, 1] (w:1, o:200, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Omonoid__add [121, 1] (w:1, o:201, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Olinordered__ab__group__add [122, 1] (w:1, o:158, a:1
% 1.35/1.70 , s:1, b:0),
% 1.35/1.70 c_Polynomial_Opcompose [123, 3] (w:1, o:282, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_Oorder [124, 3] (w:1, o:281, a:1, s:1, b:0),
% 1.35/1.70 class_RealVector_Oreal__normed__algebra [129, 1] (w:1, o:178, a:1, s:
% 1.35/1.70 1, b:0),
% 1.35/1.70 class_Rings_Ocomm__semiring [131, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Oring__no__zero__divisors [134, 1] (w:1, o:149, a:1, s:1
% 1.35/1.70 , b:0),
% 1.35/1.70 class_Rings_Osemiring [136, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.35/1.70 tc_fun [137, 2] (w:1, o:262, a:1, s:1, b:0),
% 1.35/1.70 c_COMBB [138, 3] (w:1, o:283, a:1, s:1, b:0),
% 1.35/1.70 c_COMBK [139, 2] (w:1, o:263, a:1, s:1, b:0),
% 1.35/1.70 c_COMBC [140, 4] (w:1, o:328, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_Opoly__rec [141, 5] (w:1, o:357, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Ocomm__ring__1 [142, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_Omonom [143, 3] (w:1, o:284, a:1, s:1, b:0),
% 1.35/1.70 c_Nat_Onat_Onat__size [145, 1] (w:1, o:202, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_Ocoeff [146, 2] (w:1, o:264, a:1, s:1, b:0),
% 1.35/1.70 c_If [147, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.35/1.70 c_fequal [148, 1] (w:1, o:207, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_Osmult [149, 1] (w:1, o:208, a:1, s:1, b:0),
% 1.35/1.70 tc_Int_Oint [151, 0] (w:1, o:101, a:1, s:1, b:0),
% 1.35/1.70 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [153, 3] (w:
% 1.35/1.70 1, o:285, a:1, s:1, b:0),
% 1.35/1.70 c_COMBS [154, 3] (w:1, o:286, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_Osynthetic__div [155, 3] (w:1, o:287, a:1, s:1, b:0),
% 1.35/1.70 c_Nat_Osize__class_Osize [156, 2] (w:1, o:265, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_OAbs__poly [158, 2] (w:1, o:266, a:1, s:1, b:0),
% 1.35/1.70 c_fTrue [159, 0] (w:1, o:102, a:1, s:1, b:0),
% 1.35/1.70 c_HOL_Obool_Obool__size [160, 1] (w:1, o:205, a:1, s:1, b:0),
% 1.35/1.70 tc_HOL_Obool [165, 0] (w:1, o:100, a:1, s:1, b:0),
% 1.35/1.70 c_fFalse [166, 0] (w:1, o:106, a:1, s:1, b:0),
% 1.35/1.70 c_Groups_Ouminus__class_Ouminus [167, 1] (w:1, o:203, a:1, s:1, b:0)
% 1.35/1.70 ,
% 1.35/1.70 c_Nat_Onat_Onat__case [168, 3] (w:1, o:288, a:1, s:1, b:0),
% 1.35/1.70 c_Groups_Ominus__class_Ominus [169, 1] (w:1, o:204, a:1, s:1, b:0),
% 1.35/1.70 c_Polynomial_Odegree [170, 2] (w:1, o:267, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Oab__group__add [171, 1] (w:1, o:209, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Ocomm__ring [172, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Ogroup__add [173, 1] (w:1, o:210, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Oring [174, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.35/1.70 c_COMBI [175, 1] (w:1, o:211, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Oring__1 [179, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.35/1.70 c_Rings_Odvd__class_Odvd [180, 1] (w:1, o:212, a:1, s:1, b:0),
% 1.35/1.70 hBOOL [181, 1] (w:1, o:213, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Odvd [182, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.35/1.70 class_Fields_Ofield [183, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.35/1.70 c_fNot [188, 0] (w:1, o:109, a:1, s:1, b:0),
% 1.35/1.70 c_Orderings_Oord__class_OLeast [189, 2] (w:1, o:254, a:1, s:1, b:0),
% 1.35/1.70
% 1.35/1.70 c_Polynomial_Opoly__gcd [190, 3] (w:1, o:289, a:1, s:1, b:0),
% 1.35/1.70 class_Orderings_Owellorder [191, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.35/1.70 c_Orderings_Oord__class_Oless [192, 3] (w:1, o:278, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Ouminus [194, 1] (w:1, o:214, a:1, s:1, b:0),
% 1.35/1.70 class_Groups_Ominus [196, 1] (w:1, o:215, a:1, s:1, b:0),
% 1.35/1.70 class_Rings_Olinordered__semidom [198, 1] (w:1, o:163, a:1, s:1, b:0)
% 1.35/1.70 ,
% 1.35/1.70 class_Rings_Olinordered__idom [199, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.35/1.70 class_Orderings_Olinorder [200, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.35/1.70 class_Orderings_Opreorder [201, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.48/1.85 class_Orderings_Oorder [202, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.48/1.85 class_Orderings_Oord [203, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.48/1.85 class_Groups_Oordered__ab__group__add [207, 1] (w:1, o:216, a:1, s:1
% 1.48/1.85 , b:0),
% 1.48/1.85 class_Groups_Oordered__ab__semigroup__add__imp__le [208, 1] (w:1, o:
% 1.48/1.85 217, a:1, s:1, b:0),
% 1.48/1.85 class_Groups_Oordered__cancel__ab__semigroup__add [209, 1] (w:1, o:
% 1.48/1.85 218, a:1, s:1, b:0),
% 1.48/1.85 class_Rings_Olinordered__ring [210, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.48/1.85 class_Rings_Olinordered__semiring__strict [211, 1] (w:1, o:165, a:1
% 1.48/1.85 , s:1, b:0),
% 1.48/1.85 class_Rings_Olinordered__comm__semiring__strict [212, 1] (w:1, o:166
% 1.48/1.85 , a:1, s:1, b:0),
% 1.48/1.85 class_Groups_Oordered__comm__monoid__add [213, 1] (w:1, o:219, a:1
% 1.48/1.85 , s:1, b:0),
% 1.48/1.85 class_Rings_Oordered__ring [218, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.48/1.85 class_Lattices_Oab__semigroup__idem__mult [220, 1] (w:1, o:220, a:1
% 1.48/1.85 , s:1, b:0),
% 1.48/1.85 class_Lattices_Oboolean__algebra [221, 1] (w:1, o:221, a:1, s:1, b:0)
% 1.48/1.85 ,
% 1.48/1.85 c_fconj [223, 0] (w:1, o:114, a:1, s:1, b:0),
% 1.48/1.85 c_Orderings_Oorder_Ostrict__mono [224, 4] (w:1, o:329, a:1, s:1, b:0)
% 1.48/1.85 ,
% 1.48/1.85 c_Orderings_Oorder_Omono [225, 4] (w:1, o:330, a:1, s:1, b:0),
% 1.48/1.85 c_Polynomial_Opdivmod__rel [227, 5] (w:1, o:358, a:1, s:1, b:0),
% 1.48/1.85 c_Rings_Oinverse__class_Odivide [234, 1] (w:1, o:222, a:1, s:1, b:0)
% 1.48/1.85 ,
% 1.48/1.85 c_Polynomial_Opos__poly [235, 2] (w:1, o:268, a:1, s:1, b:0),
% 1.48/1.85 class_RealVector_Oreal__normed__field [236, 1] (w:1, o:183, a:1, s:1
% 1.48/1.85 , b:0),
% 1.48/1.85 class_Rings_Odivision__ring [237, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.48/1.85 class_Fields_Ofield__inverse__zero [238, 1] (w:1, o:155, a:1, s:1, b:
% 1.48/1.85 0),
% 1.48/1.85 class_Rings_Odivision__ring__inverse__zero [239, 1] (w:1, o:185, a:1
% 1.48/1.85 , s:1, b:0),
% 1.48/1.85 class_RealVector_Oreal__field [240, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.48/1.85 class_Fields_Olinordered__field [241, 1] (w:1, o:156, a:1, s:1, b:0)
% 1.48/1.85 ,
% 1.48/1.85 class_Fields_Olinordered__field__inverse__zero [242, 1] (w:1, o:157
% 1.48/1.85 , a:1, s:1, b:0),
% 1.48/1.85 c_Divides_Odiv__class_Omod [243, 3] (w:1, o:290, a:1, s:1, b:0),
% 1.48/1.85 c_Deriv_Oderiv [244, 4] (w:1, o:331, a:1, s:1, b:0),
% 1.48/1.85 c_Groups_Osgn__class_Osgn [245, 2] (w:1, o:269, a:1, s:1, b:0),
% 1.48/1.85 class_Groups_Osgn__if [246, 1] (w:1, o:223, a:1, s:1, b:0),
% 1.48/1.85 class_RealVector_Oreal__normed__vector [247, 1] (w:1, o:187, a:1, s:1
% 1.48/1.85 , b:0),
% 1.48/1.85 class_RealVector_Oreal__normed__div__algebra [248, 1] (w:1, o:188, a:
% 1.48/1.85 1, s:1, b:0),
% 1.48/1.85 class_RealVector_Oreal__normed__algebra__1 [249, 1] (w:1, o:189, a:1
% 1.48/1.85 , s:1, b:0),
% 1.48/1.85 class_Divides_Osemiring__div [255, 1] (w:1, o:225, a:1, s:1, b:0),
% 1.48/1.85 class_Divides_Oring__div [258, 1] (w:1, o:224, a:1, s:1, b:0),
% 1.48/1.85 c_Rings_Oinverse__class_Oinverse [259, 1] (w:1, o:226, a:1, s:1, b:0)
% 1.48/1.85 ,
% 1.48/1.85 c_Divides_Odiv__class_Odiv [260, 3] (w:1, o:291, a:1, s:1, b:0),
% 1.48/1.85 c_Orderings_Oord__class_Oless__eq [261, 3] (w:1, o:279, a:1, s:1, b:0
% 1.48/1.85 ),
% 1.48/1.85 class_Rings_Oordered__cancel__semiring [262, 1] (w:1, o:190, a:1, s:1
% 1.48/1.85 , b:0),
% 1.48/1.85 class_Rings_Oordered__semiring [263, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.48/1.85
% 1.48/1.85 class_Rings_Oordered__comm__semiring [264, 1] (w:1, o:192, a:1, s:1
% 1.48/1.85 , b:0),
% 1.48/1.85 class_Groups_Ocancel__comm__monoid__add [266, 1] (w:1, o:227, a:1, s:
% 1.48/1.85 1, b:0),
% 1.48/1.85 alpha1 [274, 2] (w:1, o:270, a:1, s:1, b:1),
% 1.48/1.85 alpha2 [275, 2] (w:1, o:271, a:1, s:1, b:1),
% 1.48/1.85 alpha3 [276, 3] (w:1, o:295, a:1, s:1, b:1),
% 1.48/1.85 alpha4 [277, 2] (w:1, o:272, a:1, s:1, b:1),
% 1.48/1.85 alpha5 [278, 2] (w:1, o:273, a:1, s:1, b:1),
% 1.48/1.85 alpha6 [279, 4] (w:1, o:335, a:1, s:1, b:1),
% 1.48/1.85 alpha7 [280, 4] (w:1, o:336, a:1, s:1, b:1),
% 1.48/1.85 alpha8 [281, 2] (w:1, o:274, a:1, s:1, b:1),
% 1.48/1.85 alpha9 [282, 3] (w:1, o:296, a:1, s:1, b:1),
% 1.48/1.85 alpha10 [283, 3] (w:1, o:297, a:1, s:1, b:1),
% 1.48/1.85 alpha11 [284, 3] (w:1, o:298, a:1, s:1, b:1),
% 1.48/1.85 alpha12 [285, 3] (w:1, o:299, a:1, s:1, b:1),
% 1.48/1.85 alpha13 [286, 3] (w:1, o:300, a:1, s:1, b:1),
% 1.48/1.85 alpha14 [287, 3] (w:1, o:301, a:1, s:1, b:1),
% 1.48/1.85 alpha15 [288, 3] (w:1, o:302, a:1, s:1, b:1),
% 10.10/10.46 alpha16 [289, 3] (w:1, o:303, a:1, s:1, b:1),
% 10.10/10.46 alpha17 [290, 3] (w:1, o:304, a:1, s:1, b:1),
% 10.10/10.46 alpha18 [291, 3] (w:1, o:305, a:1, s:1, b:1),
% 10.10/10.46 alpha19 [292, 3] (w:1, o:306, a:1, s:1, b:1),
% 10.10/10.46 alpha20 [293, 4] (w:1, o:337, a:1, s:1, b:1),
% 10.10/10.46 alpha21 [294, 4] (w:1, o:338, a:1, s:1, b:1),
% 10.10/10.46 alpha22 [295, 2] (w:1, o:275, a:1, s:1, b:1),
% 10.10/10.46 alpha23 [296, 2] (w:1, o:276, a:1, s:1, b:1),
% 10.10/10.46 alpha24 [297, 4] (w:1, o:339, a:1, s:1, b:1),
% 10.10/10.46 alpha25 [298, 4] (w:1, o:340, a:1, s:1, b:1),
% 10.10/10.46 alpha26 [299, 4] (w:1, o:341, a:1, s:1, b:1),
% 10.10/10.46 alpha27 [300, 3] (w:1, o:292, a:1, s:1, b:1),
% 10.10/10.46 alpha28 [301, 3] (w:1, o:293, a:1, s:1, b:1),
% 10.10/10.46 alpha29 [302, 3] (w:1, o:294, a:1, s:1, b:1),
% 10.10/10.46 alpha30 [303, 3] (w:1, o:307, a:1, s:1, b:1),
% 10.10/10.46 alpha31 [304, 3] (w:1, o:308, a:1, s:1, b:1),
% 10.10/10.46 alpha32 [305, 4] (w:1, o:342, a:1, s:1, b:1),
% 10.10/10.46 alpha33 [306, 4] (w:1, o:343, a:1, s:1, b:1),
% 10.10/10.46 alpha34 [307, 4] (w:1, o:344, a:1, s:1, b:1),
% 10.10/10.46 alpha35 [308, 4] (w:1, o:345, a:1, s:1, b:1),
% 10.10/10.46 alpha36 [309, 3] (w:1, o:309, a:1, s:1, b:1),
% 10.10/10.46 alpha37 [310, 4] (w:1, o:346, a:1, s:1, b:1),
% 10.10/10.46 alpha38 [311, 4] (w:1, o:347, a:1, s:1, b:1),
% 10.10/10.46 alpha39 [312, 4] (w:1, o:348, a:1, s:1, b:1),
% 10.10/10.46 alpha40 [313, 3] (w:1, o:310, a:1, s:1, b:1),
% 10.10/10.46 alpha41 [314, 4] (w:1, o:349, a:1, s:1, b:1),
% 10.10/10.46 alpha42 [315, 4] (w:1, o:350, a:1, s:1, b:1),
% 10.10/10.46 alpha43 [316, 3] (w:1, o:311, a:1, s:1, b:1),
% 10.10/10.46 alpha44 [317, 4] (w:1, o:351, a:1, s:1, b:1),
% 10.10/10.46 alpha45 [318, 4] (w:1, o:352, a:1, s:1, b:1),
% 10.10/10.46 alpha46 [319, 4] (w:1, o:353, a:1, s:1, b:1),
% 10.10/10.46 alpha47 [320, 4] (w:1, o:354, a:1, s:1, b:1),
% 10.10/10.46 alpha48 [321, 4] (w:1, o:355, a:1, s:1, b:1),
% 10.10/10.46 alpha49 [322, 1] (w:1, o:228, a:1, s:1, b:1),
% 10.10/10.46 alpha50 [323, 3] (w:1, o:312, a:1, s:1, b:1),
% 10.10/10.46 alpha51 [324, 3] (w:1, o:313, a:1, s:1, b:1),
% 10.10/10.46 alpha52 [325, 3] (w:1, o:314, a:1, s:1, b:1),
% 10.10/10.46 alpha53 [326, 4] (w:1, o:332, a:1, s:1, b:1),
% 10.10/10.46 alpha54 [327, 4] (w:1, o:333, a:1, s:1, b:1),
% 10.10/10.46 alpha55 [328, 4] (w:1, o:334, a:1, s:1, b:1),
% 10.10/10.46 skol1 [329, 2] (w:1, o:257, a:1, s:1, b:1),
% 10.10/10.46 skol2 [330, 0] (w:1, o:14, a:1, s:1, b:1),
% 10.10/10.46 skol3 [331, 0] (w:1, o:17, a:1, s:1, b:1),
% 10.10/10.46 skol4 [332, 1] (w:1, o:171, a:1, s:1, b:1),
% 10.10/10.46 skol5 [333, 0] (w:1, o:18, a:1, s:1, b:1),
% 10.10/10.46 skol6 [334, 0] (w:1, o:19, a:1, s:1, b:1),
% 10.10/10.46 skol7 [335, 1] (w:1, o:172, a:1, s:1, b:1),
% 10.10/10.46 skol8 [336, 3] (w:1, o:315, a:1, s:1, b:1),
% 10.10/10.46 skol9 [337, 3] (w:1, o:316, a:1, s:1, b:1),
% 10.10/10.46 skol10 [338, 1] (w:1, o:173, a:1, s:1, b:1),
% 10.10/10.46 skol11 [339, 2] (w:1, o:258, a:1, s:1, b:1),
% 10.10/10.46 skol12 [340, 2] (w:1, o:259, a:1, s:1, b:1),
% 10.10/10.46 skol13 [341, 3] (w:1, o:317, a:1, s:1, b:1),
% 10.10/10.46 skol14 [342, 3] (w:1, o:318, a:1, s:1, b:1),
% 10.10/10.46 skol15 [343, 4] (w:1, o:356, a:1, s:1, b:1),
% 10.10/10.46 skol16 [344, 2] (w:1, o:260, a:1, s:1, b:1),
% 10.10/10.46 skol17 [345, 2] (w:1, o:261, a:1, s:1, b:1),
% 10.10/10.46 skol18 [346, 3] (w:1, o:319, a:1, s:1, b:1),
% 10.10/10.46 skol19 [347, 3] (w:1, o:320, a:1, s:1, b:1),
% 10.10/10.46 skol20 [348, 3] (w:1, o:321, a:1, s:1, b:1),
% 10.10/10.46 skol21 [349, 3] (w:1, o:322, a:1, s:1, b:1),
% 10.10/10.46 skol22 [350, 3] (w:1, o:323, a:1, s:1, b:1),
% 10.10/10.46 skol23 [351, 1] (w:1, o:174, a:1, s:1, b:1),
% 10.10/10.46 skol24 [352, 0] (w:1, o:15, a:1, s:1, b:1),
% 10.10/10.46 skol25 [353, 1] (w:1, o:175, a:1, s:1, b:1),
% 10.10/10.46 skol26 [354, 3] (w:1, o:324, a:1, s:1, b:1),
% 10.10/10.46 skol27 [355, 3] (w:1, o:325, a:1, s:1, b:1),
% 10.10/10.46 skol28 [356, 3] (w:1, o:326, a:1, s:1, b:1),
% 10.10/10.46 skol29 [357, 0] (w:1, o:16, a:1, s:1, b:1),
% 10.10/10.46 skol30 [358, 3] (w:1, o:327, a:1, s:1, b:1).
% 10.10/10.46
% 10.10/10.46
% 10.10/10.46 Starting Search:
% 10.10/10.46
% 10.10/10.46 *** allocated 170857 integers for clauses
% 10.10/10.46 Resimplifying inuse:
% 10.10/10.46 Done
% 10.10/10.46
% 10.10/10.46 *** allocated 256285 integers for clauses
% 10.10/10.46
% 10.10/10.46 Intermediate Status:
% 10.10/10.46 Generated: 3004
% 10.10/10.46 Kept: 2005
% 10.10/10.46 Inuse: 44
% 10.10/10.46 Deleted: 7
% 10.10/10.46 Deletedinuse: 0
% 10.10/10.46
% 10.10/10.46 Resimplifying inuse:
% 10.10/10.46 Done
% 10.10/10.46
% 10.10/10.46 *** allocated 384427 integers for clauses
% 10.10/10.46 Resimplifying inuse:
% 10.10/10.46 Done
% 10.10/10.46
% 10.10/10.46 *** allocated 256285 integers for termspace/termends
% 10.10/10.46
% 10.10/10.46 Intermediate Status:
% 51.35/51.77 Generated: 9223
% 51.35/51.77 Kept: 4096
% 51.35/51.77 Inuse: 196
% 51.35/51.77 Deleted: 15
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 *** allocated 576640 integers for clauses
% 51.35/51.77 *** allocated 384427 integers for termspace/termends
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 22394
% 51.35/51.77 Kept: 6397
% 51.35/51.77 Inuse: 246
% 51.35/51.77 Deleted: 15
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 30084
% 51.35/51.77 Kept: 8436
% 51.35/51.77 Inuse: 309
% 51.35/51.77 Deleted: 17
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 *** allocated 864960 integers for clauses
% 51.35/51.77 *** allocated 576640 integers for termspace/termends
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 37478
% 51.35/51.77 Kept: 10477
% 51.35/51.77 Inuse: 352
% 51.35/51.77 Deleted: 19
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 56040
% 51.35/51.77 Kept: 13074
% 51.35/51.77 Inuse: 376
% 51.35/51.77 Deleted: 20
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 *** allocated 1297440 integers for clauses
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 *** allocated 864960 integers for termspace/termends
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 68342
% 51.35/51.77 Kept: 15551
% 51.35/51.77 Inuse: 408
% 51.35/51.77 Deleted: 23
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 72702
% 51.35/51.77 Kept: 17607
% 51.35/51.77 Inuse: 418
% 51.35/51.77 Deleted: 23
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 79485
% 51.35/51.77 Kept: 19675
% 51.35/51.77 Inuse: 472
% 51.35/51.77 Deleted: 24
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying clauses:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 92285
% 51.35/51.77 Kept: 22593
% 51.35/51.77 Inuse: 497
% 51.35/51.77 Deleted: 246
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 *** allocated 1946160 integers for clauses
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 98295
% 51.35/51.77 Kept: 24865
% 51.35/51.77 Inuse: 527
% 51.35/51.77 Deleted: 246
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 *** allocated 1297440 integers for termspace/termends
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 102587
% 51.35/51.77 Kept: 27379
% 51.35/51.77 Inuse: 537
% 51.35/51.77 Deleted: 246
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 107435
% 51.35/51.77 Kept: 29522
% 51.35/51.77 Inuse: 562
% 51.35/51.77 Deleted: 246
% 51.35/51.77 Deletedinuse: 0
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 113619
% 51.35/51.77 Kept: 32149
% 51.35/51.77 Inuse: 587
% 51.35/51.77 Deleted: 247
% 51.35/51.77 Deletedinuse: 1
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 123477
% 51.35/51.77 Kept: 34180
% 51.35/51.77 Inuse: 611
% 51.35/51.77 Deleted: 247
% 51.35/51.77 Deletedinuse: 1
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 135819
% 51.35/51.77 Kept: 36231
% 51.35/51.77 Inuse: 622
% 51.35/51.77 Deleted: 248
% 51.35/51.77 Deletedinuse: 2
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 151535
% 51.35/51.77 Kept: 38619
% 51.35/51.77 Inuse: 641
% 51.35/51.77 Deleted: 249
% 51.35/51.77 Deletedinuse: 2
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 *** allocated 2919240 integers for clauses
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 172767
% 51.35/51.77 Kept: 40959
% 51.35/51.77 Inuse: 656
% 51.35/51.77 Deleted: 249
% 51.35/51.77 Deletedinuse: 2
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying clauses:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 *** allocated 1946160 integers for termspace/termends
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 193971
% 51.35/51.77 Kept: 43060
% 51.35/51.77 Inuse: 666
% 51.35/51.77 Deleted: 537
% 51.35/51.77 Deletedinuse: 2
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 207226
% 51.35/51.77 Kept: 45178
% 51.35/51.77 Inuse: 686
% 51.35/51.77 Deleted: 537
% 51.35/51.77 Deletedinuse: 2
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 220539
% 51.35/51.77 Kept: 47212
% 51.35/51.77 Inuse: 705
% 51.35/51.77 Deleted: 537
% 51.35/51.77 Deletedinuse: 2
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 230345
% 51.35/51.77 Kept: 50381
% 51.35/51.77 Inuse: 721
% 51.35/51.77 Deleted: 537
% 51.35/51.77 Deletedinuse: 2
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 234818
% 51.35/51.77 Kept: 52467
% 51.35/51.77 Inuse: 726
% 51.35/51.77 Deleted: 537
% 51.35/51.77 Deletedinuse: 2
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77 Resimplifying inuse:
% 51.35/51.77 Done
% 51.35/51.77
% 51.35/51.77
% 51.35/51.77 Intermediate Status:
% 51.35/51.77 Generated: 243980
% 51.35/51.77 Kept: 54472
% 51.35/51.77 Inuse: 746
% 51.35/51.77 Deleted: 538
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 252468
% 128.63/129.07 Kept: 56511
% 128.63/129.07 Inuse: 770
% 128.63/129.07 Deleted: 538
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 263008
% 128.63/129.07 Kept: 59351
% 128.63/129.07 Inuse: 790
% 128.63/129.07 Deleted: 538
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying clauses:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 *** allocated 4378860 integers for clauses
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 289259
% 128.63/129.07 Kept: 63270
% 128.63/129.07 Inuse: 830
% 128.63/129.07 Deleted: 1564
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 *** allocated 2919240 integers for termspace/termends
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 306866
% 128.63/129.07 Kept: 65291
% 128.63/129.07 Inuse: 835
% 128.63/129.07 Deleted: 1564
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 317570
% 128.63/129.07 Kept: 67429
% 128.63/129.07 Inuse: 875
% 128.63/129.07 Deleted: 1564
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 327586
% 128.63/129.07 Kept: 69678
% 128.63/129.07 Inuse: 885
% 128.63/129.07 Deleted: 1564
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 335940
% 128.63/129.07 Kept: 71785
% 128.63/129.07 Inuse: 905
% 128.63/129.07 Deleted: 1564
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 348946
% 128.63/129.07 Kept: 75104
% 128.63/129.07 Inuse: 920
% 128.63/129.07 Deleted: 1564
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 362881
% 128.63/129.07 Kept: 78148
% 128.63/129.07 Inuse: 935
% 128.63/129.07 Deleted: 1564
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 372499
% 128.63/129.07 Kept: 80607
% 128.63/129.07 Inuse: 940
% 128.63/129.07 Deleted: 1564
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying clauses:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 382780
% 128.63/129.07 Kept: 82762
% 128.63/129.07 Inuse: 950
% 128.63/129.07 Deleted: 1621
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 392221
% 128.63/129.07 Kept: 85134
% 128.63/129.07 Inuse: 980
% 128.63/129.07 Deleted: 1621
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 *** allocated 4378860 integers for termspace/termends
% 128.63/129.07 *** allocated 6568290 integers for clauses
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 420299
% 128.63/129.07 Kept: 88862
% 128.63/129.07 Inuse: 1005
% 128.63/129.07 Deleted: 1621
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 435784
% 128.63/129.07 Kept: 92176
% 128.63/129.07 Inuse: 1030
% 128.63/129.07 Deleted: 1621
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 447138
% 128.63/129.07 Kept: 95376
% 128.63/129.07 Inuse: 1050
% 128.63/129.07 Deleted: 1621
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 460888
% 128.63/129.07 Kept: 98384
% 128.63/129.07 Inuse: 1070
% 128.63/129.07 Deleted: 1621
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 471428
% 128.63/129.07 Kept: 100554
% 128.63/129.07 Inuse: 1080
% 128.63/129.07 Deleted: 1621
% 128.63/129.07 Deletedinuse: 2
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying clauses:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 484235
% 128.63/129.07 Kept: 102822
% 128.63/129.07 Inuse: 1110
% 128.63/129.07 Deleted: 1866
% 128.63/129.07 Deletedinuse: 4
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 495341
% 128.63/129.07 Kept: 105338
% 128.63/129.07 Inuse: 1120
% 128.63/129.07 Deleted: 1866
% 128.63/129.07 Deletedinuse: 4
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 512755
% 128.63/129.07 Kept: 109281
% 128.63/129.07 Inuse: 1135
% 128.63/129.07 Deleted: 1866
% 128.63/129.07 Deletedinuse: 4
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 520773
% 128.63/129.07 Kept: 111285
% 128.63/129.07 Inuse: 1140
% 128.63/129.07 Deleted: 1866
% 128.63/129.07 Deletedinuse: 4
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 529124
% 128.63/129.07 Kept: 113312
% 128.63/129.07 Inuse: 1155
% 128.63/129.07 Deleted: 1866
% 128.63/129.07 Deletedinuse: 4
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07
% 128.63/129.07 Intermediate Status:
% 128.63/129.07 Generated: 539850
% 128.63/129.07 Kept: 115322
% 128.63/129.07 Inuse: 1178
% 128.63/129.07 Deleted: 1866
% 128.63/129.07 Deletedinuse: 4
% 128.63/129.07
% 128.63/129.07 Resimplifying inuse:
% 128.63/129.07 Done
% 128.63/129.07
% 128.63/129.07 *Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------