TSTP Solution File: SWW246+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW246+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 23:21:32 EDT 2022
% Result : Timeout 300.07s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW246+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Jun 5 20:50:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.27/1.66 *** allocated 10000 integers for termspace/termends
% 1.27/1.66 *** allocated 10000 integers for clauses
% 1.27/1.66 *** allocated 10000 integers for justifications
% 1.27/1.66 *** allocated 15000 integers for termspace/termends
% 1.27/1.66 *** allocated 22500 integers for termspace/termends
% 1.27/1.66 *** allocated 33750 integers for termspace/termends
% 1.27/1.66 Bliksem 1.12
% 1.27/1.66
% 1.27/1.66
% 1.27/1.66 Automatic Strategy Selection
% 1.27/1.66
% 1.27/1.66 *** allocated 50625 integers for termspace/termends
% 1.27/1.66 *** allocated 75937 integers for termspace/termends
% 1.27/1.66 *** allocated 113905 integers for termspace/termends
% 1.27/1.66 *** allocated 170857 integers for termspace/termends
% 1.27/1.66
% 1.27/1.66 Clauses:
% 1.27/1.66
% 1.27/1.66 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.27/1.66 { ! class_Rings_Oidom( t_a ), !
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.27/1.66 c_Polynomial_Opoly( t_a, v_p ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), !
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.27/1.66 ( hAPP( c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.27/1.66 , Y ) ) ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.27/1.66 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ),
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.27/1.66 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.27/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.27/1.66 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.27/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.27/1.66 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.27/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.27/1.66 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.27/1.66 X, T ) = hAPP( X, U ) }.
% 1.27/1.66 { ! hAPP( X, skol2( X ) ) = hAPP( X, skol19( X ) ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 1.27/1.66 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.27/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.27/1.66 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), T ), Z ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 1.27/1.66 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), U = Z }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T
% 1.27/1.66 ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), T = Y }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), U ), T ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.27/1.66 , Z ), Y ) }.
% 1.27/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.27/1.66 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.27/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.27/1.66 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 1.27/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.27/1.66 = c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Nat_Onat ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Nat_Onat ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.27/1.66 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.27/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.27/1.66 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 1.27/1.66 ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.27/1.66 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.27/1.66 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.27/1.66 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.27/1.66 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.27/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.27/1.66 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.27/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.27/1.66 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 1.27/1.66 , Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.27/1.66 , Z ) }.
% 1.27/1.66 { ! class_Rings_Oidom( t_a ), !
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( t_a, t_a,
% 1.27/1.66 c_Polynomial_Opoly( t_a, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.27/1.66 ( t_a ) ) ) ) }.
% 1.27/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.27/1.66 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.27/1.66 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.27/1.66 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.27/1.66 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.27/1.66 = Y }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y )
% 1.27/1.66 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 1.27/1.66 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.27/1.66 ( X ) ), Z ), Y ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.27/1.66 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.27/1.66 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.27/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.27/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 1.27/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.27/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.27/1.66 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.27/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 1.27/1.66 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.27/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.27/1.66 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.27/1.66 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.27/1.66 .
% 1.27/1.66 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.27/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.27/1.66 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.27/1.66 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.27/1.66 .
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 1.27/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.27/1.66 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 1.27/1.66 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.27/1.66 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.27/1.66 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.27/1.66 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.27/1.66 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.27/1.66 , Y ), X ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Nat_Onat ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Nat_Onat ) }.
% 1.27/1.66 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 1.27/1.66 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, hAPP(
% 1.27/1.66 hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), T ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), Y ), c_Polynomial_Opcompose( X, Z, Y ) ) )
% 1.27/1.66 }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.27/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.27/1.66 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.27/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.27/1.66 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.27/1.66 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.27/1.66 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.27/1.66 X, Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.27/1.66 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.27/1.66 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.66 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 1.27/1.66 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T )
% 1.27/1.66 , Y ), Z ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.27/1.66 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.27/1.66 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.27/1.66 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.27/1.66 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.27/1.66 ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X, Z, Y )
% 1.27/1.66 = c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.27/1.66 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 1.27/1.66 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 1.27/1.66 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 1.27/1.66 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 1.27/1.66 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 1.27/1.66 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 1.27/1.66 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.27/1.66 c_Polynomial_OpCons( X ) ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ) ) ) ), hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), Y ) ) ), Z ) }.
% 1.27/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.27/1.66 Z, hAPP( hAPP( c_Polynomial_OpCons( X ), U ), T ) ) = hAPP( hAPP( hAPP( Z
% 1.27/1.66 , U ), T ), c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.27/1.66 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.27/1.66 hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.27/1.66 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.27/1.66 ( X ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T, hAPP(
% 1.27/1.66 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y
% 1.27/1.66 ), hAPP( hAPP( hAPP( c_If( W ), hAPP( c_fequal( Y ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), U ),
% 1.27/1.66 c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.27/1.66 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 1.27/1.66 hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), Z ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.27/1.66 ), c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Z ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.27/1.66 , Z ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.27/1.66 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol3( X
% 1.27/1.66 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol3( X, Y, Z ) ), Z = Y
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.27/1.66 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.27/1.66 c_Polynomial_Ocoeff( X, Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.27/1.66 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.27/1.66 ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.27/1.66 , T ), Z ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), c_Groups_Oone__class_Oone( X ) ), Y ) = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X
% 1.27/1.66 ) ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 1.27/1.66 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), hAPP(
% 1.27/1.66 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), Y ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ),
% 1.27/1.66 hAPP( hAPP( c_Polynomial_OpCons( X ), T ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.27/1.66 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.27/1.66 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP
% 1.27/1.66 ( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ), hAPP(
% 1.27/1.66 c_COMBS( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X )
% 1.27/1.66 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Groups_Oplus__class_Oplus(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), hAPP( c_Polynomial_Osmult( X ), Y ) ) ) ),
% 1.27/1.66 c_Polynomial_OpCons( X ) ) ), Z ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.66 hAPP( c_Polynomial_Osmult( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y
% 1.27/1.66 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), T ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.27/1.66 , T ), Z ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Z ), Y ) ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) = Z }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.27/1.66 ( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.27/1.66 , Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP( c_Polynomial_Osmult
% 1.27/1.66 ( X ), T ), Y ) = hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.27/1.66 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.27/1.66 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.27/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T )
% 1.27/1.66 , Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.27/1.66 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.27/1.66 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), T ), c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP
% 1.27/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.27/1.66 ), Z ), Y ) ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.27/1.66 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.27/1.66 c_Polynomial_Opoly__rec( tc_Polynomial_Opoly( X ), X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 tc_fun( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), X ), c_COMBK( tc_fun( tc_Polynomial_Opoly(
% 1.27/1.66 X ), tc_Polynomial_Opoly( X ) ), tc_Polynomial_Opoly( X ) ) ), hAPP(
% 1.27/1.66 c_COMBC( X, tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), hAPP(
% 1.27/1.66 hAPP( c_COMBB( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X )
% 1.27/1.66 ), tc_fun( tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ) ), X ),
% 1.27/1.66 c_COMBB( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Polynomial_Opoly( X
% 1.27/1.66 ), tc_fun( tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ) ), X ),
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ) ), hAPP( c_COMBC
% 1.27/1.66 ( X, tc_Polynomial_Opoly( X ), tc_Polynomial_Opoly( X ),
% 1.27/1.66 c_Polynomial_Osmult( X ) ), Y ) ) ) ), hAPP( c_Polynomial_OpCons( X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) ) ) ), Z ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.27/1.66 ) = hAPP( c_Polynomial_Opoly( X, T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.27/1.66 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), hAPP( hAPP
% 1.27/1.66 ( c_Polynomial_Osmult( X ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.27/1.66 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X
% 1.27/1.66 , Z ), Y ) ), c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 1.27/1.66 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 1.27/1.66 ( X ), Y ), Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), U ), hAPP( hAPP
% 1.27/1.66 ( c_Polynomial_Osmult( X ), T ), Z ) ) = hAPP( hAPP( c_Polynomial_OpCons
% 1.27/1.66 ( X ), Y ), Z ), Z = c_Polynomial_Osynthetic__div( X, U, T ) }.
% 1.27/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.27/1.66 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 1.27/1.66 hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat ),
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 1.27/1.66 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.66 ), Z ), Y ) = c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBB( X, X,
% 1.27/1.66 tc_Nat_Onat ), hAPP( c_Groups_Otimes__class_Otimes( X ), Z ) ),
% 1.27/1.66 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.27/1.66 hAPP( hAPP( c_Polynomial_OpCons( X ), T ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ),
% 1.27/1.66 c_Polynomial_Osynthetic__div( X, Z, Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.27/1.66 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.27/1.66 hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP( c_Polynomial_OpCons( X )
% 1.27/1.66 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Z ), Y ) ) = c_Nat_Onat_Onat__case( X, Z,
% 1.27/1.66 c_Polynomial_Ocoeff( X, Y ) ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z )
% 1.27/1.66 ), Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.27/1.66 c_Polynomial_Ocoeff( X, T ), Y ) ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.27/1.66 hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP(
% 1.27/1.66 hAPP( c_Polynomial_Osmult( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.27/1.66 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, X, X ),
% 1.27/1.66 hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat ),
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ) ), c_Polynomial_Ocoeff( X, Z ) ) ),
% 1.27/1.66 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! U = T, Z = Y }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! Z = Y, U = T }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.27/1.66 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.27/1.66 ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y
% 1.27/1.66 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.27/1.66 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), U ), T ) ), hAPP( hAPP( c_Polynomial_OpCons( X
% 1.27/1.66 ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Polynomial_Omonom( X, T, Z ) ), c_Polynomial_Omonom( X, Y, Z ) ) =
% 1.27/1.66 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T
% 1.27/1.66 ), Y ), Z ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), ! Z = Y, hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Y ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 ) = Y }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), Y ) = Z }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), Y ) =
% 1.27/1.66 Z }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) = X }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) = Y }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.27/1.66 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.27/1.66 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 1.27/1.66 c_Polynomial_Odegree( X, Z ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y )
% 1.27/1.66 = c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 1.27/1.66 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 1.27/1.66 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y }.
% 1.27/1.66 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y, hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.66 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.66 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.66 c_Polynomial_Odegree( X, hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) )
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.66 c_Polynomial_Odegree( X, hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) )
% 1.27/1.66 = c_Polynomial_Odegree( X, Y ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.27/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.27/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.27/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.27/1.66 ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.27/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.27/1.66 c_Polynomial_Odegree( X, Y ) ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.27/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OAbs__poly( X, hAPP( c_COMBK( X
% 1.27/1.66 , tc_Nat_Onat ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.27/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.27/1.66 ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.27/1.66 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.27/1.66 ), c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.27/1.66 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, Y ) =
% 1.27/1.66 c_Polynomial_OAbs__poly( X, hAPP( c_COMBC( tc_Nat_Onat, X, X, hAPP(
% 1.27/1.66 c_COMBC( tc_Nat_Onat, X, tc_fun( X, X ), hAPP( hAPP( c_COMBB(
% 1.27/1.66 tc_HOL_Obool, tc_fun( X, tc_fun( X, X ) ), tc_Nat_Onat ), c_If( X ) ),
% 1.27/1.66 c_fequal( Y ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.27/1.66 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.27/1.66 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.27/1.66 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X
% 1.27/1.66 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Y ),
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.27/1.66 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z )
% 1.27/1.66 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.27/1.66 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.27/1.66 c_Polynomial_Osynthetic__div( X, Y, Z ) ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), hAPP( c_Polynomial_Opoly( X, Y ), Z ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Polynomial_Odegree( X, Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ominus( X ), hAPP( hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_fun( U, X ) ), T ), Z ), Y ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( T, Y ) ), hAPP( Z, Y ) )
% 1.27/1.66 }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.27/1.66 , Z ), hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y )
% 1.27/1.66 , hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) ) ), Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.27/1.66 ), Y ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.27/1.66 ( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.27/1.66 ), Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), hAPP(
% 1.27/1.66 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.27/1.66 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP(
% 1.27/1.66 c_Nat_OSuc, hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.27/1.66 ) ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X
% 1.27/1.66 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( hAPP( c_Polynomial_OpCons( X
% 1.27/1.66 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ) ), Y ) =
% 1.27/1.66 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_Polynomial_Opoly( X
% 1.27/1.66 , Z ), Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) =
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ), Y ) =
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.27/1.66 { ! class_Lattices_Oboolean__algebra( X ), ! hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 1.27/1.66 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.27/1.66 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.27/1.66 , hAPP( Z, Y ) ) }.
% 1.27/1.66 { ! class_Lattices_Oboolean__algebra( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 1.27/1.66 { ! X = hAPP( c_Nat_OSuc, X ) }.
% 1.27/1.66 { ! hAPP( c_Nat_OSuc, X ) = X }.
% 1.27/1.66 { ! class_Groups_Ouminus( X ), hAPP( hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( tc_fun( T, X ) ), Z ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.27/1.66 , hAPP( Z, Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.27/1.66 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ), Z = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Z ) = Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) = Z }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Y ) = Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 1.27/1.66 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 1.27/1.66 { ! Y = X, hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Z ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z = Y }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.27/1.66 { ! hAPP( c_Nat_OSuc, Y ) = hAPP( c_Nat_OSuc, X ), Y = X }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.27/1.66 }.
% 1.27/1.66 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ), X ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.27/1.66 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Z ) ), Y ) =
% 1.27/1.66 hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( c_Polynomial_Ocoeff( X
% 1.27/1.66 , Z ), Y ) ) }.
% 1.27/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.27/1.66 ( tc_Int_Oint ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.27/1.66 ), c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.27/1.66 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) = hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Y ) }.
% 1.27/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Y = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.66 hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) = Y, Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.66 X ), Y ) = Y }.
% 1.27/1.66 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.27/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oring( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.27/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Z ) ), Y ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Z ) ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.27/1.66 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.27/1.66 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.27/1.66 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.27/1.66 Z = Y, Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Z = hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.27/1.66 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP
% 1.27/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.66 X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X
% 1.27/1.66 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP
% 1.27/1.66 ( c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Y ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = Y }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) }.
% 1.27/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.27/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.27/1.66 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Nat_OSuc, X ) }.
% 1.27/1.66 { ! hAPP( c_Nat_OSuc, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( c_Nat_OSuc,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc
% 1.27/1.66 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.27/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.27/1.66 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.27/1.66 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = hAPP( c_Nat_OSuc
% 1.27/1.66 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP(
% 1.27/1.66 c_Nat_OSuc, X ) ) = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.27/1.66 , Y ) ), X ) = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( c_Nat_OSuc
% 1.27/1.66 , Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y
% 1.27/1.66 ), hAPP( c_Nat_OSuc, X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.27/1.66 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.66 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ), Y = X }.
% 1.27/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.27/1.66 c_Nat_OSuc, Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.66 tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), X ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.27/1.66 c_Nat_OSuc, Y ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.27/1.66 ) ), hAPP( c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.27/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 1.27/1.66 , Z ), Y ) ), X ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) ) =
% 1.27/1.66 c_Polynomial_Odegree( X, Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 Z ), Y ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z
% 1.27/1.66 ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), Z )
% 1.27/1.66 , hAPP( c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y )
% 1.27/1.66 ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 hAPP( hAPP( c_Polynomial_Osmult( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ), Y = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! Y = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.27/1.66 c_Polynomial_OAbs__poly( X, hAPP( hAPP( c_COMBB( X, X, tc_Nat_Onat ),
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ) ), c_Polynomial_Ocoeff( X, Y ) ) ) }
% 1.27/1.66 .
% 1.27/1.66 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), hAPP( c_Nat_OSuc, X ) ) = hAPP( Y
% 1.27/1.66 , X ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), hAPP( c_Nat_OSuc, X )
% 1.27/1.66 ) = hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y
% 1.27/1.66 ), X ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), Y ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ), Z = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.66 X ), Y ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) = Y }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.27/1.66 ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) )
% 1.27/1.66 , Y ) }.
% 1.27/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.27/1.66 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.66 hAPP( c_Nat_OSuc, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.27/1.66 , Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, Y ) ) }.
% 1.27/1.66 { ! hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha1( X, Y
% 1.27/1.66 ), alpha21( X, Y ) }.
% 1.27/1.66 { ! alpha1( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.27/1.66 , Y ), X ) }.
% 1.27/1.66 { ! alpha21( X, Y ), hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.27/1.66 , Y ), X ) }.
% 1.27/1.66 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! alpha21( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 1.27/1.66 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 1.27/1.66 { ! alpha1( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.27/1.66 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y
% 1.27/1.66 ), alpha22( X, Y ) }.
% 1.27/1.66 { ! alpha2( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.27/1.66 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! alpha22( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.27/1.66 , Y ), X ) = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! alpha22( X, Y ), X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = hAPP( c_Nat_OSuc
% 1.27/1.66 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 1.27/1.66 { ! alpha2( X, Y ), Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.66 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = hAPP
% 1.27/1.66 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.27/1.66 hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = hAPP
% 1.27/1.66 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! Y = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X
% 1.27/1.66 = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Nat_OSuc,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.27/1.66 c_Nat_OSuc, Y ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.66 tc_Nat_Onat ), X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), hAPP(
% 1.27/1.66 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.27/1.66 ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X
% 1.27/1.66 ) ) }.
% 1.27/1.66 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.66 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.27/1.66 { hAPP( c_Nat_OSuc, X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.66 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP(
% 1.27/1.66 c_Nat_OSuc, X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP(
% 1.27/1.66 c_Nat_OSuc, X ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.27/1.66 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.27/1.66 Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), T ), Z ) ), hAPP( c_Nat_OSuc, Y ) ) = hAPP(
% 1.27/1.66 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.27/1.66 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP(
% 1.27/1.66 c_Nat_OSuc, X ) ) = hAPP( c_Nat_Onat_Onat__case( tc_Nat_Onat,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_COMBI( tc_Nat_Onat ) ),
% 1.27/1.66 hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.27/1.66 ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.27/1.66 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.27/1.66 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.27/1.66 { ! class_Groups_Ominus( X ), hAPP( hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_fun( U, X ) ), T ), Z ), Y ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( T, Y ) ), hAPP( Z, Y ) )
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Z ), Y ) ) = hAPP( c_Nat_OSuc,
% 1.27/1.66 c_Polynomial_Odegree( X, Y ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, hAPP( c_Nat_OSuc, Y
% 1.27/1.66 ) ) = hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ) ), c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), hAPP( c_Nat_OSuc, hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ), hAPP(
% 1.27/1.66 hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = X }.
% 1.27/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP( c_Nat_OSuc,
% 1.27/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Y ), Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) }.
% 1.27/1.66 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), Y ), Z ) ) = hAPP( c_Nat_OSuc,
% 1.27/1.66 c_Polynomial_Odegree( X, Z ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.27/1.66 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Polynomial_Oorder( X, Z, Y ) ) ) ), Y ) ) }.
% 1.27/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Z ) ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.27/1.66 c_Polynomial_Oorder( X, Z, Y ) ) ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y )
% 1.27/1.66 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.27/1.66 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) )
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ),
% 1.27/1.66 hAPP( c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ),
% 1.27/1.66 hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 1.27/1.66 hAPP( c_Polynomial_Opoly( X, Y ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.66 X ), Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.27/1.66 X ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ),
% 1.27/1.66 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) ), Y
% 1.27/1.66 ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 1.27/1.66 }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 1.27/1.66 .
% 1.27/1.66 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = X }.
% 1.27/1.66 { hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z = Y }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y, hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = Y }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 1.27/1.66 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.27/1.66 ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.27/1.66 ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.66 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 1.27/1.66 ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), ! hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.27/1.66 = Y }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), ! hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = Y }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , ! hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.27/1.66 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Y ), T ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.27/1.66 , Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.27/1.66 , Z ) ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.66 ( X ), Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.27/1.66 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Oone__class_Oone( X ) ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.27/1.66 ( X ), Z ) ), Y ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 1.27/1.66 hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Y ) ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , T ), Z ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , T ), Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.27/1.66 ( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ) = Y }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.27/1.66 ( X ), Y ) ), Z ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ),
% 1.27/1.66 Z ), Y ) ) ), Z = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 1.27/1.66 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.27/1.66 X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.27/1.66 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.27/1.66 hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.27/1.66 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.27/1.66 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.27/1.66 X ) ), T ), hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), Z ) ) ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.27/1.66 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.27/1.66 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 1.27/1.66 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 1.27/1.66 Z ) ), Z = Y }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.27/1.66 ( X ), Y ) ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = c_Groups_Oone__class_Oone
% 1.27/1.66 ( X ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.27/1.66 Z ) ), Y ) ), alpha3( X, Y, T ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.27/1.66 Z ) ), Y ) ), alpha23( X, Y, Z, T ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! alpha3( X, Y, T ), ! alpha23( X, Y, Z, T )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z ) ), Y ) ) }.
% 1.27/1.66 { ! alpha23( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha23( X, Y, Z, T ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , Z ), Y ) ), alpha23( X, Y, Z, T ) }.
% 1.27/1.66 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha3( X
% 1.27/1.66 , Y, Z ) }.
% 1.27/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.66 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.66 ( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ), hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ) }.
% 1.27/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ) ), T ) ) ), hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), U ), T ) ) ) }.
% 1.27/1.66 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.27/1.66 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.27/1.66 hAPP( Z, skol4( U, W, Z ) ) ) }.
% 1.27/1.66 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.27/1.66 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), skol4( X, Y, Z ) ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 1.27/1.66 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.66 ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), skol20( X, Y, Z ) ) ) ) }.
% 1.27/1.66 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ) ), ! hBOOL
% 1.27/1.66 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL
% 1.27/1.66 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ) ), X ) ), hBOOL( hAPP
% 1.27/1.66 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) ), hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), hAPP
% 1.27/1.66 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.27/1.66 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.27/1.66 tc_Nat_Onat ) ) ) }.
% 1.27/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.27/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 1.27/1.66 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ), hBOOL(
% 1.27/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), T ) ) ),
% 1.27/1.66 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.27/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), U ), T ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X = hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.66 { ! X = hAPP( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.27/1.66 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), hAPP(
% 1.27/1.66 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.27/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Z ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Oone__class_Oone( X
% 1.27/1.66 ), Y = c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X
% 1.27/1.66 ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.66 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Z, Y ) =
% 1.27/1.66 c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP( c_COMBB(
% 1.27/1.66 tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ), hAPP( c_COMBC(
% 1.27/1.66 tc_Nat_Onat, tc_Polynomial_Opoly( X ), tc_HOL_Obool, hAPP( hAPP( c_COMBB
% 1.27/1.66 ( tc_Polynomial_Opoly( X ), tc_fun( tc_Polynomial_Opoly( X ),
% 1.27/1.66 tc_HOL_Obool ), tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP( c_COMBB( tc_Nat_Onat,
% 1.27/1.66 tc_Polynomial_Opoly( X ), tc_Nat_Onat ), hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.66 c_Polynomial_OpCons( X ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z )
% 1.27/1.66 ), hAPP( hAPP( c_Polynomial_OpCons( X ), c_Groups_Oone__class_Oone( X )
% 1.27/1.66 ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ) ),
% 1.27/1.66 c_Nat_OSuc ) ) ), Y ) ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha49( X, Y, Z, T ), ! Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.27/1.66 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha49( X, Y, Z, T ), ! hAPP(
% 1.27/1.66 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.27/1.66 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.27/1.66 .
% 1.27/1.66 { ! alpha49( X, Y, Z, T ), alpha51( X, Y, Z, T ), alpha47( X, Y, T ) }.
% 1.27/1.66 { ! alpha49( X, Y, Z, T ), alpha51( X, Y, Z, T ), ! hAPP(
% 1.27/1.66 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! alpha51( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 1.27/1.66 { ! alpha47( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.27/1.66 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.66 alpha49( X, Y, Z, T ) }.
% 1.27/1.66 { ! alpha51( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha52( X, Y, Z, T ) }.
% 1.27/1.66 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 Z ), T ) ), alpha51( X, Y, Z, T ) }.
% 1.27/1.66 { ! alpha52( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 1.27/1.66 { ! alpha52( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), skol5( X, Y, U, W ) ), Y ) ) }.
% 1.27/1.66 { ! alpha52( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), skol5( X, Y, U, T ) ), T ) ) }.
% 1.27/1.66 { ! alpha52( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), skol5( X, Y, Z, T ) ), Z ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.27/1.66 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha52
% 1.27/1.66 ( X, Y, Z, T ) }.
% 1.27/1.66 { ! alpha47( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! alpha47( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha47( X, Y, Z
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.27/1.66 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.27/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.27/1.66 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 1.27/1.66 .
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.27/1.66 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.27/1.66 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.27/1.66 ), Z ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.27/1.66 Z ), Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! X = Y }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! Y = X }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , ! Y = X }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.27/1.66 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.27/1.66 ) ) }.
% 1.27/1.66 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.27/1.66 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.27/1.66 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.27/1.66 ), Z ) ) }.
% 1.27/1.66 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.27/1.66 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.27/1.66 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.27/1.66 Z ), Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), Y = X }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), Y = X }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.27/1.66 ), Z ) ) }.
% 1.27/1.66 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.27/1.66 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.27/1.66 ), Z ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.27/1.66 , X ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.27/1.66 ), Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , Y = X }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), Y = X }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), X = Y }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.27/1.66 ), Y ) ) }.
% 1.27/1.66 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.27/1.66 , X ) ) }.
% 1.27/1.66 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.27/1.66 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.27/1.66 , X ) ) }.
% 1.27/1.66 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.27/1.66 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.27/1.66 ), Y ) ) }.
% 1.27/1.66 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! alpha4( X, Y ), ! Y = X }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , Y = X, alpha4( X, Y ) }.
% 1.27/1.66 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! alpha4( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Nat_Onat ), X ), Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , alpha4( X, Y ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , alpha5( X, Y ), Y = X }.
% 1.27/1.66 { ! alpha5( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.27/1.66 , X ) ) }.
% 1.27/1.66 { ! alpha5( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.66 { ! alpha5( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.66 tc_Nat_Onat ), X ), Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.27/1.66 , alpha5( X, Y ) }.
% 1.27/1.66 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.27/1.66 , X ) ) }.
% 1.27/1.66 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 1.27/1.66 , Y ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.27/1.66 ), Y = X }.
% 1.27/1.66 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.27/1.66 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.27/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Nat_Onat ) ) ), c_Orderings_Oord__class_OLeast( tc_Nat_Onat, X ) =
% 1.27/1.66 hAPP( c_Nat_OSuc, c_Orderings_Oord__class_OLeast( tc_Nat_Onat, hAPP( hAPP
% 1.27/1.66 ( c_COMBB( tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat ), X ), c_Nat_OSuc ) )
% 1.27/1.66 ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.27/1.66 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 1.27/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 1.27/1.66 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.27/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), hAPP( T, Z ) = c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X,
% 1.27/1.66 hAPP( hAPP( c_COMBB( X, X, X ), c_Rings_Oinverse__class_Oinverse( X ) ),
% 1.27/1.66 T ), Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( T, Z ) ), hAPP( c_Nat_OSuc, hAPP
% 1.27/1.66 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) ) ) ) }
% 1.27/1.66 .
% 1.27/1.66 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) = hAPP(
% 1.27/1.66 hAPP( c_Polynomial_Osmult( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X
% 1.27/1.66 ), hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) )
% 1.27/1.66 , Y ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 1.27/1.66 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.27/1.66 c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X,
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), Y, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Power_Opower__class_Opower( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.27/1.66 ( X ), Y ) ), hAPP( c_Nat_OSuc, hAPP( c_Nat_OSuc,
% 1.27/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) ) }.
% 1.27/1.66 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 1.27/1.66 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), c_Deriv_Oderiv( X, hAPP(
% 1.27/1.66 c_COMBK( X, X ), Z ), Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, U,
% 1.27/1.66 hAPP( T, Z ), Y ), ! c_Deriv_Oderiv( X, T, Z, W ), c_Deriv_Oderiv( X,
% 1.27/1.66 hAPP( hAPP( c_COMBB( X, X, X ), U ), T ), Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), W ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! c_Deriv_Oderiv( X, W, hAPP( T, Z ), U ), c_Deriv_Oderiv( X, hAPP(
% 1.27/1.66 hAPP( c_COMBB( X, X, X ), W ), T ), Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), c_Deriv_Oderiv( X, hAPP( hAPP( c_COMBB( X, X, X ), hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ) ), T ), Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), c_Deriv_Oderiv( X, hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y, Z ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.27/1.66 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_Osmult( X ), T ), Z )
% 1.27/1.66 , Y ) = hAPP( hAPP( c_Polynomial_Osmult( X ), T ),
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! Y = U, c_Deriv_Oderiv( X, T, Z, U ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! Y = U, c_Deriv_Oderiv( X, T, Z, U ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! c_Deriv_Oderiv( X, T, Z, U ), Y = U }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.27/1.66 tc_Polynomial_Opoly( X ), Z, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), Y ) ) = c_Divides_Odiv__class_Omod(
% 1.27/1.66 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.27/1.66 tc_Polynomial_Opoly( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), Z ), Y ) = hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.27/1.66 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), U ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.27/1.66 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( X ), Y ), U ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), c_Deriv_Oderiv( X, c_COMBI
% 1.27/1.66 ( X ), Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), c_Deriv_Oderiv( X, hAPP( hAPP( c_COMBB( X, X, X ),
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ) ), T ), Z, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, hAPP( hAPP(
% 1.27/1.66 c_Polynomial_Osmult( X ), Y ), Z ) ) = c_Divides_Odiv__class_Omod(
% 1.27/1.66 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.27/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.27/1.66 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 1.27/1.66 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.27/1.66 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( W, Z ) ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( T, Z ) ) ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.27/1.66 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( T, Z ) ), U ) ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( W, Z ) ) ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), c_Deriv_Oderiv( X, hAPP( hAPP(
% 1.27/1.66 c_COMBS( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ) ), T ) ), hAPP( hAPP( c_COMBB( X, X, X )
% 1.27/1.66 , c_Groups_Ouminus__class_Ouminus( X ) ), W ) ), Z, hAPP( hAPP(
% 1.27/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( X ), U ) ) ) }.
% 1.27/1.66 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.66 Y ), hAPP( T, Z ) = c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X,
% 1.27/1.66 hAPP( hAPP( c_COMBB( X, X, X ), c_Rings_Oinverse__class_Oinverse( X ) ),
% 1.27/1.66 T ), Z, hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), hAPP( T, Z ) ) ), Y ) ), hAPP(
% 1.27/1.66 c_Rings_Oinverse__class_Oinverse( X ), hAPP( T, Z ) ) ) ) ) }.
% 1.27/1.66 { ! class_Orderings_Owellorder( X ), ! hBOOL( hAPP( Y, Z ) ), hBOOL( hAPP(
% 1.27/1.66 Y, c_Orderings_Oord__class_OLeast( X, Y ) ) ) }.
% 1.27/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 1.27/1.66 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 1.27/1.66 Z ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.27/1.66 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 1.27/1.66 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.27/1.66 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.27/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.27/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.27/1.66 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.27/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), Z )
% 1.27/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) ) }.
% 1.27/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP( hAPP
% 1.27/1.66 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP( hAPP
% 1.27/1.66 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.27/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ),
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.27/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), c_Divides_Odiv__class_Omod
% 1.27/1.66 ( tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod(
% 1.27/1.66 tc_Int_Oint, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z
% 1.27/1.66 ), X ), Y ) }.
% 1.27/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.27/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) }.
% 1.27/1.66 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), hAPP(
% 1.27/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) = hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.27/1.67 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.27/1.67 }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 1.27/1.67 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 1.27/1.67 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.27/1.67 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol6( X, Y ) ) }.
% 1.27/1.67 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.27/1.67 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol7( X, Y ) ) }.
% 1.27/1.67 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.27/1.67 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { ! hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X
% 1.27/1.67 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X ) =
% 1.27/1.67 hAPP( c_Nat_OSuc, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), hAPP(
% 1.27/1.67 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), X ) ) ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( c_Nat_OSuc, X ), Y ) }.
% 1.27/1.67 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Int_Oint, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X
% 1.27/1.67 ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Int_Oint, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X
% 1.27/1.67 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.27/1.67 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Int_Oint, Y, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X )
% 1.27/1.67 ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Int_Oint, Y, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X )
% 1.27/1.67 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.27/1.67 X, Z, Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.27/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.27/1.67 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.27/1.67 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.67 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.27/1.67 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.27/1.67 ), Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.27/1.67 , Y ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.67 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.67 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.67 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.27/1.67 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.27/1.67 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.27/1.67 ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), U ), Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Omod( X,
% 1.27/1.67 T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), c_Divides_Odiv__class_Omod
% 1.27/1.67 ( X, Z, Y ) ), Y ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.27/1.67 ), c_Divides_Odiv__class_Omod( X, T, Y ) ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 X, Z, Y ) ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.27/1.67 ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.27/1.67 ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Z ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, Y, Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ) }.
% 1.27/1.67 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.27/1.67 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.27/1.67 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.27/1.67 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), Y ), U ), Z ) }.
% 1.27/1.67 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.27/1.67 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.27/1.67 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.27/1.67 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.27/1.67 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.27/1.67 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.27/1.67 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.27/1.67 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.27/1.67 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.27/1.67 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.27/1.67 , c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.27/1.67 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.27/1.67 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 1.27/1.67 hAPP( c_Groups_Ouminus__class_Ouminus( X ), T ), Z ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, hAPP( c_Groups_Ouminus__class_Ouminus( X )
% 1.27/1.67 , Y ), Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.27/1.67 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ),
% 1.27/1.67 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, Y, T )
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 1.27/1.67 , c_Divides_Odiv__class_Omod( X, T, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.27/1.67 ( X, T, Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.27/1.67 ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Polynomial_OpCons( X ), T ), Z )
% 1.27/1.67 , Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X
% 1.27/1.67 ) ), hAPP( hAPP( c_Polynomial_OpCons( X ), T ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) ), hAPP(
% 1.27/1.67 hAPP( c_Polynomial_Osmult( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.27/1.67 ( hAPP( c_Polynomial_OpCons( X ), T ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ) ),
% 1.27/1.67 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) ), Y
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.67 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), hAPP( W, Z ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X, hAPP( hAPP( c_COMBS
% 1.27/1.67 ( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( W, Z ) ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( T, Z ) ) ) ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), hAPP( W, Z ) ), hAPP( c_Nat_OSuc, hAPP
% 1.27/1.67 ( c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.67 Y ), c_Deriv_Oderiv( X, hAPP( c_COMBC( X, tc_Nat_Onat, X, hAPP( hAPP(
% 1.27/1.67 c_COMBB( X, tc_fun( tc_Nat_Onat, X ), X ), c_Power_Opower__class_Opower(
% 1.27/1.67 X ) ), T ) ), U ), Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, U ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), hAPP( T, Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), U ), hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) ) ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.67 Y ), c_Deriv_Oderiv( X, hAPP( c_COMBC( X, tc_Nat_Onat, X, hAPP( hAPP(
% 1.27/1.67 c_COMBB( X, tc_fun( tc_Nat_Onat, X ), X ), c_Power_Opower__class_Opower(
% 1.27/1.67 X ) ), T ) ), hAPP( c_Nat_OSuc, U ) ), Z, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, U ) ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), hAPP( T, Z ) ), U ) ) ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.27/1.67 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.67 Y ), c_Deriv_Oderiv( X, hAPP( c_COMBC( X, X, X, hAPP( hAPP( c_COMBB( X,
% 1.27/1.67 tc_fun( X, X ), X ), c_Rings_Oinverse__class_Odivide( X ) ), T ) ), U ),
% 1.27/1.67 Z, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), U ) ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 1.27/1.67 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Y ), c_Groups_Oone__class_Oone( X )
% 1.27/1.67 ) = Y }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) = hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), hAPP( c_Groups_Ouminus__class_Ouminus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) =
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Nat_Osemiring__char__0( X ), ! c_Nat_Osemiring__1__class_Oof__nat
% 1.27/1.67 ( X, Z ) = c_Nat_Osemiring__1__class_Oof__nat( X, Y ), Z = Y }.
% 1.27/1.67 { ! class_Nat_Osemiring__char__0( X ), ! Z = Y,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! T = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), alpha24( X, Y, Z, T ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! T = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), alpha6( X, Y, T ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha24( X, Y, Z, T ), !
% 1.27/1.67 alpha6( X, Y, T ), T = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ),
% 1.27/1.67 Z ), Y ) }.
% 1.27/1.67 { ! alpha24( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.27/1.67 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha24( X, Y, Z, T ) }.
% 1.27/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha24(
% 1.27/1.67 X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha6( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { Y = c_Groups_Ozero__class_Ozero( X ), alpha6( X, Y, Z ) }.
% 1.27/1.67 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha6( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) = Y, alpha25( X, Y, Z, T )
% 1.27/1.67 }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) = Y, alpha7( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha25( X, Y, Z, T ), !
% 1.27/1.67 alpha7( X, Y, Z ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T )
% 1.27/1.67 , Z ) = Y }.
% 1.27/1.67 { ! alpha25( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.27/1.67 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha25( X, Y, Z, T ) }.
% 1.27/1.67 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha25(
% 1.27/1.67 X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha7( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { Z = c_Groups_Ozero__class_Ozero( X ), alpha7( X, Y, Z ) }.
% 1.27/1.67 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha7( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! T = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z, T =
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), hAPP(
% 1.27/1.67 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), hAPP(
% 1.27/1.67 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) =
% 1.27/1.67 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! Z = Y, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) =
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 1.27/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) =
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.67 hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X
% 1.27/1.67 ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Z
% 1.27/1.67 ) ), Y ) }.
% 1.27/1.67 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide(
% 1.27/1.67 X ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP
% 1.27/1.67 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ),
% 1.27/1.67 Y ) = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ),
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Y
% 1.27/1.67 ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) ) = hAPP(
% 1.27/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) ), X ) }.
% 1.27/1.67 { ! hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { ! hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), X =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 1.27/1.67 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 1.27/1.67 tc_Int_Oint ) }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 1.27/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ) =
% 1.27/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Z ) ), Y ) }.
% 1.27/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.67 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 1.27/1.67 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) }.
% 1.27/1.67 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 1.27/1.67 hAPP( c_Nat_OSuc, Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ), c_Nat_Osemiring__1__class_Oof__nat( X,
% 1.27/1.67 Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), T ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) )
% 1.27/1.67 = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.67 hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), Z ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z )
% 1.27/1.67 = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.67 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), U ), Y ) ), hAPP
% 1.27/1.67 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.67 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.67 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), Z ) ), Y ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__field( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), W ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), W ), T ) ), Y ) ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Y
% 1.27/1.67 ) }.
% 1.27/1.67 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.27/1.67 { c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, X ) )
% 1.27/1.67 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), ! c_Deriv_Oderiv( X, T, Z,
% 1.27/1.67 Y ), ! c_Deriv_Oderiv( X, W, Z, U ), hAPP( W, Z ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), c_Deriv_Oderiv( X, hAPP( hAPP( c_COMBS
% 1.27/1.67 ( X, X, X ), hAPP( hAPP( c_COMBB( X, tc_fun( X, X ), X ),
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ) ), T ) ), W ), Z, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( W, Z ) ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( T, Z ) ), U ) ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( W, Z ) ), hAPP( W, Z ) ) ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) ), T ) = hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) ), T ) ) ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) ) }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat( X, Y
% 1.27/1.67 ) = c_Nat_Osemiring__1__class_Oof__nat__aux( X, hAPP( c_COMBC( X, X, X,
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ) ), c_Groups_Oone__class_Oone( X ) ), Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.27/1.67 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.27/1.67 c_Polynomial_Ocoeff( X, hAPP( hAPP( c_Polynomial_OpCons( X ), W ), Y ) )
% 1.27/1.67 , c_Polynomial_Odegree( X, T ) ) ), hAPP( c_Polynomial_Ocoeff( X, T ),
% 1.27/1.67 c_Polynomial_Odegree( X, T ) ) ), c_Polynomial_Opdivmod__rel( X, hAPP(
% 1.27/1.67 hAPP( c_Polynomial_OpCons( X ), W ), U ), T, hAPP( hAPP(
% 1.27/1.67 c_Polynomial_OpCons( X ), V0 ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.27/1.67 c_Polynomial_OpCons( X ), W ), Y ) ), hAPP( hAPP( c_Polynomial_Osmult( X
% 1.27/1.67 ), V0 ), T ) ) ) }.
% 1.27/1.67 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ), X ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), Y = X }.
% 1.27/1.67 { ! Y = X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 1.27/1.67 { ! c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ), Y = X }.
% 1.27/1.67 { ! Y = X, c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.27/1.67 , c_Polynomial_Opdivmod__rel( X, hAPP( hAPP( c_Polynomial_Osmult( X ), W
% 1.27/1.67 ), U ), T, hAPP( hAPP( c_Polynomial_Osmult( X ), W ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Polynomial_Osmult( X ), W ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.27/1.67 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.27/1.67 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.27/1.67 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.27/1.67 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.27/1.67 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 1.27/1.67 ( X, Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) = Y }.
% 1.27/1.67 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 1.27/1.67 ( X, T, hAPP( c_Nat_OSuc, Z ), Y ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat__aux( X, T, Z, hAPP( T, Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.27/1.67 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.27/1.67 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.27/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 1.27/1.67 ), W ) ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.27/1.67 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.27/1.67 X, W, hAPP( hAPP( c_Polynomial_Osmult( X ), Y ), U ), hAPP( hAPP(
% 1.27/1.67 c_Polynomial_Osmult( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y
% 1.27/1.67 ) ), T ), Z ) }.
% 1.27/1.67 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint,
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ), hBOOL( hAPP(
% 1.27/1.67 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.27/1.67 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.27/1.67 , U = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) )
% 1.27/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.27/1.67 Z ), T ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.27/1.67 , alpha37( X, Y, Z, T ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! U = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), Z ), T ) ), Y ), ! alpha37( X, Y, Z, T ),
% 1.27/1.67 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.27/1.67 { ! alpha37( X, Y, Z, T ), alpha8( X, Z, T ) }.
% 1.27/1.67 { ! alpha37( X, Y, Z, T ), alpha26( X, Y, T ) }.
% 1.27/1.67 { ! alpha8( X, Z, T ), ! alpha26( X, Y, T ), alpha37( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha26( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), alpha38( X, Y, Z ) }.
% 1.27/1.67 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha26( X
% 1.27/1.67 , Y, Z ) }.
% 1.27/1.67 { ! alpha38( X, Y, Z ), alpha26( X, Y, Z ) }.
% 1.27/1.67 { ! alpha38( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.27/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha38( X
% 1.27/1.67 , Y, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.27/1.67 ), c_Polynomial_Odegree( X, Z ) ), alpha38( X, Y, Z ) }.
% 1.27/1.67 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X, Y
% 1.27/1.67 , Z ) }.
% 1.27/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha8( X
% 1.27/1.67 , Y, Z ) }.
% 1.27/1.67 { ! class_Rings_Oring__1( X ), c_Transcendental_Odiffs( X, Z, Y ) = hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, hAPP( c_Nat_OSuc, Y ) ) ), hAPP( Z
% 1.27/1.67 , hAPP( c_Nat_OSuc, Y ) ) ) }.
% 1.27/1.67 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP(
% 1.27/1.67 c_Nat_OSuc, X ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), hAPP( c_Nat_OSuc, X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), c_Nat_Osemiring__1__class_Oof__nat
% 1.27/1.67 ( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Nat_Osemiring__1__class_Oof__nat( X, Z ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Z ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Z ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Nat_Osemiring__1__class_Oof__nat( X, Z ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( X, Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 1.27/1.67 alpha27( X, Y, Z, T ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z, T ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.67 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha27( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.27/1.67 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha10( X, Y, Z, T ),
% 1.27/1.67 alpha28( X, Y, Z, T ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z, T ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha28( X, Y, Z, T ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! alpha28( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! alpha28( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha28( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.27/1.67 { ! alpha10( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha10( X, Y, Z, T ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, T, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), c_Groups_Ozero__class_Ozero(
% 1.27/1.67 X ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( X ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.27/1.67 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.27/1.67 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), Z ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.27/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, U, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, U, T ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 X ), Z ), hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 X ), Z ), Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ), Z ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 X ), Y ), Z ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ), Y ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Z ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.27/1.67 .
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Y, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.27/1.67 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.27/1.67 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.27/1.67 { alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.27/1.67 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.27/1.67 { alpha48( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.27/1.67 ( X, Y ), Z ) ) }.
% 1.27/1.67 { ! alpha48( X, Y, Z ), alpha50( X, Y, Z ), Z = Y }.
% 1.27/1.67 { ! alpha48( X, Y, Z ), alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! alpha50( X, Y, Z ), alpha48( X, Y, Z ) }.
% 1.27/1.67 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha48( X, Y, Z ) }.
% 1.27/1.67 { ! alpha50( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.27/1.67 }.
% 1.27/1.67 { ! alpha50( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.27/1.67 X, Y ), Z ) ), alpha50( X, Y, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP
% 1.27/1.67 ( c_Nat_OSuc, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.27/1.67 .
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), X )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), Z ) }
% 1.27/1.67 .
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hAPP( c_Nat_OSuc, Y
% 1.27/1.67 ) = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y )
% 1.27/1.67 , X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ), X
% 1.27/1.67 = Y }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ), Y
% 1.27/1.67 = X }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP
% 1.27/1.67 ( c_Nat_OSuc, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.27/1.67 .
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc, Y ), hAPP(
% 1.27/1.67 c_Nat_OSuc, X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc
% 1.27/1.67 , X ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, Y ) )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.27/1.67 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.27/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 Y ) }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 Y ), ! Z = Y }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 Z ), ! Z = Y }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.27/1.67 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.27/1.67 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.27/1.67 , ! Z = Y }.
% 1.27/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.27/1.67 , ! Z = Y }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.27/1.67 , ! Y = Z }.
% 1.27/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.27/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.27/1.67 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.27/1.67 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.27/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.27/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.27/1.67 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Orderings_Owellorder( X ), ! c_Orderings_Oord__class_Oless( X, Z
% 1.27/1.67 , c_Orderings_Oord__class_OLeast( X, Y ) ), ! hBOOL( hAPP( Y, Z ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 X ), Y ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.27/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 X ), Y ), Y ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 X ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( c_Groups_Ouminus__class_Ouminus( X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( c_Groups_Ouminus__class_Ouminus( X ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ),
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha11( X, Y,
% 1.27/1.67 Z ), alpha29( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha11( X, Y, Z
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 ), alpha29( X, Y, Z ) }.
% 1.27/1.67 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.27/1.67 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.27/1.67 ), alpha11( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ), alpha30( X, Y, Z
% 1.27/1.67 ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.27/1.67 ), alpha30( X, Y, Z ) }.
% 1.27/1.67 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.27/1.67 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.27/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 ), alpha12( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Z ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Z ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), T ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Y ), T ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), T ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), T ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Nat_Osemiring__1__class_Oof__nat( X, Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Rings_Oinverse__class_Oinverse
% 1.27/1.67 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( c_Rings_Oinverse__class_Oinverse
% 1.27/1.67 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) )
% 1.27/1.67 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha13( X, Y ) }.
% 1.27/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! alpha13( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP(
% 1.27/1.67 c_Nat_OSuc, X ) ) }.
% 1.27/1.67 { ! alpha13( X, Y ), Y = hAPP( c_Nat_OSuc, skol8( Z, Y ) ) }.
% 1.27/1.67 { ! alpha13( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol8( X,
% 1.27/1.67 Y ), X ) }.
% 1.27/1.67 { ! Y = hAPP( c_Nat_OSuc, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.27/1.67 , Z, X ), alpha13( X, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), X = hAPP( c_Nat_OSuc, skol9( X ) ) }.
% 1.27/1.67 { ! X = hAPP( c_Nat_OSuc, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.27/1.67 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.27/1.67 Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = hAPP(
% 1.27/1.67 c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.27/1.67 skol10( X, Y ) ) ) }.
% 1.27/1.67 { ! X = hAPP( c_Nat_OSuc, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.67 tc_Nat_Onat ), Y ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.27/1.67 , X ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, hAPP(
% 1.27/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Nat_OSuc, hAPP(
% 1.27/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.27/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.27/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.67 Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.67 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.67 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.27/1.67 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.67 tc_Nat_Onat ), X ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 1.27/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.27/1.67 Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.27/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.27/1.67 c_Nat_OSuc, Z ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.27/1.67 X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Nat_OSuc, Z ) ), Y
% 1.27/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.27/1.67 c_Nat_OSuc, Z ) ), X ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), hAPP( c_Nat_OSuc
% 1.27/1.67 , Y ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = Y }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.27/1.67 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.27/1.67 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.27/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.27/1.67 ), X ) ) }.
% 1.27/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.27/1.67 , c_Polynomial_Odegree( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), Y ), Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.27/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.27/1.67 , c_Polynomial_Odegree( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.27/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.27/1.67 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.27/1.67 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Z
% 1.27/1.67 ), T ) ), Y ) }.
% 1.27/1.67 { ! class_Rings_Oring__1( X ), c_Transcendental_Odiffs( X, hAPP( hAPP(
% 1.27/1.67 c_COMBB( X, X, tc_Nat_Onat ), c_Groups_Ouminus__class_Ouminus( X ) ), Z )
% 1.27/1.67 , Y ) = hAPP( c_Groups_Ouminus__class_Ouminus( X ),
% 1.27/1.67 c_Transcendental_Odiffs( X, Z, Y ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.27/1.67 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.27/1.67 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.27/1.67 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.27/1.67 X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) )
% 1.27/1.67 , Z ), T ) ), Y ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ), ! Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.27/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.27/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ),
% 1.27/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ), Y ) }.
% 1.27/1.67 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ),
% 1.27/1.67 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha31( X, Y, Z, T ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha39( X, Y, Z, T ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 1.27/1.67 , T ), ! alpha39( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, hAPP
% 1.27/1.67 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! alpha39( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha42( X, Y, Z, T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.27/1.67 , alpha39( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha42( X, Y, Z, T ), alpha39( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha42( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha42( X, Y, Z, T ), alpha14( X, Y, T ) }.
% 1.27/1.67 { ! alpha45( X, Y, Z, T ), ! alpha14( X, Y, T ), alpha42( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha45( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 alpha45( X, Y, Z, T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha45( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha31( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 alpha31( X, Y, Z, T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha31( X, Y, Z, T )
% 1.27/1.67 }.
% 1.27/1.67 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , alpha14( X, Y, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , alpha14( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ), alpha32( X, Y, Z, T
% 1.27/1.67 ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ), alpha40( X, Y, Z, T
% 1.27/1.67 ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 1.27/1.67 , T ), ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.27/1.67 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ) }.
% 1.27/1.67 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), alpha43( X, Y, Z, T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.27/1.67 , alpha40( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha43( X, Y, Z, T ), alpha40( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha43( X, Y, Z, T ), alpha46( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha43( X, Y, Z, T ), alpha15( X, Y, Z ) }.
% 1.27/1.67 { ! alpha46( X, Y, Z, T ), ! alpha15( X, Y, Z ), alpha43( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha46( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.27/1.67 alpha46( X, Y, Z, T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha46( X, Y, Z, T )
% 1.27/1.67 }.
% 1.27/1.67 { ! alpha32( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.27/1.67 alpha32( X, Y, Z, T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha32( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.27/1.67 , alpha15( X, Y, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.27/1.67 , alpha15( X, Y, Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, T, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, T, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.27/1.67 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.27/1.67 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.27/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.27/1.67 ( X ), Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.27/1.67 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc
% 1.27/1.67 , Y ) ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.67 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.27/1.67 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.27/1.67 ), Y ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.67 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.27/1.67 , Y ) ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.27/1.67 ), Y ), X ) ) ), ! alpha16( X, Y, Z ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.27/1.67 ), Y ), X ) ) ), ! alpha33( X, Y, Z ) }.
% 1.27/1.67 { alpha16( X, Y, Z ), alpha33( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.27/1.67 { ! alpha33( X, Y, Z ), ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ) }.
% 1.27/1.67 { ! alpha33( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.67 tc_Nat_Onat ), X ), skol11( X, Y, Z ) ) }.
% 1.27/1.67 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 1.27/1.67 hBOOL( hAPP( Z, T ) ), alpha33( X, Y, Z ) }.
% 1.27/1.67 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.27/1.67 }.
% 1.27/1.67 { ! alpha16( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16( X, Y, Z ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.27/1.67 ), Y ), X ) ) ), alpha17( X, Y, Z ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.27/1.67 ), Y ), X ) ) ), alpha34( X, Y, Z ) }.
% 1.27/1.67 { ! alpha17( X, Y, Z ), ! alpha34( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.27/1.67 { ! alpha34( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.67 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha34( X, Y, Z ) }.
% 1.27/1.67 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol12(
% 1.27/1.67 X, Y, Z ) ), alpha34( X, Y, Z ) }.
% 1.27/1.67 { ! alpha17( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.27/1.67 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha17( X, Y, Z ) }
% 1.27/1.67 .
% 1.27/1.67 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17
% 1.27/1.67 ( X, Y, Z ) }.
% 1.27/1.67 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.27/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.27/1.67 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.27/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), hAPP( c_Nat_OSuc, Z ) ),
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 1.27/1.67 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.27/1.67 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), X = hAPP( c_Nat_OSuc, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.67 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.27/1.67 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.67 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.27/1.67 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.27/1.67 alpha18( X, Y, Z ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.27/1.67 alpha35( X, Y, Z ) }.
% 1.27/1.67 { ! alpha18( X, Y, Z ), ! alpha35( X, Y, Z ), hBOOL( hAPP( Z,
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 1.27/1.67 { ! alpha35( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 alpha41( X, Y, Z ) }.
% 1.27/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha35( X, Y, Z ) }.
% 1.27/1.67 { ! alpha41( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.27/1.67 { ! alpha41( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.27/1.67 ), alpha44( X, Y, Z, T ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol13( X, T, U ), X ),
% 1.27/1.67 alpha41( X, Y, Z ) }.
% 1.27/1.67 { ! alpha44( X, Y, Z, skol13( X, Y, Z ) ), alpha41( X, Y, Z ) }.
% 1.27/1.67 { ! alpha44( X, Y, Z, T ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.27/1.67 X ), U ) ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.27/1.67 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol14( X, Y, T ) ) )
% 1.27/1.67 , T ), alpha44( X, Y, Z, T ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, T ) ), alpha44( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha18( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 hBOOL( hAPP( Z, Y ) ) }.
% 1.27/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha18( X, Y, Z ) }.
% 1.27/1.67 { ! hBOOL( hAPP( Z, Y ) ), alpha18( X, Y, Z ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ) ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.27/1.67 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP(
% 1.27/1.67 c_Nat_OSuc, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.27/1.67 , Y ) ), X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.27/1.67 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), Y ) }.
% 1.27/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.27/1.67 ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( c_Nat_OSuc, hAPP(
% 1.27/1.67 c_Nat_OSuc, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 1.27/1.67 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.27/1.67 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 1.27/1.67 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.27/1.67 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.27/1.67 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 1.27/1.67 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 1.27/1.67 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.27/1.67 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.27/1.67 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.27/1.67 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 1.27/1.67 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 1.27/1.67 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ) ) ) ), Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), T ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ), Z ), T ) ), c_Orderings_Oord__class_Oless( X, hAPP( Y, T )
% 1.27/1.67 , hAPP( Y, Z ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, Y ) )
% 1.27/1.67 ), c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.27/1.67 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.27/1.67 ( tc_Int_Oint, Y, X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.27/1.67 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.27/1.67 tc_Int_Oint ) ), X ) ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) )
% 1.27/1.67 , c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.27/1.67 tc_Int_Oint ) ), X ) ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) )
% 1.27/1.67 }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.67 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.27/1.67 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.27/1.67 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), X = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, skol15
% 1.27/1.67 ( X, Y ) ) ) ) }.
% 1.27/1.67 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, Z ) )
% 1.27/1.67 ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Z ) ), X ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, X ) )
% 1.27/1.67 ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Ostrict__mono(
% 1.27/1.67 tc_Nat_Onat, X, hAPP( hAPP( c_COMBS( tc_Nat_Onat, tc_fun( tc_Nat_Onat,
% 1.27/1.67 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ) ), hAPP( hAPP(
% 1.27/1.67 c_COMBB( tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.27/1.67 tc_fun( tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_fun( tc_Nat_Onat,
% 1.27/1.67 tc_HOL_Obool ) ), tc_Nat_Onat ), c_COMBS( tc_Nat_Onat, tc_HOL_Obool,
% 1.27/1.67 tc_HOL_Obool ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat, tc_HOL_Obool
% 1.27/1.67 ), tc_fun( tc_Nat_Onat, tc_fun( tc_HOL_Obool, tc_HOL_Obool ) ),
% 1.27/1.67 tc_Nat_Onat ), hAPP( c_COMBB( tc_HOL_Obool, tc_fun( tc_HOL_Obool,
% 1.27/1.67 tc_HOL_Obool ), tc_Nat_Onat ), c_fconj ) ), c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ) ) ) ), hAPP( hAPP( c_COMBB( tc_fun( tc_Nat_Onat,
% 1.27/1.67 tc_HOL_Obool ), tc_fun( tc_Nat_Onat, tc_HOL_Obool ), tc_Nat_Onat ), hAPP
% 1.27/1.67 ( c_COMBB( tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat ), c_fNot ) ), c_COMBC
% 1.27/1.67 ( tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool, c_Rings_Odvd__class_Odvd(
% 1.27/1.67 tc_Nat_Onat ) ) ) ), Y ), c_Orderings_Oorder_Omono( tc_Nat_Onat, X,
% 1.27/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.27/1.67 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.27/1.67 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.27/1.67 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 1.27/1.67 ( hAPP( c_Polynomial_OpCons( X ), Z ), Y ) ), c_Polynomial_Opos__poly( X
% 1.27/1.67 , Y ), alpha19( X, Y, Z ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.27/1.67 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! alpha19( X, Y, Z ),
% 1.27/1.67 c_Polynomial_Opos__poly( X, hAPP( hAPP( c_Polynomial_OpCons( X ), Z ), Y
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! alpha19( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.27/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.27/1.67 alpha19( X, Y, Z ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.27/1.67 ( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, hAPP
% 1.27/1.67 ( hAPP( c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ) ), Y ), Z
% 1.27/1.67 ) ), c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.27/1.67 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.27/1.67 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.27/1.67 ( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.27/1.67 c_Polynomial_Opos__poly( X, hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), Y ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( c_Nat_OSuc,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X = hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, hAPP( c_Nat_OSuc, skol16
% 1.27/1.67 ( X ) ) ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), !
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T, Z = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z ) ), ! Z =
% 1.27/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, Z, Y ) = T }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! c_Divides_Odiv__class_Odiv(
% 1.27/1.67 X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , Z = c_Groups_Ozero__class_Ozero( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), U ) ), ! hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.27/1.67 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.27/1.67 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.27/1.67 }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 1.27/1.67 , Z ) ) = Y }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Odiv( X, Y
% 1.27/1.67 , Z ) ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.27/1.67 ), Z ) = Y }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.27/1.67 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.27/1.67 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.27/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.27/1.67 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), c_Divides_Odiv__class_Odiv( X
% 1.27/1.67 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z ) = hAPP(
% 1.27/1.67 hAPP( c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Odiv( X, Y
% 1.27/1.67 , Z ) ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( X ) }.
% 1.27/1.67 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 1.27/1.67 , Y, hAPP( c_Groups_Ouminus__class_Ouminus( X ), Z ) ) = hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), c_Divides_Odiv__class_Odiv( X, Y, Z
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_Divides_Oring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Odiv( X
% 1.27/1.67 , hAPP( c_Groups_Ouminus__class_Ouminus( X ), Y ), Z ) = hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( X ), c_Divides_Odiv__class_Odiv( X, Y, Z
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.27/1.67 ), T ) = c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.27/1.67 c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.27/1.67 ( tc_Int_Oint, Z, Y ) ), Y ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 1.27/1.67 Z, Y ) ) ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint )
% 1.27/1.67 , Z ), X ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ) ), X ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) = hAPP( hAPP
% 1.27/1.67 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.27/1.67 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.27/1.67 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.27/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) ) }.
% 1.27/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.27/1.67 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 }.
% 1.27/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X ) ) =
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ), hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), ! hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.27/1.67 c_Rings_Odvd__class_Odvd( X ), c_Divides_Odiv__class_Odiv( X, Y, Z ) ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, T, Z ) ) ) }.
% 1.27/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.27/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.27/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ), X ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) )
% 1.27/1.67 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.27/1.67 , X ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ) ) = X }.
% 1.27/1.67 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.27/1.67 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), Y ), Z ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.27/1.67 }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.27/1.67 }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y
% 1.27/1.67 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.27/1.67 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y
% 1.27/1.67 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, X, Y ), X ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ), Y ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.27/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, Z, Y ), X ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ) ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( X, T, Z ) ) ), Y ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.27/1.67 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, Z, T ) ) ), c_Divides_Odiv__class_Omod( X
% 1.27/1.67 , Z, T ) ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y
% 1.27/1.67 ) }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.27/1.67 ), Y ) ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), c_Divides_Odiv__class_Odiv( X, Y
% 1.27/1.67 , Z ) ) ), c_Divides_Odiv__class_Omod( X, Y, Z ) ) = Y }.
% 1.27/1.67 { ! class_Divides_Osemiring__div( X ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( X ), c_Divides_Odiv__class_Omod( X, Z, Y ) )
% 1.27/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), Y ) ) = Z }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 1.27/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) = hAPP(
% 1.27/1.67 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, Z, Y ), X ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z
% 1.27/1.67 , Y ) ) }.
% 1.27/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, Y, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X )
% 1.27/1.67 ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) }.
% 1.27/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, Y, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), X )
% 1.27/1.67 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.27/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X
% 1.27/1.67 ) = hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) }.
% 1.27/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, hAPP( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ), Y ), X
% 1.27/1.67 ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.27/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 1.27/1.67 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.27/1.67 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 1.27/1.67 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.27/1.67 tc_Polynomial_Opoly( X ), Y ) = hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ), c_Groups_Oone__class_Oone(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 1.27/1.67 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 1.27/1.67 ) ), ! alpha20( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), alpha20( X, Y, skol17( X, Y, Z ), skol21( X, Y, Z )
% 1.27/1.67 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 1.27/1.67 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.27/1.67 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol17( X, Y, Z ) ), skol21
% 1.27/1.67 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.27/1.67 ) }.
% 1.27/1.67 { ! alpha20( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 1.27/1.67 { ! alpha20( X, Y, Z, T ), alpha36( X, Y, Z, T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha36( X, Y, Z, T )
% 1.27/1.67 , alpha20( X, Y, Z, T ) }.
% 1.27/1.67 { ! alpha36( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.27/1.67 ) }.
% 1.27/1.67 { ! alpha36( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.27/1.67 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.27/1.67 X ), Z ) ), T ) }.
% 1.27/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha36( X
% 1.27/1.67 , Y, Z, T ) }.
% 1.27/1.67 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.27/1.67 , Y ) }.
% 1.27/1.67 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.27/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, Y ) ),
% 1.27/1.67 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint, X ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.27/1.67 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 1.27/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.27/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.27/1.67 tc_Nat_Onat, Z, Y ), X ) ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z
% 1.27/1.67 , Y ) ) }.
% 1.27/1.67 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) = hAPP( hAPP
% 1.27/1.67 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.27/1.67 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.27/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.27/1.67 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ),
% 1.27/1.67 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 1.27/1.67 ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__1( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ouminus( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ominus( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.27/1.67 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.27/1.67 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.27/1.67 ( tc_fun( Y, X ) ) }.
% 1.27/1.67 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.27/1.67 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.27/1.67 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.27/1.67 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.27/1.67 tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.27/1.67 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.27/1.67 { class_Nat_Osemiring__char__0( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.27/1.67 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.27/1.67 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.27/1.67 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.27/1.67 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.27/1.67 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.27/1.67 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.27/1.67 { class_Power_Opower( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.27/1.67 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.27/1.67 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.27/1.67 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.27/1.67 tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Orderings_Owellorder( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Nat_Osemiring__char__0( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.27/1.67 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.27/1.67 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.27/1.67 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.27/1.67 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.27/1.67 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.27/1.67 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ),
% 1.27/1.67 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ),
% 1.27/1.67 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ),
% 1.27/1.67 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.27/1.67 X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ),
% 1.27/1.67 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.27/1.67 ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ),
% 1.27/1.67 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ),
% 1.27/1.67 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ),
% 1.27/1.67 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.27/1.67 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ),
% 1.27/1.67 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ),
% 1.27/1.67 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.27/1.67 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.27/1.67 ( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.27/1.67 ( tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Nat_Osemiring__char__0(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Osemiring__1(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.27/1.67 ( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.27/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.67 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.27/1.67 }.
% 1.27/1.67 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.27/1.67 ) ) }.
% 1.27/1.67 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.27/1.67 .
% 1.27/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.27/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.27/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.27/1.68 { hAPP( c_COMBI( Y ), X ) = X }.
% 1.27/1.68 { hAPP( hAPP( c_COMBK( T, Z ), Y ), X ) = Y }.
% 1.27/1.68 { hAPP( hAPP( hAPP( c_COMBB( W, U, T ), Z ), Y ), X ) = hAPP( Z, hAPP( Y, X
% 1.27/1.68 ) ) }.
% 1.27/1.68 { hAPP( hAPP( c_COMBC( W, U, T, Z ), Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 1.27/1.68 { hAPP( hAPP( hAPP( c_COMBS( W, U, T ), Z ), Y ), X ) = hAPP( hAPP( Z, X )
% 1.27/1.68 , hAPP( Y, X ) ) }.
% 1.27/1.68 { ! hBOOL( hAPP( c_fequal( Y ), X ) ), Y = X }.
% 1.27/1.68 { ! Y = X, hBOOL( hAPP( c_fequal( Y ), X ) ) }.
% 1.27/1.68 { ! hBOOL( hAPP( c_fNot, X ) ), ! hBOOL( X ) }.
% 1.27/1.68 { hBOOL( X ), hBOOL( hAPP( c_fNot, X ) ) }.
% 1.27/1.68 { ! hBOOL( X ), ! hBOOL( Y ), hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ) }.
% 1.27/1.68 { ! hBOOL( hAPP( hAPP( c_fconj, X ), Y ) ), hBOOL( X ) }.
% 1.27/1.68 { ! hBOOL( hAPP( hAPP( c_fconj, Y ), X ) ), hBOOL( X ) }.
% 1.27/1.68 { X = c_Groups_Ozero__class_Ozero( t_a ), Y = c_Groups_Ozero__class_Ozero(
% 1.27/1.68 tc_Nat_Onat ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.27/1.68 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.27/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a, Z ) ), Y ) ),
% 1.27/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.27/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( t_a,
% 1.27/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ), ! hAPP(
% 1.27/1.68 c_Polynomial_Opoly( t_a, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.27/1.68 ( t_a ) ) ), skol18( X, Y, Z ) ) = hAPP( hAPP(
% 1.27/1.68 c_Groups_Oplus__class_Oplus( t_a ), hAPP( c_Polynomial_Opoly( t_a,
% 1.27/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 1.27/1.68 c_Groups_Ozero__class_Ozero( t_a ) ) ), hAPP( hAPP(
% 1.27/1.68 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.27/1.68 c_Power_Opower__class_Opower( t_a ), skol18( X, Y, Z ) ), Y ) ), hAPP(
% 1.27/1.68 c_Polynomial_Opoly( t_a, hAPP( hAPP( c_Polynomial_OpCons( t_a ), X ), Z )
% 1.27/1.68 ), skol18( X, Y, Z ) ) ) ) }.
% 1.27/1.68 { class_Rings_Oidom( t_a ) }.
% 1.27/1.68
% 1.27/1.68 *** allocated 15000 integers for clauses
% 1.27/1.68 *** allocated 22500 integers for clauses
% 1.27/1.68 *** allocated 33750 integers for clauses
% 1.27/1.68 *** allocated 50625 integers for clauses
% 1.27/1.68 *** allocated 75937 integers for clauses
% 1.27/1.68 *** allocated 113905 integers for clauses
% 1.27/1.68 percentage equality = 0.342897, percentage horn = 0.872932
% 1.27/1.68 This is a problem with some equality
% 1.27/1.68
% 1.27/1.68
% 1.27/1.68
% 1.27/1.68 Options Used:
% 1.27/1.68
% 1.27/1.68 useres = 1
% 1.27/1.68 useparamod = 1
% 1.27/1.68 useeqrefl = 1
% 1.27/1.68 useeqfact = 1
% 1.27/1.68 usefactor = 1
% 1.27/1.68 usesimpsplitting = 0
% 1.27/1.68 usesimpdemod = 5
% 1.27/1.68 usesimpres = 3
% 1.27/1.68
% 1.27/1.68 resimpinuse = 1000
% 1.27/1.68 resimpclauses = 20000
% 1.27/1.68 substype = eqrewr
% 1.27/1.68 backwardsubs = 1
% 1.27/1.68 selectoldest = 5
% 1.27/1.68
% 1.27/1.68 litorderings [0] = split
% 1.27/1.68 litorderings [1] = extend the termordering, first sorting on arguments
% 1.27/1.68
% 1.27/1.68 termordering = kbo
% 1.27/1.68
% 1.27/1.68 litapriori = 0
% 1.27/1.68 termapriori = 1
% 1.27/1.68 litaposteriori = 0
% 1.27/1.68 termaposteriori = 0
% 1.27/1.68 demodaposteriori = 0
% 1.27/1.68 ordereqreflfact = 0
% 1.27/1.68
% 1.27/1.68 litselect = negord
% 1.27/1.68
% 1.27/1.68 maxweight = 15
% 1.27/1.68 maxdepth = 30000
% 1.27/1.68 maxlength = 115
% 1.27/1.68 maxnrvars = 195
% 1.27/1.68 excuselevel = 1
% 1.27/1.68 increasemaxweight = 1
% 1.27/1.68
% 1.27/1.68 maxselected = 10000000
% 1.27/1.68 maxnrclauses = 10000000
% 1.27/1.68
% 1.27/1.68 showgenerated = 0
% 1.27/1.68 showkept = 0
% 1.27/1.68 showselected = 0
% 1.27/1.68 showdeleted = 0
% 1.27/1.68 showresimp = 1
% 1.27/1.68 showstatus = 2000
% 1.27/1.68
% 1.27/1.68 prologoutput = 0
% 1.27/1.68 nrgoals = 5000000
% 1.27/1.68 totalproof = 1
% 1.27/1.68
% 1.27/1.68 Symbols occurring in the translation:
% 1.27/1.68
% 1.27/1.68 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.27/1.68 . [1, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.27/1.68 ! [4, 1] (w:0, o:118, a:1, s:1, b:0),
% 1.27/1.68 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.27/1.68 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.27/1.68 hAPP [38, 2] (w:1, o:234, a:1, s:1, b:0),
% 1.27/1.68 t_a [39, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Oidom [40, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.27/1.68 v_p [41, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_Opoly [42, 2] (w:1, o:237, a:1, s:1, b:0),
% 1.27/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [43, 3] (w:1, o:
% 1.27/1.68 259, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Ozero [46, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.27/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [47, 2] (w:1, o:238
% 1.27/1.68 , a:1, s:1, b:0),
% 1.27/1.68 tc_Nat_Onat [48, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.27/1.68 c_Groups_Ozero__class_Ozero [49, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.27/1.68 tc_Polynomial_Opoly [50, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Ocomm__semiring__0 [55, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_OpCons [56, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.27/1.68 c_Groups_Oplus__class_Oplus [57, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.27/1.68 c_Groups_Otimes__class_Otimes [58, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.27/1.68 class_Power_Opower [60, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Osemiring__0 [61, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.27/1.68 c_Power_Opower__class_Opower [62, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.27/1.68 c_Groups_Oone__class_Oone [63, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Ocomm__semiring__1 [64, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Omonoid__mult [67, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Omult__zero [70, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Ono__zero__divisors [71, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.27/1.68
% 1.27/1.68 class_Rings_Ozero__neq__one [72, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Ocomm__monoid__add [73, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.27/1.68
% 1.27/1.68 class_Int_Oring__char__0 [85, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.27/1.68 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [86
% 1.27/1.68 , 1] (w:1, o:179, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Oring__1__no__zero__divisors [95, 1] (w:1, o:149, a:1, s:
% 1.27/1.68 1, b:0),
% 1.27/1.68 class_Groups_Ocomm__monoid__mult [96, 1] (w:1, o:180, a:1, s:1, b:0)
% 1.27/1.68 ,
% 1.27/1.68 class_Rings_Olinordered__ring__strict [98, 1] (w:1, o:158, a:1, s:1
% 1.27/1.68 , b:0),
% 1.27/1.68 c_Polynomial_Oorder [99, 3] (w:1, o:262, a:1, s:1, b:0),
% 1.27/1.68 c_Power_Opower_Opower [100, 3] (w:1, o:263, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Oab__semigroup__mult [105, 1] (w:1, o:181, a:1, s:1, b:0
% 1.27/1.68 ),
% 1.27/1.68 class_Groups_Oab__semigroup__add [106, 1] (w:1, o:182, a:1, s:1, b:0)
% 1.27/1.68 ,
% 1.27/1.68 class_Groups_Ocancel__semigroup__add [107, 1] (w:1, o:183, a:1, s:1
% 1.27/1.68 , b:0),
% 1.27/1.68 class_Groups_Ocancel__ab__semigroup__add [108, 1] (w:1, o:184, a:1
% 1.27/1.68 , s:1, b:0),
% 1.27/1.68 class_Groups_Oone [109, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Omonoid__add [111, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Olinordered__ab__group__add [112, 1] (w:1, o:156, a:1
% 1.27/1.68 , s:1, b:0),
% 1.27/1.68 c_Polynomial_Opcompose [113, 3] (w:1, o:264, a:1, s:1, b:0),
% 1.27/1.68 class_RealVector_Oreal__normed__algebra [118, 1] (w:1, o:169, a:1, s:
% 1.27/1.68 1, b:0),
% 1.27/1.68 class_Rings_Ocomm__semiring [120, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Osemiring [124, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Ocomm__ring__1 [125, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_Omonom [126, 3] (w:1, o:265, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Oring__no__zero__divisors [127, 1] (w:1, o:150, a:1, s:1
% 1.27/1.68 , b:0),
% 1.27/1.68 tc_fun [128, 2] (w:1, o:245, a:1, s:1, b:0),
% 1.27/1.68 c_COMBB [129, 3] (w:1, o:266, a:1, s:1, b:0),
% 1.27/1.68 c_COMBK [130, 2] (w:1, o:246, a:1, s:1, b:0),
% 1.27/1.68 c_COMBC [131, 4] (w:1, o:308, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_Opoly__rec [132, 5] (w:1, o:336, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_Ocoeff [133, 2] (w:1, o:247, a:1, s:1, b:0),
% 1.27/1.68 c_If [134, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.27/1.68 c_fequal [135, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_Osmult [136, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.27/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [138, 3] (w:
% 1.27/1.68 1, o:267, a:1, s:1, b:0),
% 1.27/1.68 c_COMBS [141, 3] (w:1, o:268, a:1, s:1, b:0),
% 1.27/1.68 tc_Int_Oint [142, 0] (w:1, o:82, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_Osynthetic__div [143, 3] (w:1, o:269, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_OAbs__poly [144, 2] (w:1, o:248, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_Odegree [145, 2] (w:1, o:249, a:1, s:1, b:0),
% 1.27/1.68 c_Nat_Onat_Onat__case [146, 3] (w:1, o:270, a:1, s:1, b:0),
% 1.27/1.68 c_Groups_Ominus__class_Ominus [147, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Oab__group__add [148, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Ocomm__ring [149, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Ogroup__add [154, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Oring [156, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.27/1.68 tc_HOL_Obool [159, 0] (w:1, o:81, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Oring__1 [160, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.27/1.68 c_Groups_Ouminus__class_Ouminus [161, 1] (w:1, o:193, a:1, s:1, b:0)
% 1.27/1.68 ,
% 1.27/1.68 class_Fields_Ofield [162, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.27/1.68 c_Polynomial_Opoly__gcd [163, 3] (w:1, o:271, a:1, s:1, b:0),
% 1.27/1.68 c_Nat_OSuc [164, 0] (w:1, o:86, a:1, s:1, b:0),
% 1.27/1.68 class_Groups_Ominus [167, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.27/1.68 class_Lattices_Oboolean__algebra [168, 1] (w:1, o:196, a:1, s:1, b:0)
% 1.27/1.68 ,
% 1.27/1.68 class_Groups_Ouminus [169, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.27/1.68 c_COMBI [174, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.27/1.68 class_Lattices_Oab__semigroup__idem__mult [175, 1] (w:1, o:195, a:1
% 1.27/1.68 , s:1, b:0),
% 1.27/1.68 c_Rings_Odvd__class_Odvd [176, 1] (w:1, o:199, a:1, s:1, b:0),
% 1.27/1.68 hBOOL [177, 1] (w:1, o:200, a:1, s:1, b:0),
% 1.27/1.68 c_Rings_Oinverse__class_Oinverse [178, 1] (w:1, o:201, a:1, s:1, b:0)
% 1.27/1.68 ,
% 1.27/1.68 class_Rings_Odivision__ring__inverse__zero [179, 1] (w:1, o:172, a:1
% 1.27/1.68 , s:1, b:0),
% 1.27/1.68 class_Rings_Odvd [180, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.27/1.68 class_Rings_Odivision__ring [181, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.27/1.68 class_Fields_Ofield__inverse__zero [187, 1] (w:1, o:125, a:1, s:1, b:
% 1.27/1.68 0),
% 1.27/1.68 c_fNot [188, 0] (w:1, o:94, a:1, s:1, b:0),
% 1.27/1.68 c_Orderings_Oord__class_OLeast [189, 2] (w:1, o:236, a:1, s:1, b:0),
% 1.27/1.68
% 1.27/1.68 class_RealVector_Oreal__normed__field [190, 1] (w:1, o:175, a:1, s:1
% 1.27/1.68 , b:0),
% 1.27/1.68 c_Deriv_Oderiv [191, 4] (w:1, o:309, a:1, s:1, b:0),
% 1.27/1.68 c_Divides_Odiv__class_Omod [192, 3] (w:1, o:272, a:1, s:1, b:0),
% 1.27/1.68 class_Orderings_Owellorder [193, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.27/1.68 class_Divides_Osemiring__div [200, 1] (w:1, o:203, a:1, s:1, b:0),
% 1.27/1.68 class_Divides_Oring__div [204, 1] (w:1, o:202, a:1, s:1, b:0),
% 1.27/1.68 c_Rings_Oinverse__class_Odivide [205, 1] (w:1, o:204, a:1, s:1, b:0)
% 1.27/1.68 ,
% 1.27/1.68 c_Nat_Osemiring__1__class_Oof__nat [206, 2] (w:1, o:235, a:1, s:1, b:
% 3.07/3.45 0),
% 3.07/3.45 class_Nat_Osemiring__char__0 [207, 1] (w:1, o:142, a:1, s:1, b:0),
% 3.07/3.45 class_Rings_Osemiring__1 [208, 1] (w:1, o:176, a:1, s:1, b:0),
% 3.07/3.45 class_RealVector_Oreal__field [209, 1] (w:1, o:177, a:1, s:1, b:0),
% 3.07/3.45 c_Nat_Osemiring__1__class_Oof__nat__aux [210, 4] (w:1, o:310, a:1, s:
% 3.07/3.45 1, b:0),
% 3.07/3.45 c_Polynomial_Opdivmod__rel [211, 5] (w:1, o:337, a:1, s:1, b:0),
% 3.07/3.45 c_Orderings_Oord__class_Oless [221, 3] (w:1, o:260, a:1, s:1, b:0),
% 3.07/3.45 c_Transcendental_Odiffs [222, 3] (w:1, o:273, a:1, s:1, b:0),
% 3.07/3.45 class_Rings_Olinordered__semidom [223, 1] (w:1, o:160, a:1, s:1, b:0)
% 3.07/3.45 ,
% 3.07/3.45 class_Rings_Olinordered__comm__semiring__strict [224, 1] (w:1, o:161
% 3.07/3.45 , a:1, s:1, b:0),
% 3.07/3.45 class_Rings_Olinordered__semiring__strict [225, 1] (w:1, o:162, a:1
% 3.07/3.45 , s:1, b:0),
% 3.07/3.45 class_Rings_Olinordered__ring [226, 1] (w:1, o:159, a:1, s:1, b:0),
% 3.07/3.45 class_Groups_Oordered__comm__monoid__add [227, 1] (w:1, o:205, a:1
% 3.07/3.45 , s:1, b:0),
% 3.07/3.45 class_Rings_Olinordered__idom [228, 1] (w:1, o:163, a:1, s:1, b:0),
% 3.07/3.45 class_Groups_Oordered__ab__group__add [229, 1] (w:1, o:206, a:1, s:1
% 3.07/3.45 , b:0),
% 3.07/3.45 class_Groups_Oordered__ab__semigroup__add__imp__le [231, 1] (w:1, o:
% 3.07/3.45 207, a:1, s:1, b:0),
% 3.07/3.45 class_Groups_Oordered__cancel__ab__semigroup__add [232, 1] (w:1, o:
% 3.07/3.45 208, a:1, s:1, b:0),
% 3.07/3.45 class_Orderings_Opreorder [235, 1] (w:1, o:146, a:1, s:1, b:0),
% 3.07/3.45 class_Orderings_Olinorder [236, 1] (w:1, o:147, a:1, s:1, b:0),
% 3.07/3.45 class_Orderings_Oorder [237, 1] (w:1, o:144, a:1, s:1, b:0),
% 3.07/3.45 class_Orderings_Oord [238, 1] (w:1, o:145, a:1, s:1, b:0),
% 3.07/3.45 class_Fields_Olinordered__field__inverse__zero [239, 1] (w:1, o:126
% 3.07/3.45 , a:1, s:1, b:0),
% 3.07/3.45 class_Fields_Olinordered__field [240, 1] (w:1, o:127, a:1, s:1, b:0)
% 3.07/3.45 ,
% 3.07/3.45 class_Rings_Oordered__ring [244, 1] (w:1, o:178, a:1, s:1, b:0),
% 3.07/3.45 c_fconj [247, 0] (w:1, o:107, a:1, s:1, b:0),
% 3.07/3.45 c_Orderings_Oorder_Ostrict__mono [248, 4] (w:1, o:311, a:1, s:1, b:0)
% 3.07/3.45 ,
% 3.07/3.45 c_Orderings_Oorder_Omono [249, 4] (w:1, o:312, a:1, s:1, b:0),
% 3.07/3.45 c_Polynomial_Opos__poly [250, 2] (w:1, o:250, a:1, s:1, b:0),
% 3.07/3.45 c_Divides_Odiv__class_Odiv [251, 3] (w:1, o:274, a:1, s:1, b:0),
% 3.07/3.45 c_Groups_Osgn__class_Osgn [252, 2] (w:1, o:251, a:1, s:1, b:0),
% 3.07/3.45 c_Orderings_Oord__class_Oless__eq [253, 3] (w:1, o:261, a:1, s:1, b:0
% 3.07/3.45 ),
% 3.07/3.45 class_Groups_Ocancel__comm__monoid__add [255, 1] (w:1, o:209, a:1, s:
% 3.07/3.45 1, b:0),
% 3.07/3.45 alpha1 [265, 2] (w:1, o:252, a:1, s:1, b:1),
% 3.07/3.45 alpha2 [266, 2] (w:1, o:254, a:1, s:1, b:1),
% 3.07/3.45 alpha3 [267, 3] (w:1, o:277, a:1, s:1, b:1),
% 3.07/3.45 alpha4 [268, 2] (w:1, o:255, a:1, s:1, b:1),
% 3.07/3.45 alpha5 [269, 2] (w:1, o:256, a:1, s:1, b:1),
% 3.07/3.45 alpha6 [270, 3] (w:1, o:279, a:1, s:1, b:1),
% 3.07/3.45 alpha7 [271, 3] (w:1, o:280, a:1, s:1, b:1),
% 3.07/3.45 alpha8 [272, 3] (w:1, o:281, a:1, s:1, b:1),
% 3.07/3.45 alpha9 [273, 4] (w:1, o:313, a:1, s:1, b:1),
% 3.07/3.45 alpha10 [274, 4] (w:1, o:314, a:1, s:1, b:1),
% 3.07/3.45 alpha11 [275, 3] (w:1, o:282, a:1, s:1, b:1),
% 3.07/3.45 alpha12 [276, 3] (w:1, o:283, a:1, s:1, b:1),
% 3.07/3.45 alpha13 [277, 2] (w:1, o:253, a:1, s:1, b:1),
% 3.07/3.45 alpha14 [278, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.07/3.45 alpha15 [279, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.07/3.45 alpha16 [280, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.07/3.45 alpha17 [281, 3] (w:1, o:287, a:1, s:1, b:1),
% 3.07/3.45 alpha18 [282, 3] (w:1, o:288, a:1, s:1, b:1),
% 3.07/3.45 alpha19 [283, 3] (w:1, o:289, a:1, s:1, b:1),
% 3.07/3.45 alpha20 [284, 4] (w:1, o:315, a:1, s:1, b:1),
% 3.07/3.45 alpha21 [285, 2] (w:1, o:257, a:1, s:1, b:1),
% 3.07/3.45 alpha22 [286, 2] (w:1, o:258, a:1, s:1, b:1),
% 3.07/3.45 alpha23 [287, 4] (w:1, o:316, a:1, s:1, b:1),
% 3.07/3.45 alpha24 [288, 4] (w:1, o:317, a:1, s:1, b:1),
% 3.07/3.45 alpha25 [289, 4] (w:1, o:318, a:1, s:1, b:1),
% 3.07/3.45 alpha26 [290, 3] (w:1, o:275, a:1, s:1, b:1),
% 3.07/3.45 alpha27 [291, 4] (w:1, o:319, a:1, s:1, b:1),
% 3.07/3.45 alpha28 [292, 4] (w:1, o:320, a:1, s:1, b:1),
% 3.07/3.45 alpha29 [293, 3] (w:1, o:276, a:1, s:1, b:1),
% 3.07/3.45 alpha30 [294, 3] (w:1, o:290, a:1, s:1, b:1),
% 3.07/3.45 alpha31 [295, 4] (w:1, o:321, a:1, s:1, b:1),
% 3.07/3.45 alpha32 [296, 4] (w:1, o:322, a:1, s:1, b:1),
% 22.78/23.21 alpha33 [297, 3] (w:1, o:291, a:1, s:1, b:1),
% 22.78/23.21 alpha34 [298, 3] (w:1, o:292, a:1, s:1, b:1),
% 22.78/23.21 alpha35 [299, 3] (w:1, o:293, a:1, s:1, b:1),
% 22.78/23.21 alpha36 [300, 4] (w:1, o:323, a:1, s:1, b:1),
% 22.78/23.21 alpha37 [301, 4] (w:1, o:324, a:1, s:1, b:1),
% 22.78/23.21 alpha38 [302, 3] (w:1, o:294, a:1, s:1, b:1),
% 22.78/23.21 alpha39 [303, 4] (w:1, o:325, a:1, s:1, b:1),
% 22.78/23.21 alpha40 [304, 4] (w:1, o:326, a:1, s:1, b:1),
% 22.78/23.21 alpha41 [305, 3] (w:1, o:295, a:1, s:1, b:1),
% 22.78/23.21 alpha42 [306, 4] (w:1, o:327, a:1, s:1, b:1),
% 22.78/23.21 alpha43 [307, 4] (w:1, o:328, a:1, s:1, b:1),
% 22.78/23.21 alpha44 [308, 4] (w:1, o:329, a:1, s:1, b:1),
% 22.78/23.21 alpha45 [309, 4] (w:1, o:330, a:1, s:1, b:1),
% 22.78/23.21 alpha46 [310, 4] (w:1, o:331, a:1, s:1, b:1),
% 22.78/23.21 alpha47 [311, 3] (w:1, o:296, a:1, s:1, b:1),
% 22.78/23.21 alpha48 [312, 3] (w:1, o:297, a:1, s:1, b:1),
% 22.78/23.21 alpha49 [313, 4] (w:1, o:332, a:1, s:1, b:1),
% 22.78/23.21 alpha50 [314, 3] (w:1, o:278, a:1, s:1, b:1),
% 22.78/23.21 alpha51 [315, 4] (w:1, o:333, a:1, s:1, b:1),
% 22.78/23.21 alpha52 [316, 4] (w:1, o:334, a:1, s:1, b:1),
% 22.78/23.21 skol1 [317, 2] (w:1, o:239, a:1, s:1, b:1),
% 22.78/23.21 skol2 [318, 1] (w:1, o:132, a:1, s:1, b:1),
% 22.78/23.21 skol3 [319, 3] (w:1, o:300, a:1, s:1, b:1),
% 22.78/23.21 skol4 [320, 3] (w:1, o:301, a:1, s:1, b:1),
% 22.78/23.21 skol5 [321, 4] (w:1, o:335, a:1, s:1, b:1),
% 22.78/23.21 skol6 [322, 2] (w:1, o:240, a:1, s:1, b:1),
% 22.78/23.21 skol7 [323, 2] (w:1, o:241, a:1, s:1, b:1),
% 22.78/23.21 skol8 [324, 2] (w:1, o:242, a:1, s:1, b:1),
% 22.78/23.21 skol9 [325, 1] (w:1, o:133, a:1, s:1, b:1),
% 22.78/23.21 skol10 [326, 2] (w:1, o:243, a:1, s:1, b:1),
% 22.78/23.21 skol11 [327, 3] (w:1, o:302, a:1, s:1, b:1),
% 22.78/23.21 skol12 [328, 3] (w:1, o:303, a:1, s:1, b:1),
% 22.78/23.21 skol13 [329, 3] (w:1, o:304, a:1, s:1, b:1),
% 22.78/23.21 skol14 [330, 3] (w:1, o:305, a:1, s:1, b:1),
% 22.78/23.21 skol15 [331, 2] (w:1, o:244, a:1, s:1, b:1),
% 22.78/23.21 skol16 [332, 1] (w:1, o:130, a:1, s:1, b:1),
% 22.78/23.21 skol17 [333, 3] (w:1, o:306, a:1, s:1, b:1),
% 22.78/23.21 skol18 [334, 3] (w:1, o:307, a:1, s:1, b:1),
% 22.78/23.21 skol19 [335, 1] (w:1, o:131, a:1, s:1, b:1),
% 22.78/23.21 skol20 [336, 3] (w:1, o:298, a:1, s:1, b:1),
% 22.78/23.21 skol21 [337, 3] (w:1, o:299, a:1, s:1, b:1).
% 22.78/23.21
% 22.78/23.21
% 22.78/23.21 Starting Search:
% 22.78/23.21
% 22.78/23.21 *** allocated 170857 integers for clauses
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 *** allocated 256285 integers for clauses
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 3015
% 22.78/23.21 Kept: 2003
% 22.78/23.21 Inuse: 38
% 22.78/23.21 Deleted: 3
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 *** allocated 384427 integers for clauses
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 7711
% 22.78/23.21 Kept: 4037
% 22.78/23.21 Inuse: 181
% 22.78/23.21 Deleted: 10
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 *** allocated 256285 integers for termspace/termends
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 *** allocated 576640 integers for clauses
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 14688
% 22.78/23.21 Kept: 6075
% 22.78/23.21 Inuse: 246
% 22.78/23.21 Deleted: 10
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 *** allocated 384427 integers for termspace/termends
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 29182
% 22.78/23.21 Kept: 8096
% 22.78/23.21 Inuse: 286
% 22.78/23.21 Deleted: 10
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 *** allocated 864960 integers for clauses
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 *** allocated 576640 integers for termspace/termends
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 36413
% 22.78/23.21 Kept: 10172
% 22.78/23.21 Inuse: 343
% 22.78/23.21 Deleted: 13
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 54291
% 22.78/23.21 Kept: 12538
% 22.78/23.21 Inuse: 367
% 22.78/23.21 Deleted: 14
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 *** allocated 1297440 integers for clauses
% 22.78/23.21 *** allocated 864960 integers for termspace/termends
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 69884
% 22.78/23.21 Kept: 15499
% 22.78/23.21 Inuse: 402
% 22.78/23.21 Deleted: 14
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 74180
% 22.78/23.21 Kept: 17510
% 22.78/23.21 Inuse: 412
% 22.78/23.21 Deleted: 14
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 22.78/23.21
% 22.78/23.21
% 22.78/23.21 Intermediate Status:
% 22.78/23.21 Generated: 79670
% 22.78/23.21 Kept: 19581
% 22.78/23.21 Inuse: 446
% 22.78/23.21 Deleted: 15
% 22.78/23.21 Deletedinuse: 0
% 22.78/23.21
% 22.78/23.21 Resimplifying inuse:
% 22.78/23.21 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying clauses:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 85552
% 73.87/74.26 Kept: 21721
% 73.87/74.26 Inuse: 471
% 73.87/74.26 Deleted: 254
% 73.87/74.26 Deletedinuse: 0
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 97495
% 73.87/74.26 Kept: 24015
% 73.87/74.26 Inuse: 496
% 73.87/74.26 Deleted: 254
% 73.87/74.26 Deletedinuse: 0
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 *** allocated 1946160 integers for clauses
% 73.87/74.26 *** allocated 1297440 integers for termspace/termends
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 116316
% 73.87/74.26 Kept: 26987
% 73.87/74.26 Inuse: 525
% 73.87/74.26 Deleted: 256
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 134269
% 73.87/74.26 Kept: 29000
% 73.87/74.26 Inuse: 542
% 73.87/74.26 Deleted: 256
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 153796
% 73.87/74.26 Kept: 31090
% 73.87/74.26 Inuse: 555
% 73.87/74.26 Deleted: 256
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 170304
% 73.87/74.26 Kept: 33801
% 73.87/74.26 Inuse: 580
% 73.87/74.26 Deleted: 256
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 181892
% 73.87/74.26 Kept: 36572
% 73.87/74.26 Inuse: 605
% 73.87/74.26 Deleted: 256
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 188410
% 73.87/74.26 Kept: 38575
% 73.87/74.26 Inuse: 621
% 73.87/74.26 Deleted: 257
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 *** allocated 1946160 integers for termspace/termends
% 73.87/74.26 *** allocated 2919240 integers for clauses
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying clauses:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 198159
% 73.87/74.26 Kept: 40672
% 73.87/74.26 Inuse: 644
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 209662
% 73.87/74.26 Kept: 42900
% 73.87/74.26 Inuse: 674
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 222830
% 73.87/74.26 Kept: 45803
% 73.87/74.26 Inuse: 689
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 229644
% 73.87/74.26 Kept: 47837
% 73.87/74.26 Inuse: 704
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 239341
% 73.87/74.26 Kept: 49865
% 73.87/74.26 Inuse: 724
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 258322
% 73.87/74.26 Kept: 52272
% 73.87/74.26 Inuse: 739
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 276717
% 73.87/74.26 Kept: 54412
% 73.87/74.26 Inuse: 749
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 *** allocated 2919240 integers for termspace/termends
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 289032
% 73.87/74.26 Kept: 56680
% 73.87/74.26 Inuse: 784
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 *** allocated 4378860 integers for clauses
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 299123
% 73.87/74.26 Kept: 59192
% 73.87/74.26 Inuse: 804
% 73.87/74.26 Deleted: 453
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying clauses:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 309157
% 73.87/74.26 Kept: 61415
% 73.87/74.26 Inuse: 819
% 73.87/74.26 Deleted: 1319
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 321836
% 73.87/74.26 Kept: 64031
% 73.87/74.26 Inuse: 834
% 73.87/74.26 Deleted: 1319
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 330584
% 73.87/74.26 Kept: 66208
% 73.87/74.26 Inuse: 839
% 73.87/74.26 Deleted: 1319
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 339525
% 73.87/74.26 Kept: 68222
% 73.87/74.26 Inuse: 874
% 73.87/74.26 Deleted: 1319
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 348648
% 73.87/74.26 Kept: 70386
% 73.87/74.26 Inuse: 894
% 73.87/74.26 Deleted: 1319
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 369543
% 73.87/74.26 Kept: 73026
% 73.87/74.26 Inuse: 899
% 73.87/74.26 Deleted: 1319
% 73.87/74.26 Deletedinuse: 1
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26 Resimplifying inuse:
% 73.87/74.26 Done
% 73.87/74.26
% 73.87/74.26
% 73.87/74.26 Intermediate Status:
% 73.87/74.26 Generated: 384128
% 73.87/74.26 Kept: 76512
% 73.87/74.26 Inuse: 924
% 205.59/206.00 Deleted: 1319
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 *** allocated 4378860 integers for termspace/termends
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 395848
% 205.59/206.00 Kept: 79219
% 205.59/206.00 Inuse: 934
% 205.59/206.00 Deleted: 1319
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying clauses:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 407920
% 205.59/206.00 Kept: 82315
% 205.59/206.00 Inuse: 959
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 417094
% 205.59/206.00 Kept: 84317
% 205.59/206.00 Inuse: 969
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 *** allocated 6568290 integers for clauses
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 428573
% 205.59/206.00 Kept: 86569
% 205.59/206.00 Inuse: 984
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 441066
% 205.59/206.00 Kept: 89481
% 205.59/206.00 Inuse: 999
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 451443
% 205.59/206.00 Kept: 91998
% 205.59/206.00 Inuse: 1009
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 463786
% 205.59/206.00 Kept: 94226
% 205.59/206.00 Inuse: 1039
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 475968
% 205.59/206.00 Kept: 96588
% 205.59/206.00 Inuse: 1064
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 491017
% 205.59/206.00 Kept: 99534
% 205.59/206.00 Inuse: 1094
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 502875
% 205.59/206.00 Kept: 103851
% 205.59/206.00 Inuse: 1104
% 205.59/206.00 Deleted: 1382
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying clauses:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 516609
% 205.59/206.00 Kept: 108380
% 205.59/206.00 Inuse: 1119
% 205.59/206.00 Deleted: 1407
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 528492
% 205.59/206.00 Kept: 110595
% 205.59/206.00 Inuse: 1149
% 205.59/206.00 Deleted: 1407
% 205.59/206.00 Deletedinuse: 1
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 *** allocated 6568290 integers for termspace/termends
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 544232
% 205.59/206.00 Kept: 112679
% 205.59/206.00 Inuse: 1156
% 205.59/206.00 Deleted: 1411
% 205.59/206.00 Deletedinuse: 2
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 552144
% 205.59/206.00 Kept: 114939
% 205.59/206.00 Inuse: 1162
% 205.59/206.00 Deleted: 1435
% 205.59/206.00 Deletedinuse: 2
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 569573
% 205.59/206.00 Kept: 118921
% 205.59/206.00 Inuse: 1174
% 205.59/206.00 Deleted: 1463
% 205.59/206.00 Deletedinuse: 2
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 584770
% 205.59/206.00 Kept: 122609
% 205.59/206.00 Inuse: 1177
% 205.59/206.00 Deleted: 1475
% 205.59/206.00 Deletedinuse: 2
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 593620
% 205.59/206.00 Kept: 124906
% 205.59/206.00 Inuse: 1181
% 205.59/206.00 Deleted: 1491
% 205.59/206.00 Deletedinuse: 2
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying clauses:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 *** allocated 9852435 integers for clauses
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 609135
% 205.59/206.00 Kept: 126912
% 205.59/206.00 Inuse: 1190
% 205.59/206.00 Deleted: 1804
% 205.59/206.00 Deletedinuse: 3
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 642306
% 205.59/206.00 Kept: 130405
% 205.59/206.00 Inuse: 1194
% 205.59/206.00 Deleted: 1804
% 205.59/206.00 Deletedinuse: 3
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 659606
% 205.59/206.00 Kept: 132549
% 205.59/206.00 Inuse: 1219
% 205.59/206.00 Deleted: 1805
% 205.59/206.00 Deletedinuse: 4
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 671667
% 205.59/206.00 Kept: 135784
% 205.59/206.00 Inuse: 1234
% 205.59/206.00 Deleted: 1805
% 205.59/206.00 Deletedinuse: 4
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 684898
% 205.59/206.00 Kept: 138966
% 205.59/206.00 Inuse: 1244
% 205.59/206.00 Deleted: 1805
% 205.59/206.00 Deletedinuse: 4
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 693555
% 205.59/206.00 Kept: 140971
% 205.59/206.00 Inuse: 1249
% 205.59/206.00 Deleted: 1805
% 205.59/206.00 Deletedinuse: 4
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00 Resimplifying inuse:
% 205.59/206.00 Done
% 205.59/206.00
% 205.59/206.00
% 205.59/206.00 Intermediate Status:
% 205.59/206.00 Generated: 703046
% 205.59/206.00 KepCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------